Browse Algebra problems Studdy Solved!

Problem 22301

The following question is taken from a Practice SAT test on the NonCalculator section.
The graph of $y=2 x^{2}+10 x+12$ is shown. If the graph crosses the $y$ -axis at the point $(0, k)$ , what is the value of $k$ ? 12 2 10 6

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Problem 22302

horizontal 1.10 A stunt rider is propelled upward from his motorbike by a spring loaded ejector seat. The rider was travelling horizontally at $60 \mathrm{~km} \mathrm{~h}^{-1}$ when the ejector seat was triggered, and as they leave the seat they are travelling with a vertical velocity of $15 \mathrm{~m} \mathrm{~s}^{-1}$ . The seat is 1.0 m off the ground. (a) What is the initial velocity of the stunt rider (in $\mathrm{km} \mathrm{h}^{-1}$ )? (b) How high does the stunt rider reach? (c) How far along the track does the stunt rider land on the ground? (d) What is the velocity of the stunt rider when they hit the ground (in $\mathrm{km} \mathrm{h}^{-1}$ )?
Answer: (a) $81 \mathrm{~km} \mathrm{~h}^{-1}, 42^{\circ}$ above the horizontal (b) 12 m (c) 51 m (d) $82 \mathrm{~km} \mathrm{~h}^{-1}, 43^{\circ}$ below the horizontal 1.11 A bullet is fired horizontally from a gun that is 1.5 m from the ground. The bullet travels at $1000 \mathrm{~m} \mathrm{~s}^{-1}$ and strikes a tree 150 m

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Problem 22303

If possible, find $A B, B A$ , and $A^{2}$ . (If not possible, enter IMPOSSIBLE in any cell of the matrix.) $A=\left[\begin{array}{llll} 1 & 2 & 4 & 5 \end{array}\right], \quad B=\left[\begin{array}{l} 3 \\ 4 \\ 0 \\ 1 \end{array}\right]$ (a) $A B$ (b) $B A$

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Problem 22304

The equations of three lines are given below. Line 1: $y=\frac{2}{3} x+7$ Line 2: $3 y=2 x+5$ Line 3: $4 x-6 y=8$
For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither

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Problem 22305

The equations of three lines are given below. Line 1: $y=-2 x-8$ Line 2: $3 x-6 y=-6$ Line 3: $y=-2 x+1$
For each pair of lines, determine whether they are parallel, perpendicular, or neith
Line 1 and Line 2 : Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3 : Parallel Perpendicular Neither

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Problem 22306

Write an equation of the line below. Explanation Check

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Problem 22307

Which intercepts will help you find the roots of the equation if $\sqrt{3 x+4}=-2$ ?
Select one: a. $x$ -intercepts of the graph of the function $y=\sqrt{3 x+4}-2$ b. $x$ -intercepts of the graph of the function $y=\sqrt{3 x+4}+2$ c. $y$ -intercepts of the graph of the function $y=\sqrt{3 x+4}-2$ d. $y$ -intercepts of the graph of the function $y=\sqrt{3 x+4}+2$

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Problem 22308

Point $S$ is the midpoint of line RT. RS is $3 x+20$ and RT is $12 x-10$ . What is the length of RS? Round your answer to the nearest hundredth if necessary. Your Answer:
Answer
Question 3 (2 points)

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Problem 22309

(c) At the school across the street, $\frac{7}{12}$ of the students like neither superhero nor s This represents 189 members of the student body. Set up and solve an calculate the total number of students, $T$ , that go to this school. in Louisiana have a $10 \%$ sales tax. Talal buys a coat for $\$ 45$

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Problem 22310

9. simplify $\frac{2 x+12}{x+6}$

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Problem 22311

3. Two horizontal forces act on a $5.0-\mathrm{kg}$ mass. One force has a magnitude of 8.0 N and is directed due north. The second force toward the east has a magnitude of 6.0 N . What is the acceleration of the mass? A) $1.6 \mathrm{~m} / \mathrm{s}^{2}$ due north B) $1.2 \mathrm{~m} / \mathrm{s}^{2}$ due east C) $2.0 \mathrm{~m} / \mathrm{s}^{2}$ at 53 e N of E
ㅇ) $2.0 \mathrm{~m} / \mathrm{s}^{2}$ at $53 \mathrm{~m} E$ of N

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Problem 22312

$\left(n^{10}\right)^{\frac{1}{5}}$

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Problem 22313

Which of the following illustrates the commutative property of multiplication?
Enter a, b, c, d, or e. a. $z y=y z$ b. $a+(c+d)=(a+c)+d$ c. $y+a=a+y$ d. $(d b)(e+f)=d[b(e+f)]$ e. $(a c+d e)(e f)=(d e+a c)(e f)$

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Problem 22314

8 Abiturprüfung 2011 (Bayern), Analysis, Aufgabengruppe I, Teil 1, Aufgabe 3 Die Anzahl der auf der Erde lebenden Menschen wuchs von 6,1 Milliarden zu Beginn des Jahres 2000 auf 6,9 Milliarden zu Beginn des Jahres 2010. Dieses Wachstum lässt sich näherungsweise durch eine Exponentialfunktion mit einem Term der Form $N(x)=N_{0} \cdot e^{k \cdot(x-2000)}$ beschreiben, wobei $\mathrm{N}(\mathrm{x})$ die Anzahl der Menschen zu Beginn des Jahres $x$ ist. Bestimmen Sie $N_{0}$ und $k$ .

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Problem 22315

Die Anzahl der auf der Erde lebenden Menschen wuchs von 6,1 Milliarden zu Beginn des Jahres 2000 auf 6,9 Milliarden zu Beginn des Jahres 2010. Dieses Wachstum lässt sich näherungsweise durch eine Exponentialfunktion mit einem Term der Form $N(x)=N_{0} \cdot e^{k \cdot(x-2000)}$ beschreiben, wobei N(x) die Anzahl der Menschen zu Beginn des Jahres $x$ ist. Bestimmen Sie $N_{0}$ und $k$ .

