Algebra

Problem 30901

Find values of $t$ that make the expression $\frac{5 t-2}{3 t-9}$ undefined. List them as $t=$ .

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Problem 30902

Find the domain restriction for the function $f(x) = \frac{1}{x-3}$ . Explain your reasoning.

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Problem 30903

Graph the solution for the inequality $x \leq -1$ .

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Problem 30904

Simplify the expression: $(-8 u^{4} v - 6 u^{3} v^{3} - 2 v^{3} - 7 u v^{4}) - (-4 u^{3} v^{3} - 8 v^{3} - 4 u v^{4} - 5 u^{4} v) + (3 u v^{4} - 8 u^{3} v^{3} - v^{3} + 4 u^{3} v^{4})$ .

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Problem 30905

Factor the expression $2 x^{3}+6 x^{2}-8 x-24$ .

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Problem 30906

Rewrite the quadratic $x^{2}+8x-3$ in vertex form $y=(x+h)^{2}+k$ by completing the square. Choose a step:
1. $y=x^{2}+8x+8-3-8$
2. $y=x^{2}+8x+8-3+8$
3. $y=x^{2}+8x+16-3-16$
4. $y=x^{2}+8x+16-3+16$

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Problem 30907

What interval does the inequality $x \leq -1$ represent?

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Problem 30908

A car's tank is $80\%$ full. After using $30\%$ of that fuel, it needs 19 gallons to fill up. Find the tank's full capacity.

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Problem 30909

Simplify the expression: $\sqrt{\frac{7 x^{3}}{3}}$

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Problem 30910

What interval does the inequality $x \geq 5$ represent?

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Problem 30911

Write a cost function for a ski resort that charges \$20 plus \$4.25 per hour. Identify the correct variable.

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Problem 30912

Choose the correct verbal expression for $4s - 4$ , where $s$ is the side length of a square.

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Problem 30913

Solve the inequality $-5z + 6 \geq -3z - 4$ and express the solution in interval notation.

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Problem 30914

Find the linear cost function $C(x)$ given a fixed cost of \$300 and that producing 60 items costs \$3,300.

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Problem 30915

Find the average cost per item given the cost function $C(x)=18x+1400$ for producing 100 items. What is the average cost?

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Problem 30916

Decompose the function $1+x \cos (x)$ into its even and odd parts.

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Problem 30917

Decompose $\sin^{2}(y) - 8y^{4}\sin(y)$ into even and odd functions.

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Problem 30918

Find the linear depreciation function for a car priced at \$25,250, expected to be worth \$14,234 in 4 years. Also, estimate its value in 6 years and find the depreciation rate.

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Problem 30919

Calculate the specific heat of a liquid given that $47.1 \mathrm{~J}$ raises $13.8 \mathrm{~g}$ by $1.79^{\circ} \mathrm{C}$ .

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Problem 30920

Solve the inequality $x + 1 \geq 5$ and express the solution in interval notation.

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Problem 30921

Solve the inequality $x + 1 \geq 5$ and express the solution in interval notation.

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Problem 30922

4,860 people visited a fair on Saturday, which was $20\%$ more than Friday. Find Friday's visitor count.

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Problem 30923

Solve for $x$ : $\frac{220,000}{x+475}=0$

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Problem 30924

Five 6th graders raced 3 miles. Johnny was 3rd in 34 min. Other times were -5, -3, +4 min. Find 5th place time.

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Problem 30925

Simplify: $16 - 24 \div 4(-4)^{2} + 21 =$

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Problem 30926

Find values of $a$ and $b$ such that $3(2x+15)=ax+b$ has exactly one solution. Options for $a$ and $b$ are given.

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Problem 30927

Evaluate a) $(-8)^{2}$ , b) $-(-8)^{2}$ , and c) $-8^{2}$ . What are the results?

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Problem 30928

Evaluate these expressions for $x = -8$ : a) $x^{2}$ , b) $-x^{2}$ , c) $(-x)^{2}$ .

