Browse Algebra problems Studdy Solved!

Problem 22401

1 Forces
19. Two ropes are attached to a tree, and forces of $\vec{F}_{1}=2.0 \hat{i}+4.0 \hat{j} \mathrm{~N}$ and $\vec{F}_{2}=3.0 \hat{i}+6.0 \hat{j} \mathrm{~N}$ are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.

See Solution

Problem 22402

20. A telephone pole has three cables pulling as shown from above, with $\vec{F}_{1}=(300.0 \hat{i}+500.0 \hat{j}), \vec{F}_{2}=-200.0 \hat{i}$ , and $\vec{F}_{3}=-800.0 \hat{j}$ . (a) Find the net force on the telephone pole in component form. (b) Find the magnitude and direction of this net force.

See Solution

Problem 22403

with David's rope. 5.2 Newton's First Law
22. Two forces of $\vec{F}_{1}=75.02(\hat{i}-\hat{j}) \mathrm{N}$ and $\vec{F}_{2}=\frac{150.0}{\sqrt{2}}(\hat{i}-\hat{j}) \mathrm{N}$ act on an object. Find the third force $\vec{F}_{3}$ that is needed to balance the first two forces.

See Solution

Problem 22404

23. While sliding a couch across a floor, Andrea and Jennifer exert forces $\vec{F}_{A}$ and $\vec{F}_{J}$ on the couch. Andrea's force is due north with a magnitude of 130.0 N and Jennifer's force is $32^{\circ}$ east of north with a magnitude of 180.0 N . (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force $\vec{F}_{D S}$ should they push so that the couch does not move?

See Solution

Problem 22405

astronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this knowledge to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured by a nearby observer. (c) Discuss how this would affect the measurement of the astronaut's acceleration. Propose a method by which recoil of the vehicle is avoided.
28. In Figure 5.4.3, the net external force on the $24-\mathrm{kg}$ mower is given as 51 N . If the force of friction opposing the motion is 24 N , what force F '(in newtons is the person exerting on the mower? Suppose the mower is moving at $1.5 \mathrm{~m} / \mathrm{s}$ when the force $F$ is removed. How far will the mower go before stopping?

See Solution

Problem 22406

29. The rocket sled shown below decelerates at a rate of $196 \mathrm{~m} / \mathrm{s}^{2}$ . What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is $2.10 \times 10^{3} \mathrm{~kg}$ .

See Solution

Problem 22407

the system is $2.10 \times 10^{3} \mathrm{~kg}$ , the thrust T is $2.40 \times 10^{4} \mathrm{~N}$ , and the force of friction opposing the motion is 650.0 N . (b) Why is the acceleration not onefourth of what it is with all rockets burning? What is the deceleration of the rocket sled if it comes to rest in 1.10 s from a speed of $1000.0 \mathrm{~km} / \mathrm{h}$ ? (Such deceleration caused one test subject to black out and have temporary blindness.)

See Solution

Problem 22408

2. Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N , the second exerts a force of 90.0 N , friction is 12.0 N , and the mass of the third child plus wagon is 23.0 kg . (a) What is the system of interest if the acceleration of the child in the wagon is to be calculated? (See the free-body diagram.) (b) Calculate the acceleration. (c) What would the acceleration be if friction were 15.0 N ?

See Solution

Problem 22409

nomework11.4: Problem 1 (1 point)
Compare and discuss the long-run behaviors of the functions below. In each blank, enter either the constant or the polynomial that the rational function behaves like as $x \rightarrow \pm \infty$ : $f(x)=\frac{x^{4}-7}{x^{3}-6}, g(x)=\frac{x^{3}-7}{x^{3}-6}$ , and $h(x)=\frac{x^{2}-7}{x^{3}-6}$ $f(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas) $g(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas) $h(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas)
Note: You can earn partial credit on this problem.

See Solution

Problem 22410

9. Solve the equation. $2 \log _{2}(x)=1+\log _{2}(x+60)$

See Solution

Problem 22411

Factories often add filler when making meatballs sold by the bag. One factory obtained 135 kg of beef from overseas. They want to add 1.3 oz of filler for each pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef?
Use $1 \mathrm{lb}=0.45 \mathrm{~kg}$ and do not round any computations. $\square$ oz

See Solution

Problem 22412

17. $\begin{aligned} r-2 s & =0 \\ 4 r-3 s & =15\end{aligned}$

See Solution

Problem 22413

Find a basis for the null space of the matrix given below. $\left[\begin{array}{rrrrr} 1 & 1 & -2 & -2 & 4 \\ 0 & 1 & 0 & -3 & -3 \\ 0 & 0 & -6 & 0 & 12 \end{array}\right]$
A basis for the null space is $\square$ (Use a comma to separate answers as needed.)