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Problem 22316

peform the Indicated operation $\frac{1}{3 x^{2} y^{4}} \div \frac{1}{21 x^{3} y}$

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Problem 22317

2. (4 punti)
Una gru, il cui motore ha una potenza di $3,00 \mathrm{~kW}$ , solleva di $10,4 \mathrm{~m}$ , a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.

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Problem 22318

11 Bei dem Reaktorunfall in Tschernobyl am 26. April 1986 wurde u.a. radioaktives Cäsium-137 freigesetzt. Cäsium-137 zerfällt exponentiell mit einer Halbwertszeit von ca. 30 Jahren. Über der damaligen Bundesrepublik Deutschland hatten sich nach Angaben der Gesellschaft für Strahlenund Umweltforschung etwa 230 Gramm radioaktives Cäsium-137 abgelagert, ein Großteil davon in Bayern. a) Beschreiben Sie den Zerfall dieser Menge Cäsium-137 durch eine Funktion $f: t \mapsto b \cdot e^{k t}$ ( $t$ in Jahren und $f(t)$ in Gramm). b) Geben Sie die Bedeutung des Faktors b im Sachzusammenhang an und berechnen Sie den prozentualen Anteil, um den die Masse des Cäsium-137 jedes Jahr abnimmt. c) Berechnen Sie, nach welcher Zeit weniger als ein Gramm des Cäsium-137 übrig ist. d) Bestimmen Sie die Funktion der Wachstumsgeschwindigkeit für die gegebene Menge Cäsi-um-137. Berechnen Sie die Wachstumsgeschwindigkeit zu Beginn und zum heutigen Zeitpunkt. Beschreiben Sie die Werte im Sachzusammenhang.

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Problem 22319

Simplify. Assume that the variable represents any real number. $\sqrt[19]{x^{19}}$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $\sqrt[19]{\mathrm{x}^{19}}=$ $\square$ B. The root does not represent a real number.

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Problem 22320

86 FUNCTIONS (Chapter 3) 11 Suppose $f(x)=\sqrt{1-x}$ and $g(x)=x^{2}$ . Find: a $(f \circ g)(x)$ b the domain and range of $(f \circ g)(x)$ .

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Problem 22321

Simplify the radical. Assume that the variable represents a positive real number. $\sqrt[4]{\frac{x^{12}}{16}}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\sqrt[4]{\frac{x^{12}}{16}}=$ $\square$ (Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The radical does not represent a real number.

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Problem 22322

If $g(x)=\sqrt[3]{x-20}$ , find $g(12)$ $g(12)=$

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Problem 22323

Use radical notation to rewrite the expression. Simplify if possible $16^{1 / 2}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. $16^{1 / 2}=$ $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.) B. The answer is not a real number.

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Problem 22324

Зэс цайр хоёрыг зохих хэмжээгээр нийлүүлж хайлууоахад гууль болдог.124г жинтэй гуулийг усанд живүүлэхэд жин нь 15гаар хөнгөрнө.Хэрэв 89г зэсийг усанд живүүлэхэд жин нь 10гаар,7г цайрыг усанд живүүлэхэд жин нь 1гaap хөнгөрдөг бол тэр хэсэг гуульд хэдэн г зэс цайр орох вэ

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Problem 22325

How many years are required for an investment to double in value if it is appreciating at the rate of $11 \%$ compounded continuously?
At 11\% compounded continuously, the investment doubles in $\square$ years. (Round to one decimal place as needed.)

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Problem 22326

Factor the given factor from the expression. $\begin{array}{c} x^{\frac{2}{5}} ; x^{\frac{2}{5}}+x^{\frac{4}{5}} \\ x^{\frac{2}{5}}+x^{\frac{4}{5}}=\square \end{array}$ $\square$ (Type your answer in factored form. Type your answer using exponential notation. Use integers or fractions for any numbers in the expression.)

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Problem 22327

Factor the given factor from the expression. $\begin{array}{l} x^{\frac{1}{9}} ; x^{\frac{2}{9}}-5 x^{\frac{1}{9}} \\ x^{\frac{2}{9}}-5 x^{\frac{1}{9}}=\square \end{array}$ $\square$ (Type your answer in factored form. Type your answer using exponential notation. Use integers or fractions for any numbers in the expression.)

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Problem 22328

How much money must you invest now at $4.1 \%$ interest compounded continuously in order to have $\$ 10,000$ at the end of 4 years?
You must invest \\square$ (Round to the nearest cent as needed.)

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Problem 22329

tisten
This inpus-outpul tabte shows some values that satisty the equation $y=4 x+21$ . 2 2 4 5
What number correctily tils in the biank in the tatie?

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Problem 22330

Use the graph of the function to answer the question. (s) 2017 StrongMind. Created using GeoGebra.
What is the output of the function when the input is 0 ? Enter your answer as a number, like this: 42

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Problem 22331

13. A function $f(x)$ is one-to-one. If the graph of $f^{-1}(x)$ lies in the fourth quadrant. In which quadrant does the graph of $f(x)$ lie? A. First Quadrant B. Second Quadrant b) Given the graph of the function $h(x)$ . graph $h^{-1}(x)$ C. Third Quadrant D. Fourth Quadrant

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Problem 22332

Let $A(t)=4000 e^{0.06 t}$ be the balance in a savings account after $t$ years. Complete parts (a) through (f) below. (a) How much money was originally deposited?
There was $\$$ $\square$ originally deposited. (Type an integer or a decimal.)

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Problem 22333

Let $A(t)=4000 e^{0.06 t}$ be the balance in a savings account after $t$ years. Complete parts (a) through (f) below. (a) How much money was originally deposited?
There was \$ 4000 originally deposited. (Type an integer or a decimal.) (b) What is the interest rate?
The interest rate is $\square \%$ . (Type an integer or a decimal.)