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Problem 30929

Convert the equation $x - 4y = -4$ to slope-intercept form ( $y = mx + b$ ).

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Problem 30930

Evaluate a) $x^{2}$ , b) $-x^{2}$ , and c) $(-x)^{2}$ for $x = -8$ . What are the results?

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Problem 30931

Evaluate $-9z - 6$ for $z = 3$ . What is the result?

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Problem 30932

Evaluate the piecewise function $f(x)$ where $f(-9)$ and find $f(4)$ .

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Problem 30933

Evaluate $r^{2}-s^{2}$ for $r=-6$ and $s=-7$ . What is $r^{2}-s^{2}=?$

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Problem 30934

Mix how many gallons of $80\%$ antifreeze with 60 gallons of $30\%$ antifreeze for a $70\%$ mixture? Use six steps.

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Problem 30935

In a jar, $30\%$ of the beads are red, and there are 500 more blue beads than red. Find the total number of beads.

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Problem 30936

A cyclist took 3 h to cycle from Town X to Town Y at 12 km/h. If speed increases by 3 km/h, how long will the journey take?

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Problem 30937

Simplify: $6 - 18 \div 6(-5)^{2} + 8$

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Problem 30938

Solve the inequality $-4x > 8$ and express the solution in interval notation.

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Problem 30939

A moving company delivers to two sites. What is the probability of the shortest route using the factorial rule? Calculate $2!$ .

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Problem 30940

Solve the inequality $-5 x \leq 30$ and express the solution in interval notation.

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Problem 30941

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ for given functions $f(x)$ and $g(x)$ in three cases.

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Problem 30942

Evaluate $r^{2}-s^{2}$ for $r=-3$ and $s=-4$ . What is the result?

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Problem 30943

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ for $f(x)=3x+4$ and $g(x)=2x-1$ .

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Problem 30944

Evaluate a) $x^{2}$ , b) $-x^{2}$ , and c) $(-x)^{2}$ for $x = -8$ . Find values for a), b), and c).

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Problem 30945

What interval does the inequality $-3 \leq x < 6$ represent?

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Problem 30946

Given $f(x)=2x-5$ and $g(x)=4x^{2}$ , find: a. $f+g$ , b. $f-g$ , c. $fg$ , d. $\frac{f}{g}$ .

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Problem 30947

Find the following for $f(x)=2x-5$ and $g(x)=4x^{2}$ : a. $f+g$ , b. $f-g$ , c. $fg$ , d. $\frac{f}{g}$ .

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Problem 30948

Find prices $p_{1}$ and $p_{2}$ for Ultra Mini and Big Stack such that $q_{1}=0$ and $q_{2}=0$ using given demand functions.

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Problem 30949

Find expressions equivalent to $(5 g+3 h+4) \cdot 2$ . Choose all that apply: A $(5 g+3 h) \cdot 8$ , B $(5 g+3 h) \cdot 6$ , C None.

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Problem 30950

Solve the inequality $\frac{2 x+5}{4}>\frac{x-2}{3}+2$ and express the solution in interval notation.

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Problem 30951

A motorist traveled from Town A to B, averaging $54 \mathrm{~km/h}$ . If the first $\frac{1}{3}$ was at $45 \mathrm{~km/h}$ and he traveled 480 km after, find the speed for the last $\frac{2}{3}$ .

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Problem 30952

Find the sums, differences, products, and quotients of the following functions:
1. $f(x)=3x+4, g(x)=2x-1$
2. $f(x)=2x-5, g(x)=4x^2$
3. $f(x)=x-4, g(x)=\sqrt{x}$

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Problem 30953

Which expressions equal $x + 2y + x + 2$ ? Select all that apply: A $2(x+y+1)$ B $2x + 4y + 4$ C None.

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Problem 30954

Find expressions equivalent to $2(4 f+2 g)$ . Choose 3: A $8 f+2 g$ , B $2 f(4+2 g)$ , C $8 f+4 g$ , D $4(2 f+g)$ , E $4 f+4 f+4 g$ .