See Solution

Problem 22414

Simplify. Assume all variables are positive. $r^{\frac{12}{7}} \cdot r^{-\frac{8}{7}}$
Write your answer in the form $A$ or $\frac{A}{B^{\prime}}$ where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\square$ Submit
Work it out Not feeling ready yet? These can help: here to search

See Solution

Problem 22415

35. The driver in the previous problem applies the brakes when the car is moving at $90.0 \mathrm{~km} / \mathrm{h}$ , and the car comes to rest after traveling 40.0 m . What is the net force on the car during its deceleration?
36. An $80.0-\mathrm{kg}$ passenger in an SUV traveling at $1.00 \times 10^{2} \mathrm{~km} / \mathrm{h}$ is wearing a seat belt. The driver slams on the brakes and the SUV stops in 45.0 m . Find th force of the seat belt on the passenger.

See Solution

Problem 22416

38. Suppose that the particle of the previous problem also experiences forces $\vec{F}_{2}=-15 \hat{i} \mathrm{~N}$ and $\vec{F}_{3}=6.0 \hat{j} \mathrm{~N}$ . What is its acceleration in this
39. Find the acceleration of the body of mass 5.0 kg shown below.

See Solution

Problem 22417

15. Water whose temperature is at $100^{\circ} \mathrm{C}$ is left to cool in a room where the temperature is $30^{\circ} \mathrm{C}$ . After 2 minutes, the water temperature is $88^{\circ} \mathrm{C}$ . If the water temperature $T$ is a function of time $t$ given by $T=30+70 e^{k t}$ , find $k$ . Round your answer to the nearest hundredth.

See Solution

Problem 22418

lass and Weight
1. The weight of an astronaut plus his space suit on the Moon is only 250 N . (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

See Solution

Problem 22419

on the Moon? On Earth? Suppose the mass of a fully loaded module in which astronauts take off from the Moon is $1.00 \times 10^{4} \mathrm{~kg}$ . The thrust of its engines is $3.00 \times 10^{4} \mathrm{~N}$ . (a) Calculate the module's magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

See Solution

Problem 22420

Arianna is working two summer jobs, washing cars and tutoring. She must work nc less than 10 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours washing cars, $w$ , and the number of hours tutoring, $t$ , that Arianna can work in a given week.

See Solution

Problem 22421

the magnitude of its acceleration. A rocket sled accelerates at a rate of $49.0 \mathrm{~m} / \mathrm{s}^{2}$ . Its passenger has a mass of 75.0 kg . (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body. Repeat the previous problem for a situation in which the rocket sled decelerates at a rate of $201 \mathrm{~m} / \mathrm{s}^{2}$ . In this problem, the forces are exerted by the seat and the seat belt. A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is its acceleration?

See Solution

Problem 22422

Solve for $x$ : $\begin{array}{l} \log _{3}\left(x^{7}\right)=-1 \\ x= \end{array}$

See Solution

Problem 22423

42. The device shown below is the Atwood's machine considered in Example 6.5. Assuming that the masses of the string and the frictionless pulley are negligible, (a) find an equation for the acceleration of the two blocks; (b) find an equation for the tension in the string; and (c) find both the acceleration and tension when block 1 has mass 2.00 kg and block 2 has mass 4.00 kg .

See Solution

Problem 22424

43. Two blocks are connected by a massless rope as shown below. The mass of the block on the table is 4.0 kg and the hanging mass is 1.0 kg . The table and the pulley are frictionless. (a) Find the acceleration of the system. (b) Find the tension in the rope. (c) Find the speed with which the hanging mass hits the floor if it starts from rest and is initially located 1.0 m from the floor.

See Solution

Problem 22425

Simplify $(2+3)^{2}-16 \div 2$ .
The solution is

See Solution

Problem 22426

23. Solve the equation. If necessary, round the answer to four decimal places. $7^{x+2}-7^{x}=96$

See Solution

Problem 22427

A 2.00 kg block (mass 1 ) and a 4.00 kg block (mass 2 ) are connected by a light string as shown; the inclination of the ramp is $40.0^{\circ}$ . Friction is negligib What is (a) the acceleration of each block and (b) the tension in the string?

See Solution

Problem 22428

覑 W Write a quadratic function with zeros 6 and 7. "新] Write your answer using the variable x and in standard form with a leading coefficient of 1 . $f(x)=$ $\square$ 2 3 4

See Solution

Problem 22429

[效, Write a quadratic function with zeros 7 and -4. [i]. Write your answer using the variable x and in standard form with a leading coefficient of 1. $g(x)=$ $\square$ 2 3 4

See Solution

Problem 22430

$\left|\frac{x-1}{2}-\frac{x+2}{3}\right|=\frac{x}{6}-\frac{4}{3}$

See Solution

Problem 22431

29. Solve the equation. $\log _{6}(x)=\log _{6}\left(\frac{1}{x}\right)+8$

See Solution

Problem 22432

Number Problems Find two numbers whose difference is 10 and whose product is a minimum.