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Problem 22334

Jerome wants to rent a rowboat to go fishing at the lake. The cost of the rental can be represented by the equation $y=18 x$ , where $x$ is the number of hours the boat is rented for, and $y$ is the total cost.
What is the cost per hour for renting the boat? There is no cost per hour, because the value for $b$ in the slope-intercept form of the equation $y=m \boldsymbol{x}+\boldsymbol{b}$ equals 0 . It costs $\$ 18$ to rent the boat all day. Renting the boat costs $\$ 0.18$ per hour. The cost per hour can't be determined without determining the number of hours it is used. Renting the boat costs $\$ 18$ per hour.

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Problem 22335

Examine the input-output table, which contains some of the ordered pairs of a linear function. \begin{tabular}{|c|c|} \hline Input $(x)$ & Output $(y)$ \\ \hline-4 & 4 \\ \hline-2 & 1 \\ \hline 0 & -2 \\ \hline 4 & -5 \\ \hline \end{tabular}
What is the initial value of the function? $-4$ $-2$ 0 4

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Problem 22336

2. Find all values of $x$ such that $x^{3}-x^{2}-x-2>0$

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Problem 22337

1. Find the minimum value of $2 x^{2}+12 x+4$ and the value/values of $x$ where the minimum is attained.

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Problem 22338

$6 x^{2}=-x$
Select the correct choice below and, if necessary, fill in the ans A. The solution set is $\square$ \}. (Simplify your answer. Use a comma to separate answ B. The scifution set is $\varnothing$ .

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Problem 22339

Consider the weighted Euclidean inner product defined by $<u, v>=7 u_{1} v_{1}+6 u_{2} v_{2}+4 u_{3} v_{3}$ . The generating matrix for this inner product is given by $A=$ $\left[\begin{array}{ccc} \sqrt{7} & 0 & 0 \\ 0 & \sqrt{6} & 0 \\ 0 & 0 & 2 \end{array}\right]$ True False

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Problem 22340

Consider the weighted Euclidean inner product defined by $\langle\mathbf{u}, \mathbf{v}\rangle=3 u_{1} v_{1}+7 u_{2} v_{2}+4 u_{3} v_{3}$ . The generating matrix for this inner product is given by $A=$ $\left[\begin{array}{ccc} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{7} & 0 \\ 0 & 0 & 2 \end{array}\right] .$ True False

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Problem 22341

Consider the weighted Euclidean inner product defined by $<u, v>=3 u_{1} v_{1}+7 u_{2} v_{2}+4 u_{3} v_{3}$ . The generating matrix for this inner product is given by $A=$ $\left[\begin{array}{ccc} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{7} & 0 \\ 0 & 0 & 2 \end{array}\right]$ True False

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Problem 22342

Consider the inner product on $M_{22}$ defined by $<U, V>=u_{1} v_{1}+u_{2} v_{2}+u_{3} v_{3}+u_{4} v_{4}$ where $U=\left[\begin{array}{ll}u_{1} & u_{2} \\ u_{3} & u_{4}\end{array}\right]$ and $V=\left[\begin{array}{ll}v_{1} & v_{2} \\ v_{3} & v_{4}\end{array}\right]$ . Using this inner product, the matrices $\left[\begin{array}{ll}-1 & 47 \\ -5 & 5\end{array}\right]$ and $\left[\begin{array}{cc}2 & 1 \\ 5 & -4\end{array}\right]$ are orthogonal.
True False

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Problem 22343

Find $<3 \bar{u}, 4 \bar{v}+5 \bar{w}>$ , given that $\langle\bar{u}, \bar{v}>=6,<\bar{v}, \bar{w}>=-5$ , and $<\bar{u}, \bar{w}>=-1$ Number

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Problem 22344

Question 50 The temperature of a nuclear reactor rises at a steady rate of 100 degrees per minute, while the temperature of a thermal reactor doubles every minute. Given that the starting temperatures of the nuclear reactor and the thermal reactor are 400 degrees and 15 degrees, respectively, after how many whole minutes will the temperature of the thermal reactor exceed that of the nuclear reactor?
Marks:1.0 Negative Marks: 0.25

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Problem 22345

b) $(-27)^{\frac{-1}{3}}$

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Problem 22346

1. Risolvi l'equazione parametrica: $a x+b=c x+d$ , dove $a, b, c$ e $d$ sono costanti.
2. Trova $x$ se $2 x+a=b x-5$ , con $a$ e $b$ costanti.

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Problem 22347

3. Risolvi l'equazione parametrica: $m x+3=n x-2$ , dove $m$ e $n$ sono parametri.
4. Trova $x$ se $\frac{1}{2} x+p=q x+\frac{q}{2}$ , con $p$ e $q$ come parametri.
5. Risolvi l'equazione parametrica: $r x-4=s x+6$ , dove $r$ e $s$ sono costanti.
6. Trova $x$ se $2 x-p=q x+p$ , con $p$ e $q$ parametri.

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Problem 22348

Consider the following lines. Line 1: $3 x-4 y=12$ Line 2: a line perpendicular to $3 x-4 y=12$ that contains the point $(3,-4)$ Write the equation of Line 1 in slope-intercept form. $\square$ Find the slope of Line 1. $\square$ Find the slope of Line 2. $\square$ Find the equation of Line 2 in point-slope form using the point $(3,-4)$ . $\square$ Find the equation of Line 2 in the form $A x+B y=C$ . $\square$ Need Help? Read It

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Problem 22349

Expand the following (a) $(2 x-3)(4 x+1)$

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Problem 22350

Consider the following lines. Line 1: $3 x-4 y=12$ Line 2: a line perpendicular to $3 x-4 y=12$ that contains the point $(3,-4)$ Write the equation of Line 1 in slope-intercept form. $\square$ Find the slope of Line 1. $\square$

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Problem 22351

1. Risolvi l'equazione: $x-\sqrt{a} x+1=0$ , dove $a$ è un parametro reale positivo.
2. Trova le soluzioni di $2 x^{2}+\frac{a}{x}-3=0$ , dove $a$ è un parametro reale positivo.