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Problem 30955

Identify expressions equivalent to $4 b$ : A) $b + 2(b + 2b)$ B) $3b + b$ C) $2(2b)$

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Problem 30956

Given matrix $A$ and vectors $u$ and $v$ , find $T(u)$ and $T(v)$ where $T(x) = A x$ .

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Problem 30957

Find the following for $f(x)=x-4$ and $g(x)=\sqrt{x}$ : a. $f+g$ , b. $f-g$ , c. $fg$ , d. $\frac{f}{g}$ .

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Problem 30958

Raul works 2h/day, Mon-Fri, and 8h on Sat at \$2 more/hour. He earns \$142/week. Find his weekday hourly rate.

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Problem 30959

Find $(f \circ g)(x)$ , $(g \circ f)(x)$ , and $(f \circ g)(3)$ for $f(x)=2x$ , $g(x)=x+5$ .

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Problem 30960

Given the matrix $A$ and vectors $u$ and $v$ , find $T(u)$ and $T(v)$ where $T(x)=Ax$ . Simplify your answers.

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Problem 30961

Tanisa and her sister bought 5 pairs of shoes for a total of \$170, including \$15 shipping. Find the cost per pair.

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Problem 30962

Kayla drew a tangent line to $f(x)$ at $(10, f(10))$ with slope 2 and $y$ -intercept -1. Find $f(10)$ .

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Problem 30963

Solve for $x$ in the equation $5 x=9 x-16$ .

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Problem 30964

What dimensions must matrix $A$ have to map $\mathbb{R}^{6}$ to $\mathbb{R}^{7}$ using $T(\mathbf{x})=A \mathbf{x}$ ? A. 6 rows, 7 columns B. 6 rows, 6 columns C. 7 rows, 6 columns D. 7 rows, 7 columns

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Problem 30965

Find all $\mathbf{x}$ in $\mathbb{R}^{4}$ such that $A \mathbf{x} = \mathbf{0}$ for the matrix $A=\begin{bmatrix} 1 & 2 & 7 & -1 \\ 1 & 0 & 3 & -4 \\ 0 & 1 & 2 & 3 \\ -1 & 5 & 7 & 4 \end{bmatrix}$ . Choose A, B, C, or D.

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Problem 30966

Show that multiplication is commutative by proving $q \cdot c = c \cdot q$ for variables 'q' and 'c'.

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Problem 30967

EXN.1.SL.TZO.8 [9 marks] The following diagram shows the graph of $y=-2+\sqrt{x-3}$ for $x \geq 3$ . (a) Describe a sequence of transformations that transforms the graph of $y=\sqrt{x}$ for $x \geq 0$ to the graph of $y=-2+\sqrt{x-3}$ for $x \geq 3$ . [3 marks]
A function $f$ is defined by $f(x)=-2+\sqrt{x-3}$ for $x \geq 3$ . (b) State the range of $f$ . [1 marks] (c) Find an expression for $f^{-1}(x)$ , stating its domain. [5 marks]

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Problem 30968

Solve the inequality for $y$ . $-2-\frac{2}{5} y \geq-18$
Simplify your answer as much as possible.

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Problem 30969

Solve the inequality for $x$ . $\frac{1}{4} x+8 \leq 17$
Simplify your answer as much as possible.

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Problem 30970

Solve the inequality for $w$ . $13-\frac{8}{3} w>19$
Simplify your answer as much as possible.

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Problem 30971

Exponents, Polynomials, and Radicals Converting between scientific notation and standard form in a real-world... Madely
Answer the following. (a) An astronomer's infrared telescope is able to detect radiation with a wavelength of $1.96 \times 10^{-5}$ meters. Write this number in standard notation. (b) The diameter of Pluto at its equator is approximately 2390 kilometers. Write this number in scientific notation. (a) $\square$ meters $\square$ $\times 10^{\circ}$ (b) $\square$ kilometers

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Problem 30972

(16) A $90 \%$ antifreeze solution is to be mixed with a $75 \%$ solution to make 120 liters of a $78 \%$ solution. How many liters of the $90 \%$ and $75 \%$ solutions will be used?