See Solution

Problem 22433

Doppler Effect - The whistle of a train emits a frequency of 440 Hz. - As it recedes from a stationary receiver at 30 $\mathrm{m} / \mathrm{s}$ , what frequency does the observer hear?

See Solution

Problem 22434

Algebra 1 W. 5 Add polynomials to find perimeter BAS Video Questions answered
Find the perimeter. Simplify your answer. 38 Time clapsed 00 34 16 HR M N जह SmartScore out of 100 5ミх $\square$ Submit
Work it out Not feeling ready yet? These can help: Add and subtract like terms Lesson: Simplifying expressions 10:09 AM 12/2/2024

See Solution

Problem 22435

A one-to-one function is given. Write an equation for the inverse function. $\begin{array}{r} s(x)=\frac{2}{x+3} \\ s^{-1}(x)= \end{array}$ $\square$

See Solution

Problem 22436

$-x^{2}+7 x-10=0$

See Solution

Problem 22437

Assume $X$ has a normal distribution $N\left(9,5^{2}\right)$ . Find $E(5 X-4)^{2}$
Answer: $\square$

See Solution

Problem 22438

Type the correct answer in the box. Use numerals instead of wolds. If necessary, use / for the fraction bar. $\begin{array}{l} y=x^{2}-2 x-19 \\ y+4 x=5 \end{array}$
The pair of points representing the solution set of this system of equations is $(-6,29)$ and $\square$

See Solution

Problem 22439

Part 1 of 4 (a) Show that $f(x)=3 x+3$ defines a one-to-one function.
A function is one-to-one if it can be shown that if $f(a)=f(b)$ , then $\square=\square$ . Assume $f(a)=f(b)$ .

See Solution

Problem 22440

Let $p$ and $q$ be the following statements. $p$ : The bake sale is on Saturday. $q$ : Ahmad will make cookies. Consider this argument. Premise 1: If the bake sale is on Saturday, then Ahmad will make cookies. Premise 2: The bake sale is on Saturday. Conclusion: Therefore, Ahmad will make cookies. (a) Write the argument in symbolic form.
Premise 1: p $q$ Premise 2: Conclusion: $\square$

See Solution

Problem 22441

3) $6 x^{2}-7 x+2=0$

See Solution

Problem 22442

nomework11.1: Problem / (1 point)
A 30-second commercial during Super Bowl XLII in 2008 cost advertisers 2.7 million. For the first Super Bowl in 1967, an advertiser could have purchased approximately 26.19 minutes of advertising time for the same amount of money. (a) Assuming that advertising cost is proportional to its length of time, find the cost of advertising, in dollars/second, during the 2008 Super Bowl. cost $=$ $\square$ dollars/second. (round to nearest cent and do not enter commas) (b) Assuming that advertising cost is proportional to its length of time, find the cost of advertising, in dollars/second, during the 1967 Super Bowl. cost $=$ $\square$ dollars/second. (round to nearest cent and do not enter commas) (c) How many times more expensive was Super Bowl advertising in 2008 than in 1967? $\square$ times more expensive (round to nearest whole number)

See Solution

Problem 22443

Part: $0 / 8$
Part 1 of 8 (a) Graph $f(x)=x^{2}-2 ; x \leq 0$ .

See Solution

Problem 22444

Evaluate the expression below if $x=-1$ and $y=3$ $3 x^{2}-y^{2}$ 1 Pt A B C
A -6 B 6 C -12
D 22

See Solution

Problem 22445

Question Evaluate the function $f(x)=3 \log (x+7)+2$ for $x=1$ . Round the final answer to the nearest two decimal places.

See Solution

Problem 22446

2. Describe the behavior of the function in words. A complete description would describe the initial value and would use descriptors such as "decays/grows by", "factor of," "\% growth/decay", etc. If the initial value was not specified in the article, make up a reasonable initial value and defend your choice. You are welcome to rescale the input (for example, time) at your convenience; if you do this just explain why you did it. Initial value is zero. The function describes exponential grouth. 100 deaths at day 0 . $600=a b^{t}$ $1900(1+r)^{t}$
3. Give an algebraic formula for the function, and define each of your variables with units. $\begin{array}{l} D(t)=D_{0}+b_{k G F}^{t} \\ D=\text { \#of deaths } t=\text { days }>1500=100 \cdot b^{15} \\ b^{15}=\frac{1500}{100}=15 \\ 6^{1 / 10} \approx 1.174 \\ 1,174^{15}=15 \end{array}$
4. Identify the growth factor and the growth or decay rate for the function. aproxmitly 1.174 , growth rate is about $17.4 \%$
5. Construct a table of values for the function. Include at least 5 sets of data points.
6. In your table, demonstrate where/how you can see the growth factor.

See Solution

Problem 22447

Part 1 of 9 (a) Graph $f(x)=\sqrt{x+3}$ .