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Problem 22352

2 Ein Betrieb stellt ein Produkt mit den Inputfaktoren $x$ (in ME) und $y$ ( Output soll 1000 ME betragen. Die Faktormengenkombinationen, die zu diesem Output führen, lassen sich mit der Isoquantengleichung $y(x)=\frac{40}{x-2}+3$ beschreiben. Bei einem Kostenbudget in Höhe von 730 GE lautet die Gleichung der Isokostengeraden $y(x)=-10 x+73$ , bei einem Kostenbudget von 550 GE lautet sie $y(x)=-10 x+55$ . a) Untersuchen Sie, ob sich mit diesen Kostenbudgets der angestrebte Output erzielen lässt. Geben Sie ggf. die Kombinationsmengen der Inputfaktoren an. b) Berechnen Sie die Minimalkostenkombination. c) Bestimmen Sie die Gleichung der kostenminimalen Isokostengeraden. d) Berechnen Sie, wie hoch das Kostenbudget mindestens sein muss, wenn ein Output von 1000 ME produziert werden soll. e) Erstellen Sie eine Grafik, die Ihre Ergebnisse veranschaulicht. Geben Sie für die Isoquante die Gleichung der Polgeraden und der Asymptote an.

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Problem 22353

Unit 4 Retest Question 1 of 30 (1 point) | Question Attempt: 1 of 1 1 2 3 4 5. 6 7
Divide. $\left(20 x^{3}+13 x^{2}+15 x^{4}+12+5 x\right) \div\left(-5 x^{2}-1\right)$
Write your answer in the following form: Quotient $+\frac{\text { Remainder }}{-5 x^{2}-1}$ . $\frac{20 x^{3}+13 x^{2}+15 x^{4}+12+5 x}{-5 x^{2}-1}=\square+\frac{\square}{-5 x^{2}-1}$

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Problem 22354

Solve $45=(w+7)^{2}$ , where $w$ is a real number. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". $w=$ $\square$ ㅁ,,..... No solution

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Problem 22355

Factor completely. $-3 u^{2}+19 u+14$

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Problem 22356

Factor. 2 81x² - 36xw+4w² Π X

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Problem 22357

Solve for $r$ : $\begin{array}{l} \log _{3}(r+3)=-1 \\ r=\square \end{array}$

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Problem 22358

10.1 Given $f(x)=3-x^{2}$ (with domain $\left.(-\infty, \infty)\right)$ , $g(x)=2-x($ with domain $(-\infty, \infty))$ , $h(x)=\frac{1}{x}$ (with domain $\left.(0, \infty)\right)$ , find the following compositions (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ h$ (d) $g \circ h$ (+) hof; What is the domain this function? $(+)$ hog; What is the domain this function? 10.2 Determine the inverses of the following functions (a) $f(x)=4-5 x$ , (with domain $(-\infty, \infty)$ ) (b) $h(x)=x^{2}-3 x+2$ , (with domain $\left.\left.(2, \infty)\right)\right]$ $(+) f(x)=\frac{2 x+1}{3-x}$ , (also find the domain and range of $\ell$ and of $f^{-1}$ )

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Problem 22359

Consider the following lines. Line 1: $3 x-4 y=12$ Line 2: a line perpendicular to $3 x-4 y=42$ that contains the point $(3,-4)$ Write the equation of Line 1 in slope-intercept form. $y=\frac{3}{4} x-3$
Find the slope of Line 1. $3 / 4$
Find the slope of Line 2. $-4 / 3$
Find the equation of Line 2 in point-slope form using the point $(3,-4)$ . $y+4=-\frac{4}{3}(x-3)$
Find the equation of Line 2 in the form $A x+B y=C$ . $\square$

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Problem 22360

Let $f(x)=-3 x+4$ . Then $f^{-1}(x)=$

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Problem 22361

Factor. $x^{2}+13 x y+36 y^{2}$

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Problem 22362

Factor completely: $3 v^{4} x^{3}-48 x^{3}$

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Problem 22363

Solve for $s$ : $\begin{array}{l} 16^{9 s-5} \cdot 32^{-5 s-1}=\left(\frac{1}{2^{5 s+5}}\right) \\ s=\square \end{array}$

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Problem 22364

6. What is the coefficient of $x^{13}$ in the expression $\left(\sqrt{x}-\frac{1}{x^{4}}\right)^{89}$ .

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Problem 22365

$-4(-4 d+5)$
1 2 $\square$ $16 d+-20$ $16 s-20$ $16+20$ $-16 d+20$

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Problem 22366

Fill in the blank. The expression $\frac{x^{2}+2}{2+x^{2}}$ simplifies to $\qquad$
The expression $\frac{x^{2}+2}{2+x^{2}}$ simplifies to $\square$

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Problem 22367

What is the solution of $(4 x-16)^{\frac{1}{2}}=3 B^{?}$ $x=5$ $x=13$ $x=20$ $x=328$

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Problem 22368

What is the solution of $\sqrt{-4 x}=100$ ? $x=-2500$ $x=-50$ $x=-2.5$ no solution

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Problem 22369

The Sugar Sweet Company is going to transport its sugar to market. It will cost $\$ 4500$ to rent trucks plus $\$ 225$ for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function. $C(n)=4500+225 n$
Answer the following questions. (a) If the total cost is $\$ 9900$ , how many tons is the company transporting? $\square$ ns (b) What is the total cost of transporting 12 tons? \\square$