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Problem 30973

Graph the line. $y=2 x-6$ Explanation Check

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Problem 30974

↓ LaunchPad X NC Applications | Rapid identity A ALEKS-Madelyn Swift - Learn × + → C ㄖㄨ www-awy.aleks.com/alekscgi/x/1sl.exe/10_u-lgNslkr7j8P3jH-v-KZJxvdFe9CBW0Gbtpb560CWSdDRHsYrY6zNgB4kR5ernRsf2aQ_rCZFu2YQhBhWKvOX99JQsBduk... ⭑ All Bookmarks O Equations and Inequalities Solving a word problem using a two-step linear Inequality Madelyn V To rent a certain meeting room, a college charges a reservation fee of $14 and an additional fee of$ 6 per hour. The chemistry club wants to spend at most $68 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room? Use t for the number of hours. Write your answer as an inequality solved for t. Español

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Problem 30975

Equations and irequalities Solving a word problem using a two-step unear inequallty Lucy wants to rent a boat and spend less than $\$ 43$ . The boat costs $\$ 8$ per hour, and Lucy has a discount coupon for $\$ 5$ off. What are the possible numbers of hours Lucy could rent the boat?
Use $t$ for the number of hours. Write your answer as an inequality solved for $t$ .

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Problem 30976

1) A rope is cut into three pieces $P, Q$ , and $R$ . The lengths of the pieces are in the ratio $3: 5: 7$ . If the rope is 33 feet 9 inches long, find the lengths of $P, Q$ , and $R$ .

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Problem 30977

Factor the expression completely. $x^{2} y^{5}+x^{4}$
Answer Attempt iout of 2

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Problem 30978

Grades 41
Announcements IXL Learning iReady Question 13 5 pts
Which equation correctly represents the line in slope-intercept form of $y+4=2(x-3) ?$
Enter your answer like this: $y=3 x+7$ (this is just an example, not the answer). $y=$ $\square$ Next

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Problem 30979

Question
Factor the expression completely. $5 x-x^{2}$
Answer Atsmpt sout of 2

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Problem 30980

Examine the following graph of a line. (c) 2017 FlipSwitch. Created using GeoGebra.
Which equation, in point-slope form, correctly represents

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Problem 30981

Before toothpaste was invented, people sometimes used calcium carbonate, $\mathrm{CaCO}_{3}(\mathrm{~s})$ , to clean their teeth. What mass of calcium carbonate can be precipitated by reacting 80.0 mL of a $0.100 \mathrm{~mol} / \mathrm{L}$ solution of sodium carbonate, $\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})$ , with 50.0 mL of a $0.100 \mathrm{~mol} / \mathrm{L}$ solution of calcium chloride, $\mathrm{CaCl}_{2}(\mathrm{aq})$ ?

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Problem 30982

Question Watch Video Show Examples
Bilquis accepted a new job at a company with a contract guaranteeing annual raises. Bilquis will get a raise of $\$ 2000$ every year and had a starting salary of $\$ 35000$ . Make a table of values and then write an equation for $S$ , in terms of $n$ , representing Bilquis' salary after working $n$ years for the company. \begin{tabular}{|c|c|} \hline Number of Years at the Company & Bilquis' Salary (Dollars) \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{tabular}

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Problem 30983

$\begin{array}{l}\text { rem Complete the pattern: } \\ \begin{array}{l} 4 \times \square \\ 4 \times=4 \\ 4 \times \\ 4 \times=400 \\ 4 \times \\ 4 \times=4,000 \\ 4 \times=40,000 \\ 4 \times=400,000 \\ 4\end{array}\end{array}$

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Problem 30984

Score: 0/2 Penalty: none
Question Watch Video Show Examples
Use synthetic division to find the result when $x^{3}-7 x^{2}-28 x+6$ is divided by $x+3$ .
Answer Altempt 1. out of 2 $\square$ Submit Answer