See Solution

Problem 22448

Consider the following polynomial function. $f(x)=(x+1)(x-1)(x-3)$
Answer the questions regarding the graph of $f$ . Then, use this information to graph the function. (a) Choose the end behavior of the graph of $f$ .
Choose One (b) Ust each real zero of $f$ according to the behavior of the graph at the $X$ -axis near that zero. If there is more than one answer, separate them with commas. If there is no answer, click on "None",
Zero(s) where the graph crosses the $X_{\text {-axis: }}$ $\square$ Zero(s) where the graph touches, but does not cross the $X$ -axis: $\square$ (c) Find the $y$ -Intercept of the graph of $f$ : (d) Graph $f(x)=(x+1)(x-1)(x-3)$ by doing the following. - Plot all polnts where the graph of $f$ intersects the $x$ -axis or $y$ -axis. - For each polnt on the $\boldsymbol{X}$ -axis, select the correct behavior. - click on the graph icon.

See Solution

Problem 22449

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$
ANS:

See Solution

Problem 22450

point. Please enter the ic devic not hand in working out. Time devices are to be used including phones. decreasing for all $n \geqslant n_{0}$ .

See Solution

Problem 22451

Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. \begin{tabular}{|c|c|} \hline System A $\begin{array}{r} 5 x-y=-5 \\ -5 x+y=-5 \end{array}$ & \begin{tabular}{l} The system has no solution. The system has a unique solution: $(x, y)=(\square, \square)$ The system has infinitely many solutions. \\ They must satisfy the following equation: $y=$ $\square$ \end{tabular} \\ \hline System B $\begin{aligned} 3 x-y-6 & =0 \\ -3 x+y & =-6 \end{aligned}$ & \begin{tabular}{l} The system has no solution. The system has a unique solution: $(x, y)=(\square, \square)$ The system has infinitely inany solutions. \\ They must satisfy the following equation: $y=$ $\square$ \end{tabular} \\ \hline \end{tabular}

See Solution

Problem 22452

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x-1)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}+2$ .

See Solution

Problem 22453

- $\frac{5}{\sqrt{x}} \leq \frac{3 \sqrt{x}}{2}$ - $\frac{1}{-x+2} \geq-4$

See Solution

Problem 22454

2. Find all values of $x$ such that $x^{3}-14 x^{2}+53 x-40>0$ .
ANS:

See Solution

Problem 22455

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$

See Solution

Problem 22456

9 El diagrama muestra el gráfico de $y=2^{x}+3$ . La curva pasa por los puntos $\mathrm{A}(0, a)$ y $\mathrm{B}(1, b)$ . a Halle el valor de $a$ y el valor de $b$ . b Escriba la ecuación de la asíntota de la curva.

See Solution

Problem 22457

$3-\sqrt{x}=-2$
1 $\sqrt{5}$
25

See Solution

Problem 22458

Solve the system of equations using elimination, show your work, and explain why the method works. $\left\{\begin{array}{l} 3 x+y=6 \\ 4 x-3 y=-5 \end{array}\right.$
Type your answer in the box. Use the $\square$ $X$ button to enter math expressions and equations.

See Solution

Problem 22459

ANS:
5. If a savings account offers a nominal interest rate of $3 \%$ per year, compounded every four months, then how many years will it take for a deposit to double in value?
ANS:

See Solution

Problem 22460

$\sqrt[4]{\frac{1}{x^{4}}+\frac{9 x+6}{x^{3}}}$

See Solution

Problem 22461

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k} .$

See Solution

Problem 22462

Suppose functions $f$ and $g$ are defined as follows. \begin{tabular}{ccc} \hline $x$ & $f(x)$ & $g(x)$ \\ \hline 1 & 3 & 3 \\ 2 & 5 & 4 \\ 3 & 6 & 1 \\ 4 & 7 & 5 \\ 5 & 4 & 2 \\ \hline \end{tabular}
That is, $f(1)=3, g(1)=3, f(2)=5, g(2)=4$ , and so on. (a) Evaluate $f^{-1}$ (7). (2 Points)

See Solution

Problem 22463

Use the polynomial to answer the questions: $-23 x^{7}+x^{9}-6 x^{3}+10+2 x^{2}$
What is the degree of the polynomial?
What is the leading coefficient of the polynomial? $\square$

See Solution

Problem 22464

Add or subtract the polynomial. $\left(7 x^{3}+68 x^{4}-14 x+1\right)-\left(-10 x^{3}+8 x+23\right)=$ $\square$ $x^{4}+$ $\square$ $x^{3}+$ $\square$ $x+$ $\square$

See Solution

Problem 22465

$\frac{\left(x^{3}\right)^{2}}{\left(x^{2}\right)^{-1}}$

See Solution

Problem 22466

a. What does each of these points represent in this situation: $(0,0),(1,55)$ , and $(5,275)$ ? b. What is the constant of proportionality?
Mr. Brown's Road Trip c. What equation relates the distance, $y$ , and the time, $x$ ? $y=55 x$