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Problem 22370

The Sugar Sweet Company is going to transport its sugar to market. It will cost $\$ 4500$ to rent trucks plus $\$ 225$ for each ton of sugar transported. The total cost, $C$ (in dollars), for transporting $n$ tons is given by the following function. $C(n)=4500+225 n$
Answer the following questions. (a) If the total cost is $\$ 9900$ , how many tons is the company transporting? $\square$ tons (b) What is the total cost of transporting 12 tons? \$7200

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Problem 22371

Which expression is equivalent to $\left(2^{\frac{1}{2}}-2^{\frac{3}{4}}\right)^{2}$ ? $\sqrt[4]{2^{3}}$ $\sqrt{2^{5}}$ $\sqrt[4]{4^{3}}$ $\sqrt{4^{5}}$

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Problem 22372

Which statement is true about the solution of $\sqrt[3]{x^{2}-12}=\sqrt[3]{4 x}$ ? $x=-2$ is an extraneous solution, and $x=6$ is a true solution. $x=6$ is an extraneous solution, and $x=-2$ is a true solution. Both $x=-2$ and $x=6$ are extraneous solutions. Both $x=-2$ and $x=6$ are true solutions.

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Problem 22373

Solve using the addition principle. $2 \frac{1}{5}+x=7$

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Problem 22374

Given that $\sqrt[3]{\frac{904}{3051}}=\sqrt[3]{\frac{b \cdot d}{c \cdot d}}$ , where $b$ and $d$ ; and $c$ and $d$ are the factors of $904 \& 3051$ , respectively. If $b$ and $c$ are perfect cubes, find the value of $d$ .
Q (Enter a number/value)

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Problem 22375

Which equation shows a valid step in solving $\sqrt[3]{2 x-6}+\sqrt[3]{2 x+6}=0$ ? $(\sqrt[3]{2 x-6})^{2}=(\sqrt[3]{2 x+6})^{2}$ $(\sqrt[3]{2 x-6})^{2}=(-\sqrt[3]{2 x+6})^{2}$ $(\sqrt[3]{2 x-6})^{3}=(\sqrt[3]{2 x+6})^{3}$ $(\sqrt[3]{2 x-6})^{3}=(-\sqrt[3]{2 x+6})^{3}$ Mark this and return sessmentViewer/Activit...

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Problem 22376

Simplify this expression. $(\sqrt{2}+\sqrt{3})(\sqrt{5}-\sqrt{7})$ $\sqrt{5}+\sqrt{-2}$ $\sqrt{10}+\sqrt{15}-\sqrt{14}-\sqrt{21}$ $2 \sqrt{5}-2 \sqrt{7}$ $2 \sqrt{5}+3 \sqrt{5}-2 \sqrt{7}-3 \sqrt{7}$

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Problem 22377

Given $f(x)=3 x+9$ a) Evaluate $f(5)$ $f(5)=$ $\square$ b) Evaluate $f(-4)$ $f(-4)=$ $\square$ Question Help: $\square$ Message instructor

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Problem 22378

What is the solution of $\sqrt{x^{2}+49}=x+5$ ? $x=\frac{12}{5}$ $x=-\frac{12}{5}$ $x=-6$ or $x=-3$ no solution

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Problem 22379

Suppose that a company's profit (in terms of $x$ , the number of units sold) is given by the model $P(x)=-4 x^{2}+221 x-650$ . Find the profit when 23 units are sold.
Answer: $\square$ dollars. Question Help: Message instructor Submit Question

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Problem 22380

Simplify this radical. $\sqrt{x^{13}}$ $13 \sqrt{x}$ $6 x \sqrt{x}$ $x \sqrt{x^{12}}$ $x^{6} \sqrt{x}$

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Problem 22381

Which is the rationalized form of the expression $\frac{\sqrt{x}}{\sqrt{x}+\sqrt{7}}$ ? a. $\frac{x-\sqrt{7 x}}{x-7}$ c. $\frac{x+\sqrt{7 x}}{x-7}$ b. $\frac{\sqrt{7 x}}{7}$ d. $\frac{x}{x+7}$

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Problem 22382

Which equation shows a valid, practical step in solving $\sqrt[4]{2 x-8}+\sqrt[4]{2 x+8}=0$ ? $(\sqrt[4]{2 x-8})^{3}=-(\sqrt[4]{2 x+8})^{3}$ $(\sqrt[4]{2 x-8})^{3}=(-\sqrt[4]{2 x+8})^{3}$ $(\sqrt[4]{2 x-8})^{4}=-(\sqrt[4]{2 x+8})^{4}$ $(\sqrt[4]{2 x-8})^{4}=(-\sqrt[4]{2 x+8})^{4}$

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Problem 22383

Which equation can be rewritten as $x+4=x^{2}$ ? Assume $x>0$
$\sqrt{x}+2=x$
$\sqrt{x+2}=x$ $\sqrt{x+4}=x$ $\sqrt{x^{2}+16}=x$

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Problem 22384

20. $x=\frac{1}{3} y+2$ , $-2 x-y=1$

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Problem 22385

5) One of the following statements is true - a) $\operatorname{det}\left(A B^{-1} d=\operatorname{det}(A) \operatorname{det}(B)\right.$ (D) $a_{21} A_{31}+a_{22} A_{32}+a_{23} A_{33}=\operatorname{det}(A)$ c) $\operatorname{det}\left(2 A^{-1}\right)^{2}=2 \operatorname{det}\left(A^{T}\right)$ d) If $A=\left[\begin{array}{cc}\cos x & -\sin x \\ \sin x & \cos x\end{array}\right]$ , then $\operatorname{det}(\mathrm{A})=1$ e) $\operatorname{det}(\mathrm{A})-\operatorname{det}\left(A^{T}\right)=1$

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Problem 22386

What is $\sqrt{x^{5} y^{6}}$ expressed in simplified form? $x^{2} y \sqrt{x}$ $x^{2} y^{2} \sqrt{x y}$ $x y \sqrt{x y}$ $x^{2} y^{3} \sqrt{x}$