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Problem 30985

5. For each of the following, find the number described by setting up and solving an equation. Use the variable $n$ in each case. (a) When two-thirds of a number is (b) When the sum of a number and 14 is increased by 8 , the result is 20 . divided by 3 , the result is 4 .
USING YOUR MATH
6. Mark is six years older than his brother Sam. The sum of their ages is 30. Let $a$ be Sam's age. Set up and solve an equation using the information given to find the value of $a$ .
7. Alonzo and Mandy are selling raffle tickets at school for a fundraiser. Alonzo sells 5 tickets less than three times what Mandy sells. Together they sell a total of 43 tickets. Let $n$ equal the number of tickets Mandy sells. Use an equation to determine the number of tickets Alonzo sells. Show how you arrived at your answer.
8. Elena, Karla, and Faye are playing a card game where they score points. Karla scores twice the number of points Elena does, and Faye scores 30 points more than Elena does. The sum of their three scores is 114 . Who scores more points, Karla or Faye? Show how you found your answer. (Hint: Let $n$ equal the number of points that Elena scores.) N-Gen Matie 7, Unit 6-Lintar Equations and Inequalities - Lesson 6

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Problem 30986

Write the equation of this line in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Problem 30987

4. $8(-4 b-9)$

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Problem 30988

20. $8-\frac{3}{2} x \geq-13$ $-\frac{3}{2} \times \geq 21$

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Problem 30989

32. Multiply. Write the answer in standard form. $15 i(-1+2 i)$

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Problem 30990

Score I 、Fill in the blanks. (Questions 1 to 5 carry 2 marks each. 10 marks totally.)
1. Let $\vec{u}=(2,5,-3), \vec{v}=(-4,1,9)$ . Then $2 \vec{u}-3 \vec{v}=$ $\qquad$
2. The dot product of $\vec{u}=(1,-2,4)$ and $\vec{v}=(3,1,2)$ is $\qquad$ .
3. The trace of the matrix $A=\left(\begin{array}{ccc}4 & 1 & -2 \\ 2 & -3 & 6 \\ 7 & 3 & 0\end{array}\right)$ is $\qquad$ .
4. A square matrix $A$ is said to be singular if $\qquad$
5. The distance between the noints $\vec{\gamma}-1$

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Problem 30991

Question 1 of 10 Use the grouping method to factor $x^{3}+x^{2}+5 x+5$ A. $(x+1)(x+5)$ B. $\left(x^{2}+1\right)(x+5)$ C. $x(x+5)(x+1)$ D. $(x+1)\left(x^{2}+5\right)$

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Problem 30992

7. Let $A, B$ and $C$ be $n \times n$ matrices. $I$ is an $n \times n$ matrix. The following statement is correct ( ). A. If $A B=A C$ and $A \neq 0$ , then $B=C$ . B. If $A^{2}=A$ , then $A=0$ or $A=I$ . C. If $A^{2}=0$ , then $A=0$ . D. If $A B=B A$ , then $(A+B)^{2}=A^{2}+2 A B+B^{2}$ .

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Problem 30993

13. $x+\frac{1}{2} y=3$

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Problem 30994

8. Let $A, B$ be invertible $3 \times 3$ matrices. The following conclusion is correct ( ). A. $(A+B)^{-1}=A^{-1}+B^{-1}$ B. $(A B)^{-1}=A^{-1} B^{-1}$ C. $(A B)^{t}=B^{t} A^{t}$ D. $|3 A|=3|A|$
9. The cofactor $C_{21}$ of matrix $\left(\begin{array}{ccc}1 & 2 & -3 \\ 5 & 0 & 6 \\ 7 & 1 & -4\end{array}\right)$ is $(\quad)$ . A. 5 B. -1 C. -5 D. 1
10. Let $A$ be an $n \times n$ matrix and $|A|=2$ . Then $\left||A| A^{t}\right|=(\quad)$ . A. $2^{n}$ B. $2^{n-1}$ C. $2^{n+1}$ D. 4 III. Solve the questions. (Questions 11 to 15 carry 10 marks each. 50 marks Score totally.)
11. Let $A=\left[\begin{array}{ccc}3 & 4 & -2 \\ 5 & -1 & 2\end{array}\right], \quad B=\left[\begin{array}{ccc}1 & -2 & 1 \\ 1 & -4 & 3\end{array}\right], \quad C=\left[\begin{array}{cc}5 & 2 \\ -2 & 1\end{array}\right]$ . Compute $2 A-3 B, C A$ .