See Solution

Problem 22467

For a given arithmetic sequence, the common difference, $d$ , is equal to 5 , and the $12^{\text {th }}$ term, $a_{12}$ , is equal to 40 . Find the value of the $88^{\text {th }}$ term, $a_{88}$ . $a_{88}=$

See Solution

Problem 22468

7. $6 x-5 y=12$
8. $y=6 x-8$

See Solution

Problem 22469

$L=\frac{6.5 \times 12-6}{3 \times(15.2-7.2)}-3$

See Solution

Problem 22470

$6 x+3 y<0$

See Solution

Problem 22471

Financial Alg Unit 2A Quiz A
7. How long will it take $\$ 3,000$ to earn $\$ 350$ in interest at a rate of $5.3 \%$ ? Express your answer in years and months.

See Solution

Problem 22472

11. How many real third roots does 1,728 have?
12. How many real sixth roots does 15,625 have?
13. Solve the equation $4 x^{3}=324$ .
14. Solve the equation $2 x^{4}=2,500$ .
Simplify each expression.
15. $\sqrt[3]{27 x^{12} y^{6}}$
16. $\sqrt[5]{-32 x^{5} y^{30}}$

See Solution

Problem 22473

Write the domain in interval notation. $f(x)=\ln \left(x^{2}+9\right)$
The domain is $\square$

See Solution

Problem 22474

Solve for $x$ . $2 x+3 \geq 7 \quad \text { OR } \quad 2 x+9>11$
Choose 1 answer: (A) $x>1$ (B) $x \geq 2$ (C) $x \leq 2$ (D) There are no solutions (E) All values of $x$ are solutions

See Solution

Problem 22475

3. IE $S(N)=\sum_{k=1}^{N}$ \& then which value of $N$ solves the following equation? $\sum_{n=1}^{S N 1} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$
ANS: value of

See Solution

Problem 22476

11. How many real third roots does 1,728 have?
12. How many real sixth roots does 15,625 have?

See Solution

Problem 22477

18 19 20 21 22 23 24 25 26 27
Write the domain in interval notation. Write your answers as integers or simplified fractions if necessary. $h(x)=\log _{2}(6 x+7)$
The domain is $\square$ . \begin{tabular}{ccc} \hline $\sqrt{\square}$ & $(\square, \square)$ & $\frac{\square}{\square}$ \\ { $[\square, \square]$ } & $(\square, \square]$ & { $[\square, \square)$ } \\ $\square \cup \square$ & $\infty$ & $-\infty$ \end{tabular}

See Solution

Problem 22478

15. If an investment is growing continuously for $t$ years, its annual growth rate $r$ is given by the formula $r=\frac{1}{t} \ln \frac{P}{P_{0}}$ where $P$ is the current value and $P_{0}$ is the amount originally invested.
An investment of $\$ 13,400$ in a particular Internet company in 1992 was worth $\$ 8,040,000$ in 1998 . Find this investment's average annual growth rate during this period.

See Solution

Problem 22479

The population of a city, $P(t)$ , is given by the function $P(t)=14 t^{2}+820 t+42000$ , where $t$ is time in years. Note: $t=0$ corresponds to the year 2000. a) When will the population reach 56224 ?

See Solution

Problem 22480

6. Find the positive value of $x$ that solves the following equation: $x^{\infty}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}$
ANS: $\qquad$

See Solution

Problem 22481

Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expression. $3 \ln (9 x)=15$
Rewrite the given equation without logarithms. Do not solve for x . $\square$

See Solution

Problem 22482

Simplify the expression without using a calculator. $\ln e^{a^{2}+8}=$ $\square$ n口 $e$

See Solution

Problem 22483

Factor $y^{3}-5 y^{2}+6 y-30$ completely. $y^{3}-5 y^{2}+6 y-30=$

See Solution

Problem 22484

Soit la réaction $\mathrm{A} \rightarrow \mathrm{B}$ . La concentration du substrat A est 5 mM . Au bout de 2 minutes elle est de 4 mM . Calculez la concentration en substrat au bout de 5 minutes :
1 - Si la réaction est d'ordre 0 . 2- Si la réaction est d'ordre 1.

See Solution

Problem 22485

Which point is on the graph of $f(x)=3 \cdot 5^{x} ?$ A. $(1,15)$ B. $(15,1)$ C. $(0,0)$ D. $(0,15)$

See Solution

Problem 22486

Simplify the expression without using a calculator. $7^{\log _{7}(p-q)}=\square$ $\log _{\mathrm{B}} \bar{\square}$

See Solution

Problem 22487

Question Watch Video Show Examples
If $f(x)=x^{5}+5 x^{4}+4$ , then what is the remainder when $f(x)$ is divided by $x+3$ ?
Answer Attempt 1 out of 2

See Solution

Problem 22488

Which pair of binomials matches the given polynomial? $25 a^{2}+70 a b+49 b^{2}$ $(5 a+7)(5 a+b)$ $(5 a+7)(5 a-b)$ $(5 a+7 b)(5 a+7 b)$ $(5 a+7)(5 a+5 b)$