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Problem 22387

10. What is the imaginary part of the complex number $7-5 i$ ? a. 7 b. -5 c. 5 d. 0 a b C d not given

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Problem 22388

20. Which complex number lies on the imaginary axis? a. $4+0 i$ b. $0+3 i$ c. $-2+2 i$ d. $1-i$ a b C d not given

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Problem 22389

Graph $y=\frac{5}{3} x-9$

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Problem 22390

Find the $x$ - and $y$ -intercepts of the following lines.
1. $2 x+3 y=24$
2. $3 x-5 y=30$
3. $7 x-4 y=84$
4. $x+y=8$ $5, x=5$
6. $3 y=66$

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Problem 22391

Find the domain of the function $f(x)$ . $f(x)=\frac{4}{5 x-9}$
Select the correct choice below and, if necessary, fill in the answer box to complete you A. The domain is $\{x \mid$ $\square$ \}. (Simplify your answer. Type an inequality or a compound inequality.) B. The domain is $\square$ 3. (Simplify your answer. Use a comma to separate answers as needed.) C. The domain is $\{x \mid x$ is a real number and $x \neq$ $\square$ \}. (Simplify your answer. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers.

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Problem 22392

27) Find the function of $g(x)$ by using function $f(x)$ . A) $g(x)=-f(x-3)+2$ B) $g(x)=-f(x+3)+6$ C) $g(x)=-f(3-x)+2$ D) $g(x)=-f(x-3)+6$

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Problem 22393

13 Finde den Fehler! a) Zeige durch Einsetzen eines Werts für x oder mithilfe einer Probe, dass die Rechnungen falsch sein müssen. b) Erkläre, was falsch gemacht wurde, und korrigiere im Heft. $\text { (1) } \begin{aligned} & 4 x-(x+2) \\ = & 4 x-x+2 \\ = & 3 x+2 \end{aligned}$ (2) $5 x+3=0 \quad \mid-2$ $7 x=0 \quad 1: 7$ (3) $\begin{array}{c} 4 x+2=2 x-2 \\ 2 x=-4 \quad \mid-2 \\ x=-6 \end{array}$ $\text { (4) } \begin{aligned} \frac{2}{5} x+\frac{1}{5} & =0,3 \quad \mid \cdot 5 \\ 2 x+\frac{1}{5} & =0,15 \quad \left\lvert\,-\frac{1}{5}\right. \\ 2 x & =-0,05 \quad \mid: 2 \\ x & =-0,25 \end{aligned}$

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Problem 22394

3. A certain mass hangs from a spring above a table. It is released from a height of 0.9 metres above the table and falls to a height of 0.1 m above the table before reversing direction and bouncing back to 0.9 m . The mass continues to move in a periodic up and down motion. It takes 1.2 seconds for the mass to return to the same position each time. b) Write an equation which expresses the height $h$ as a function of $\sin \theta$ .

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Problem 22395

1. Find the real values of $x$ which satisfies the inequality $\frac{x}{(x-2)(x-1)} \leq \frac{2}{(x-1)}$

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Problem 22396

Evaluate the indicated function for $f(x)=x^{2}+2$ and $g(x)=x-3$ $\begin{array}{c} (f+g)(2) \\ (f+g)(2)= \end{array}$ Submit Answer

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Problem 22397

2. Assume the following transactions occured during 2023:
Jan I, Purple purchases $30 \%$ of Yellow's common stock for $\$ 150,000$ . June 30, Yellow reported net income of $\$ 50,000$ . June 30, Yellow declared \ $20,000 Dividends. July 1, Purple purchases additional$ 10 \% $of Yellow's common stock for$ \ $50,000$ . Dec 31, Yellow reported net income of $\$ 65,000$ . Dec 31, Yellow declared $\$ 20,000$ dividends. The Investment in Yellow account balance reported by Purple at December 31, 2023 would be A. $\$ 250,000$ B. $\$ 275,000$ C. $\$ 227,000$ D. $\$ 222,500$

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Problem 22398

43 $\frac{(x+2)(x-2)-x^{2}}{5 x-5} \geq 0$ $\frac{(x+3)(x-2)-x^{2}}{(x-3)(x+2)-x^{2}}<0$

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Problem 22399

Evaluate: $\left.+5^{2}-8^{3}\right]^{0}+\left(5^{26}\right)\left(125^{-8}\right)-$ (Enter a value/number)

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Problem 22400

16 \text{ Verschiedene Grundstücke unterscheiden sich nur durch die Länge einer Strecke } x. \text{ Judith, Pia, Cem und Lukas haben Terme für den Flächeninhalt der Grundstücke in } \mathrm{m}^{2} \text{ notiert.}
\text{Judith: } 11,4 \cdot x-4,3 \cdot(x-9,9)
\text{Cem: } 9,9 \cdot 11,4+(x-9,9) \cdot 7,1
\text{Pia: } 9,9 \cdot 4,3+9,9 \cdot 7,1+7,1 \cdot(x-9,9)
\text{Lukas: } 9,9 \cdot 4,3+x \cdot 7,1
\text{a) Gib an, welcher Term zu welcher Zeichnung gehört. Begründe deine Entscheidung.}
\text{b) Gib einen Term für den Umfang des Grundstücks an und berechne, für welchen Wert von } x \text{ der Umfang 52 m beträgt.}

See Solution

Algebra

Problem 22301

The following question is taken from a Practice SAT test on the NonCalculator section.The graph of y=2x2+10x+12y=2 x^{2}+10 x+12y=2x2+10x+12 is shown. If the graph crosses the yyy-axis at the point (0,k)(0, k)(0,k), what is the value of kkk ? 12 2 10 6