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Problem 30995

Determine whether the function is even, odd, or neither. $f(x)=5 x^{7}+2 x^{5}$
Which term describes the function? Choose the correct answer below. A. neither B. odd C. even

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Problem 30996

Solve the following inequality algebraically. $3 x^{2}-15 x-112<-4$

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Problem 30997

(30) $6 \log _{0,1}^{2} x+\log _{0,1} x<6$ .

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Problem 30998

Which of the following expressions can be rewritten using the Power Rule? Expression 1: $\log x \cdot \log y$ Expression 2: $\frac{\log x}{\log y}$ Expression 3: $\log x^{y}$ (1 point)
Expression $\square$

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Problem 30999

O Linear Inequalities Solving a decimal word problem using a linear inequality with the variabl... 0/3 JOSHERLY
A phone company offers two monthly charge plans. In Plan A, there is Español no monthly fee, but the customer pays 6 cents per minute of use. In Plan B, the customer pays a monthly fee of $\$ 9$ and then an additional 3 cents per minute of use. For what amounts of monthly phone use will Plan A cost more than Plan B? Use $m$ for the number of minutes of phone use in a month, and solve your inequality for $m$ . $\square$ ㅁ< ロ>ロ $\square \leq \square$ $\square \geq \square$ $\times$ 5 Explanation Check

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Problem 31000

1.2 Calculate $\sum_{\mathrm{m}-2}^{50}(5-2 \mathrm{~m})$

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1 ...307 308 309 310 311 312

Algebra

Problem 30901

Find values of ttt that make the expression 5t−23t−9\frac{5 t-2}{3 t-9}3t−95t−2​ undefined. List them as t=t=t=.

Problem 30902

Find the domain restriction for the function f(x)=1x−3f(x) = \frac{1}{x-3}f(x)=x−31​. Explain your reasoning.

Problem 30903

Graph the solution for the inequality x≤−1x \leq -1x≤−1.

Problem 30904

Problem 30905

Factor the expression 2x3+6x2−8x−242 x^{3}+6 x^{2}-8 x-242x3+6x2−8x−24.

Problem 30906

Problem 30907

What interval does the inequality x≤−1x \leq -1x≤−1 represent?

Problem 30908

A car's tank is 80%80\%80% full. After using 30%30\%30% of that fuel, it needs 19 gallons to fill up. Find the tank's full capacity.

Problem 30909

Simplify the expression: 7x33\sqrt{\frac{7 x^{3}}{3}}37x3​​

Problem 30910

What interval does the inequality x≥5x \geq 5x≥5 represent?

Problem 30911

Write a cost function for a ski resort that charges \$20 plus \$4.25 per hour. Identify the correct variable.

Problem 30912

Choose the correct verbal expression for 4s−44s - 44s−4, where sss is the side length of a square.

Problem 30913

Solve the inequality −5z+6≥−3z−4-5z + 6 \geq -3z - 4−5z+6≥−3z−4 and express the solution in interval notation.

Problem 30914

Find the linear cost function C(x)C(x)C(x) given a fixed cost of \$300 and that producing 60 items costs \$3,300.

Problem 30915

Find the average cost per item given the cost function C(x)=18x+1400C(x)=18x+1400C(x)=18x+1400 for producing 100 items. What is the average cost?

Problem 30916

Decompose the function 1+xcos⁡(x)1+x \cos (x)1+xcos(x) into its even and odd parts.

Problem 30917

Decompose sin⁡2(y)−8y4sin⁡(y)\sin^{2}(y) - 8y^{4}\sin(y)sin2(y)−8y4sin(y) into even and odd functions.