See Solution

Problem 22489

15) $\begin{array}{l} y>2 x-3 \\ y<\frac{1}{3} x+2 \end{array}$

See Solution

Problem 22490

Simplify the expression without using a calculator. $\log _{5} 5^{14}=$ $\square$ $\square \log _{\square}$

See Solution

Problem 22491

16) $\begin{array}{l} y \geq x-1 \\ y<-2 \end{array}$

See Solution

Problem 22492

The exponential model $A=147.6 e^{0.016 t}$ describes the population, $A$ , of a country in millions, $t$ years after 2003. Use the model to determine the population of the country in 2003.
The population of the country in 2003 wäs $\square$ million.

See Solution

Problem 22493

Find the slope of the line through each pair of points. 3) $(-3,-9),(12,19)$ 4) $(-16,10),(11,16)$
Find the slope of each line. 5) $y=-x+4$ 6) $y=-2 x+2$
Find the slope of a line parallel to each given line. 7) $y=6 x+4$ 8) $y=4$
Find the slope of a line perpendicular to each given line. 10) $x=2$ 9) $y=\frac{1}{2} x+1$

See Solution

Problem 22494

Solve the system by the method of elimination and check any solutions algebraically. (If the real number a.) $\begin{array}{r} \left\{\begin{array}{l} 0.2 x-0.3 y=3.2 \\ 0.7 x+0.5 y=5.0 \end{array}\right. \\ (x, y)=(\square) \end{array}$ Need Help? Read It Watch It

See Solution

Problem 22495

Simplify the expression without using a calculator. $\log _{\frac{1}{2}}\left(\frac{1}{128}\right)=$ $\square$ $\square \log _{\square} \square$

See Solution

Problem 22496

Simplify the expression without using a calculator. $\ln e^{6}=$

See Solution

Problem 22497

Simplify the expression without using a calculator. $\log _{9}\left(\frac{1}{81}\right)=$ $\square$ $\square$

See Solution

Problem 22498

3. If $S(N)=\sum_{k=1}^{N} k$ then which value $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$

See Solution

Problem 22499

2. Determine whether the following sets $V_{1}$ and $V_{2}$ correspond to vector spaces by verifying the 10 axioms. b) Let $V_{2}=\mathbb{R}^{+}$ and define addition and scaler multiplication as follows: If $\vec{a}=a$ and $\vec{b}=b$ (for $a, b \in \mathbb{R}^{+}$ ) then define $\vec{a} \oplus \vec{b}=a \cdot b$
And if $c \in \mathbb{R}$ , then define $c \odot \vec{a}=a^{c} .$

See Solution

Problem 22500

$\left(2 x^{2}+4 x-5\right)+\left(x^{2}+3\right)=$

See Solution

Algebra

Problem 22401

Problem 22402

Problem 22403

Problem 22404

Problem 22405

Problem 22406

29. The rocket sled shown below decelerates at a rate of 196 m/s2196 \mathrm{~m} / \mathrm{s}^{2}196 m/s2. What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2.10×103 kg2.10 \times 10^{3} \mathrm{~kg}2.10×103 kg.

Problem 22407

Problem 22408

Problem 22409

Problem 22410

9. Solve the equation. 2log⁡2(x)=1+log⁡2(x+60)2 \log _{2}(x)=1+\log _{2}(x+60)2log2​(x)=1+log2​(x+60)

Problem 22411

Problem 22412

17. r−2s=04r−3s=15\begin{aligned} r-2 s & =0 \\ 4 r-3 s & =15\end{aligned}r−2s4r−3s​=0=15​

Problem 22413

Problem 22414

Problem 22415

Problem 22416

Problem 22417

Problem 22418

lass and Weight1. The weight of an astronaut plus his space suit on the Moon is only 250 N . (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

Problem 22419

Problem 22420

Problem 22421

Problem 22422

Solve for xxx : log⁡3(x7)=−1x=\begin{array}{l} \log _{3}\left(x^{7}\right)=-1 \\ x= \end{array}log3​(x7)=−1x=​

Problem 22423

Problem 22424

Problem 22425

Simplify (2+3)2−16÷2(2+3)^{2}-16 \div 2(2+3)2−16÷2.The solution is

Problem 22426

23. Solve the equation. If necessary, round the answer to four decimal places. 7x+2−7x=967^{x+2}-7^{x}=967x+2−7x=96

Problem 22427

A 2.00 kg block (mass 1 ) and a 4.00 kg block (mass 2 ) are connected by a light string as shown; the inclination of the ramp is 40.0∘40.0^{\circ}40.0∘. Friction is negligib What is (a) the acceleration of each block and (b) the tension in the string?