Problem 22302

Problem 22303

Problem 22304

Problem 22305

Problem 22306

Write an equation of the line below. Explanation Check

Problem 22307

Problem 22308

Point SSS is the midpoint of line RT. RS is 3x+203 x+203x+20 and RT is 12x−1012 x-1012x−10. What is the length of RS? Round your answer to the nearest hundredth if necessary. Your Answer:AnswerQuestion 3 (2 points)

Problem 22309

Problem 22310

9. simplify 2x+12x+6\frac{2 x+12}{x+6}x+62x+12​

Problem 22311

Problem 22312

(n10)15\left(n^{10}\right)^{\frac{1}{5}}(n10)51​

Problem 22313

Problem 22314

Problem 22315

Problem 22316

peform the Indicated operation 13x2y4÷121x3y\frac{1}{3 x^{2} y^{4}} \div \frac{1}{21 x^{3} y}3x2y41​÷21x3y1​

Problem 22317

2. (4 punti)Una gru, il cui motore ha una potenza di 3,00 kW3,00 \mathrm{~kW}3,00 kW, solleva di 10,4 m10,4 \mathrm{~m}10,4 m, a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.

Problem 22318

Problem 22319

Simplify. Assume that the variable represents any real number. x1919\sqrt[19]{x^{19}}19x19​Select the correct choice below and, if necessary, fill in the answer box within your choice. A. x1919=\sqrt[19]{\mathrm{x}^{19}}=19x19​= □\square□ B. The root does not represent a real number.

Problem 22320

86 FUNCTIONS (Chapter 3) 11 Suppose f(x)=1−xf(x)=\sqrt{1-x}f(x)=1−x​ and g(x)=x2g(x)=x^{2}g(x)=x2. Find: a (f∘g)(x)(f \circ g)(x)(f∘g)(x) b the domain and range of (f∘g)(x)(f \circ g)(x)(f∘g)(x).

Problem 22321

Problem 22322

If g(x)=x−203g(x)=\sqrt[3]{x-20}g(x)=3x−20​, find g(12)g(12)g(12) g(12)=g(12)=g(12)=

Problem 22323

Problem 22324

Problem 22325

How many years are required for an investment to double in value if it is appreciating at the rate of 11%11 \%11% compounded continuously?At 11\% compounded continuously, the investment doubles in □\square□ years. (Round to one decimal place as needed.)

Problem 22326

Problem 22327

Problem 22328

How much money must you invest now at 4.1%4.1 \%4.1% interest compounded continuously in order to have $10,000\$ 10,000$10,000 at the end of 4 years?You must invest \ \square$ (Round to the nearest cent as needed.)

Problem 22329

tistenThis inpus-outpul tabte shows some values that satisty the equation y=4x+21y=4 x+21y=4x+21. 2 2 4 5What number correctily tils in the biank in the tatie?

Problem 22330

Use the graph of the function to answer the question. (s) 2017 StrongMind. Created using GeoGebra.What is the output of the function when the input is 0 ? Enter your answer as a number, like this: 42

Problem 22331

Problem 22332

Let A(t)=4000e0.06tA(t)=4000 e^{0.06 t}A(t)=4000e0.06t be the balance in a savings account after ttt years. Complete parts (a) through (f) below. (a) How much money was originally deposited?There was $\$$ □\square□ originally deposited. (Type an integer or a decimal.)

Problem 22333

Problem 22334

Problem 22335

Problem 22336

2. Find all values of xxx such that x3−x2−x−2>0x^{3}-x^{2}-x-2>0x3−x2−x−2>0

Problem 22337

1. Find the minimum value of 2x2+12x+42 x^{2}+12 x+42x2+12x+4 and the value/values of xxx where the minimum is attained.

Problem 22338

6x2=−x6 x^{2}=-x6x2=−xSelect the correct choice below and, if necessary, fill in the ans A. The solution set is □\square□ \}. (Simplify your answer. Use a comma to separate answ B. The scifution set is ∅\varnothing∅.

Problem 22339

Problem 22340

Problem 22341

Problem 22342

Problem 22343

Find <3uˉ,4vˉ+5wˉ><3 \bar{u}, 4 \bar{v}+5 \bar{w}><3uˉ,4vˉ+5wˉ>, given that ⟨uˉ,vˉ>=6,<vˉ,wˉ>=−5\langle\bar{u}, \bar{v}>=6,<\bar{v}, \bar{w}>=-5⟨uˉ,vˉ>=6,<vˉ,wˉ>=−5, and <uˉ,wˉ>=−1<\bar{u}, \bar{w}>=-1<uˉ,wˉ>=−1 Number

Problem 22344

Problem 22345

b) (−27)−13(-27)^{\frac{-1}{3}}(−27)3−1​

Problem 22346

1. Risolvi l'equazione parametrica: ax+b=cx+da x+b=c x+dax+b=cx+d, dove a,b,ca, b, ca,b,c e ddd sono costanti.2. Trova xxx se 2x+a=bx−52 x+a=b x-52x+a=bx−5, con aaa e bbb costanti.

Problem 22347

Problem 22348

Problem 22349

Expand the following (a) (2x−3)(4x+1)(2 x-3)(4 x+1)(2x−3)(4x+1)

Problem 22350

Consider the following lines. Line 1: 3x−4y=123 x-4 y=123x−4y=12 Line 2: a line perpendicular to 3x−4y=123 x-4 y=123x−4y=12 that contains the point (3,−4)(3,-4)(3,−4) Write the equation of Line 1 in slope-intercept form. □\square□ Find the slope of Line 1. □\square□

Problem 22351

1. Risolvi l'equazione: x−ax+1=0x-\sqrt{a} x+1=0x−a​x+1=0, dove aaa è un parametro reale positivo.2. Trova le soluzioni di 2x2+ax−3=02 x^{2}+\frac{a}{x}-3=02x2+xa​−3=0, dove aaa è un parametro reale positivo.