Problem 22428

覑 W Write a quadratic function with zeros 6 and 7. "新] Write your answer using the variable x and in standard form with a leading coefficient of 1 . f(x)=f(x)=f(x)= □\square□ 2 3 4

Problem 22429

[效, Write a quadratic function with zeros 7 and -4. [i]. Write your answer using the variable x and in standard form with a leading coefficient of 1. g(x)=g(x)=g(x)= □\square□ 2 3 4

Problem 22430

∣x−12−x+23∣=x6−43\left|\frac{x-1}{2}-\frac{x+2}{3}\right|=\frac{x}{6}-\frac{4}{3}∣∣​2x−1​−3x+2​∣∣​=6x​−34​

Problem 22431

29. Solve the equation. log⁡6(x)=log⁡6(1x)+8\log _{6}(x)=\log _{6}\left(\frac{1}{x}\right)+8log6​(x)=log6​(x1​)+8

Problem 22432

Number Problems Find two numbers whose difference is 10 and whose product is a minimum.

Problem 22433

Doppler Effect - The whistle of a train emits a frequency of 440 Hz. - As it recedes from a stationary receiver at 30 m/s\mathrm{m} / \mathrm{s}m/s, what frequency does the observer hear?

Problem 22434

Problem 22435

A one-to-one function is given. Write an equation for the inverse function. s(x)=2x+3s−1(x)=\begin{array}{r} s(x)=\frac{2}{x+3} \\ s^{-1}(x)= \end{array}s(x)=x+32​s−1(x)=​ □\square□

Problem 22436

−x2+7x−10=0-x^{2}+7 x-10=0−x2+7x−10=0

Problem 22437

Assume XXX has a normal distribution N(9,52)N\left(9,5^{2}\right)N(9,52). Find E(5X−4)2E(5 X-4)^{2}E(5X−4)2Answer: □\square□

Problem 22438

Problem 22439

Part 1 of 4 (a) Show that f(x)=3x+3f(x)=3 x+3f(x)=3x+3 defines a one-to-one function.A function is one-to-one if it can be shown that if f(a)=f(b)f(a)=f(b)f(a)=f(b), then □=□\square=\square□=□. Assume f(a)=f(b)f(a)=f(b)f(a)=f(b).

Problem 22440

Problem 22441

3) 6x2−7x+2=06 x^{2}-7 x+2=06x2−7x+2=0

Problem 22442

Problem 22443

Part: 0/80 / 80/8Part 1 of 8 (a) Graph f(x)=x2−2;x≤0f(x)=x^{2}-2 ; x \leq 0f(x)=x2−2;x≤0.

Problem 22444

Evaluate the expression below if x=−1x=-1x=−1 and y=3y=3y=3 3x2−y23 x^{2}-y^{2}3x2−y2 1 Pt A B CA -6 B 6 C -12D 22

Problem 22445

Question Evaluate the function f(x)=3log⁡(x+7)+2f(x)=3 \log (x+7)+2f(x)=3log(x+7)+2 for x=1x=1x=1. Round the final answer to the nearest two decimal places.

Problem 22446

Problem 22447

Part 1 of 9 (a) Graph f(x)=x+3f(x)=\sqrt{x+3}f(x)=x+3​.

Problem 22448

Problem 22449

3. If S(N)=∑k=1NkS(N)=\sum_{k=1}^{N} kS(N)=∑k=1N​k then which value of NNN solves the following equation? ∑n=1S(N)4n=43(455−1)\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)n=1∑S(N)​4n=34​(455−1)ANS:

Problem 22450

point. Please enter the ic devic not hand in working out. Time devices are to be used including phones. decreasing for all n⩾n0n \geqslant n_{0}n⩾n0​.

Problem 22451

Problem 22452

Translate each graph as specified below. (a) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=(x−1)2y=(x-1)^{2}y=(x−1)2. (b) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=x2+2y=x^{2}+2y=x2+2.

Problem 22453

29. The rocket sled shown below decelerates at a rate of $196 \mathrm{~m} / \mathrm{s}^{2}$ . What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is $2.10 \times 10^{3} \mathrm{~kg}$ .

9. Solve the equation. $2 \log _{2}(x)=1+\log _{2}(x+60)$

17. $\begin{aligned} r-2 s & =0 \\ 4 r-3 s & =15\end{aligned}$

lass and Weight
1. The weight of an astronaut plus his space suit on the Moon is only 250 N . (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

Solve for $x$ : $\begin{array}{l} \log _{3}\left(x^{7}\right)=-1 \\ x= \end{array}$

Simplify $(2+3)^{2}-16 \div 2$ .
The solution is

23. Solve the equation. If necessary, round the answer to four decimal places. $7^{x+2}-7^{x}=96$

A 2.00 kg block (mass 1 ) and a 4.00 kg block (mass 2 ) are connected by a light string as shown; the inclination of the ramp is $40.0^{\circ}$ . Friction is negligib What is (a) the acceleration of each block and (b) the tension in the string?

覑 W Write a quadratic function with zeros 6 and 7. "新] Write your answer using the variable x and in standard form with a leading coefficient of 1 . $f(x)=$ $\square$ 2 3 4

[效, Write a quadratic function with zeros 7 and -4. [i]. Write your answer using the variable x and in standard form with a leading coefficient of 1. $g(x)=$ $\square$ 2 3 4

$\left|\frac{x-1}{2}-\frac{x+2}{3}\right|=\frac{x}{6}-\frac{4}{3}$

29. Solve the equation. $\log _{6}(x)=\log _{6}\left(\frac{1}{x}\right)+8$

Doppler Effect - The whistle of a train emits a frequency of 440 Hz. - As it recedes from a stationary receiver at 30 $\mathrm{m} / \mathrm{s}$ , what frequency does the observer hear?

A one-to-one function is given. Write an equation for the inverse function. $\begin{array}{r} s(x)=\frac{2}{x+3} \\ s^{-1}(x)= \end{array}$ $\square$

$-x^{2}+7 x-10=0$

Assume $X$ has a normal distribution $N\left(9,5^{2}\right)$ . Find $E(5 X-4)^{2}$
Answer: $\square$

Part 1 of 4 (a) Show that $f(x)=3 x+3$ defines a one-to-one function.
A function is one-to-one if it can be shown that if $f(a)=f(b)$ , then $\square=\square$ . Assume $f(a)=f(b)$ .

3) $6 x^{2}-7 x+2=0$

Part: $0 / 8$
Part 1 of 8 (a) Graph $f(x)=x^{2}-2 ; x \leq 0$ .

Evaluate the expression below if $x=-1$ and $y=3$ $3 x^{2}-y^{2}$ 1 Pt A B C
A -6 B 6 C -12
D 22

Question Evaluate the function $f(x)=3 \log (x+7)+2$ for $x=1$ . Round the final answer to the nearest two decimal places.

Part 1 of 9 (a) Graph $f(x)=\sqrt{x+3}$ .

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$
ANS:

point. Please enter the ic devic not hand in working out. Time devices are to be used including phones. decreasing for all $n \geqslant n_{0}$ .

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x-1)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}+2$ .

- $\frac{5}{\sqrt{x}} \leq \frac{3 \sqrt{x}}{2}$ - $\frac{1}{-x+2} \geq-4$

2. Find all values of $x$ such that $x^{3}-14 x^{2}+53 x-40>0$ .
ANS:

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$

9 El diagrama muestra el gráfico de $y=2^{x}+3$ . La curva pasa por los puntos $\mathrm{A}(0, a)$ y $\mathrm{B}(1, b)$ . a Halle el valor de $a$ y el valor de $b$ . b Escriba la ecuación de la asíntota de la curva.

$3-\sqrt{x}=-2$
1 $\sqrt{5}$
25

ANS:
5. If a savings account offers a nominal interest rate of $3 \%$ per year, compounded every four months, then how many years will it take for a deposit to double in value?
ANS:

$\sqrt[4]{\frac{1}{x^{4}}+\frac{9 x+6}{x^{3}}}$

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k} .$

Use the polynomial to answer the questions: $-23 x^{7}+x^{9}-6 x^{3}+10+2 x^{2}$
What is the degree of the polynomial?
What is the leading coefficient of the polynomial? $\square$

Add or subtract the polynomial. $\left(7 x^{3}+68 x^{4}-14 x+1\right)-\left(-10 x^{3}+8 x+23\right)=$ $\square$ $x^{4}+$ $\square$ $x^{3}+$ $\square$ $x+$ $\square$

$\frac{\left(x^{3}\right)^{2}}{\left(x^{2}\right)^{-1}}$

a. What does each of these points represent in this situation: $(0,0),(1,55)$ , and $(5,275)$ ? b. What is the constant of proportionality?
Mr. Brown's Road Trip c. What equation relates the distance, $y$ , and the time, $x$ ? $y=55 x$

For a given arithmetic sequence, the common difference, $d$ , is equal to 5 , and the $12^{\text {th }}$ term, $a_{12}$ , is equal to 40 . Find the value of the $88^{\text {th }}$ term, $a_{88}$ . $a_{88}=$

7. $6 x-5 y=12$
8. $y=6 x-8$

$L=\frac{6.5 \times 12-6}{3 \times(15.2-7.2)}-3$

$6 x+3 y<0$

Financial Alg Unit 2A Quiz A
7. How long will it take $\$ 3,000$ to earn $\$ 350$ in interest at a rate of $5.3 \%$ ? Express your answer in years and months.

Write the domain in interval notation. $f(x)=\ln \left(x^{2}+9\right)$
The domain is $\square$

Solve for $x$ . $2 x+3 \geq 7 \quad \text { OR } \quad 2 x+9>11$
Choose 1 answer: (A) $x>1$ (B) $x \geq 2$ (C) $x \leq 2$ (D) There are no solutions (E) All values of $x$ are solutions