Problem 22352

Problem 22353

Problem 22354

Solve 45=(w+7)245=(w+7)^{2}45=(w+7)2, where www is a real number. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". w=w=w= □\square□ ㅁ,,..... No solution

The following question is taken from a Practice SAT test on the NonCalculator section.
The graph of $y=2 x^{2}+10 x+12$ is shown. If the graph crosses the $y$ -axis at the point $(0, k)$ , what is the value of $k$ ? 12 2 10 6

Point $S$ is the midpoint of line RT. RS is $3 x+20$ and RT is $12 x-10$ . What is the length of RS? Round your answer to the nearest hundredth if necessary. Your Answer:
Answer
Question 3 (2 points)

9. simplify $\frac{2 x+12}{x+6}$

$\left(n^{10}\right)^{\frac{1}{5}}$

peform the Indicated operation $\frac{1}{3 x^{2} y^{4}} \div \frac{1}{21 x^{3} y}$

2. (4 punti)
Una gru, il cui motore ha una potenza di $3,00 \mathrm{~kW}$ , solleva di $10,4 \mathrm{~m}$ , a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.

Simplify. Assume that the variable represents any real number. $\sqrt[19]{x^{19}}$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $\sqrt[19]{\mathrm{x}^{19}}=$ $\square$ B. The root does not represent a real number.

86 FUNCTIONS (Chapter 3) 11 Suppose $f(x)=\sqrt{1-x}$ and $g(x)=x^{2}$ . Find: a $(f \circ g)(x)$ b the domain and range of $(f \circ g)(x)$ .

If $g(x)=\sqrt[3]{x-20}$ , find $g(12)$ $g(12)=$

How many years are required for an investment to double in value if it is appreciating at the rate of $11 \%$ compounded continuously?
At 11\% compounded continuously, the investment doubles in $\square$ years. (Round to one decimal place as needed.)

How much money must you invest now at $4.1 \%$ interest compounded continuously in order to have $\$ 10,000$ at the end of 4 years?
You must invest \\square$ (Round to the nearest cent as needed.)

tisten
This inpus-outpul tabte shows some values that satisty the equation $y=4 x+21$ . 2 2 4 5
What number correctily tils in the biank in the tatie?

Use the graph of the function to answer the question. (s) 2017 StrongMind. Created using GeoGebra.
What is the output of the function when the input is 0 ? Enter your answer as a number, like this: 42

Let $A(t)=4000 e^{0.06 t}$ be the balance in a savings account after $t$ years. Complete parts (a) through (f) below. (a) How much money was originally deposited?
There was $\$$ $\square$ originally deposited. (Type an integer or a decimal.)

2. Find all values of $x$ such that $x^{3}-x^{2}-x-2>0$

1. Find the minimum value of $2 x^{2}+12 x+4$ and the value/values of $x$ where the minimum is attained.

$6 x^{2}=-x$
Select the correct choice below and, if necessary, fill in the ans A. The solution set is $\square$ \}. (Simplify your answer. Use a comma to separate answ B. The scifution set is $\varnothing$ .

Find $<3 \bar{u}, 4 \bar{v}+5 \bar{w}>$ , given that $\langle\bar{u}, \bar{v}>=6,<\bar{v}, \bar{w}>=-5$ , and $<\bar{u}, \bar{w}>=-1$ Number

b) $(-27)^{\frac{-1}{3}}$

1. Risolvi l'equazione parametrica: $a x+b=c x+d$ , dove $a, b, c$ e $d$ sono costanti.
2. Trova $x$ se $2 x+a=b x-5$ , con $a$ e $b$ costanti.

Expand the following (a) $(2 x-3)(4 x+1)$

Consider the following lines. Line 1: $3 x-4 y=12$ Line 2: a line perpendicular to $3 x-4 y=12$ that contains the point $(3,-4)$ Write the equation of Line 1 in slope-intercept form. $\square$ Find the slope of Line 1. $\square$

1. Risolvi l'equazione: $x-\sqrt{a} x+1=0$ , dove $a$ è un parametro reale positivo.
2. Trova le soluzioni di $2 x^{2}+\frac{a}{x}-3=0$ , dove $a$ è un parametro reale positivo.

Solve $45=(w+7)^{2}$ , where $w$ is a real number. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". $w=$ $\square$ ㅁ,,..... No solution

Factor completely. $-3 u^{2}+19 u+14$

Solve for $r$ : $\begin{array}{l} \log _{3}(r+3)=-1 \\ r=\square \end{array}$

Let $f(x)=-3 x+4$ . Then $f^{-1}(x)=$

Factor. $x^{2}+13 x y+36 y^{2}$

Factor completely: $3 v^{4} x^{3}-48 x^{3}$

Solve for $s$ : $\begin{array}{l} 16^{9 s-5} \cdot 32^{-5 s-1}=\left(\frac{1}{2^{5 s+5}}\right) \\ s=\square \end{array}$

6. What is the coefficient of $x^{13}$ in the expression $\left(\sqrt{x}-\frac{1}{x^{4}}\right)^{89}$ .

$-4(-4 d+5)$
1 2 $\square$ $16 d+-20$ $16 s-20$ $16+20$ $-16 d+20$

Fill in the blank. The expression $\frac{x^{2}+2}{2+x^{2}}$ simplifies to $\qquad$
The expression $\frac{x^{2}+2}{2+x^{2}}$ simplifies to $\square$

What is the solution of $(4 x-16)^{\frac{1}{2}}=3 B^{?}$ $x=5$ $x=13$ $x=20$ $x=328$

What is the solution of $\sqrt{-4 x}=100$ ? $x=-2500$ $x=-50$ $x=-2.5$ no solution

Which expression is equivalent to $\left(2^{\frac{1}{2}}-2^{\frac{3}{4}}\right)^{2}$ ? $\sqrt[4]{2^{3}}$ $\sqrt{2^{5}}$ $\sqrt[4]{4^{3}}$ $\sqrt{4^{5}}$

Solve using the addition principle. $2 \frac{1}{5}+x=7$