Problem 30918

Find the linear depreciation function for a car priced at \$25,250, expected to be worth \$14,234 in 4 years. Also, estimate its value in 6 years and find the depreciation rate.

Problem 30919

Calculate the specific heat of a liquid given that 47.1 J47.1 \mathrm{~J}47.1 J raises 13.8 g13.8 \mathrm{~g}13.8 g by 1.79∘C1.79^{\circ} \mathrm{C}1.79∘C.

Problem 30920

Solve the inequality x+1≥5x + 1 \geq 5x+1≥5 and express the solution in interval notation.

Problem 30921

Solve the inequality x+1≥5x + 1 \geq 5x+1≥5 and express the solution in interval notation.

Problem 30922

4,860 people visited a fair on Saturday, which was 20%20\%20% more than Friday. Find Friday's visitor count.

Problem 30923

Solve for xxx: 220,000x+475=0\frac{220,000}{x+475}=0x+475220,000​=0

Problem 30924

Five 6th graders raced 3 miles. Johnny was 3rd in 34 min. Other times were -5, -3, +4 min. Find 5th place time.

Problem 30925

Simplify: 16−24÷4(−4)2+21=16 - 24 \div 4(-4)^{2} + 21 = 16−24÷4(−4)2+21=

Problem 30926

Find values of aaa and bbb such that 3(2x+15)=ax+b3(2x+15)=ax+b3(2x+15)=ax+b has exactly one solution. Options for aaa and bbb are given.

Problem 30927

Evaluate a) (−8)2(-8)^{2}(−8)2, b) −(−8)2-(-8)^{2}−(−8)2, and c) −82-8^{2}−82. What are the results?

Problem 30928

Evaluate these expressions for x=−8x = -8x=−8: a) x2x^{2}x2, b) −x2-x^{2}−x2, c) (−x)2(-x)^{2}(−x)2.

Problem 30929

Convert the equation x−4y=−4x - 4y = -4x−4y=−4 to slope-intercept form (y=mx+by = mx + by=mx+b).

Problem 30930

Evaluate a) x2x^{2}x2, b) −x2-x^{2}−x2, and c) (−x)2(-x)^{2}(−x)2 for x=−8x = -8x=−8. What are the results?

Problem 30931

Evaluate −9z−6-9z - 6−9z−6 for z=3z = 3z=3. What is the result?

Problem 30932

Evaluate the piecewise function f(x)f(x)f(x) where f(−9)f(-9)f(−9) and find f(4)f(4)f(4).

Problem 30933

Evaluate r2−s2r^{2}-s^{2}r2−s2 for r=−6r=-6r=−6 and s=−7s=-7s=−7. What is r2−s2=?r^{2}-s^{2}=?r2−s2=?

Problem 30934

Mix how many gallons of 80%80\%80% antifreeze with 60 gallons of 30%30\%30% antifreeze for a 70%70\%70% mixture? Use six steps.

Problem 30935

In a jar, 30%30\%30% of the beads are red, and there are 500 more blue beads than red. Find the total number of beads.

Problem 30936

A cyclist took 3 h to cycle from Town X to Town Y at 12 km/h. If speed increases by 3 km/h, how long will the journey take?

Problem 30937

Simplify: 6−18÷6(−5)2+86 - 18 \div 6(-5)^{2} + 86−18÷6(−5)2+8

Problem 30938

Solve the inequality −4x>8-4x > 8−4x>8 and express the solution in interval notation.

Problem 30939

A moving company delivers to two sites. What is the probability of the shortest route using the factorial rule? Calculate 2!2!2!.

Problem 30940

Solve the inequality −5x≤30-5 x \leq 30−5x≤30 and express the solution in interval notation.

Problem 30941

Find values of $t$ that make the expression $\frac{5 t-2}{3 t-9}$ undefined. List them as $t=$ .

Find the domain restriction for the function $f(x) = \frac{1}{x-3}$ . Explain your reasoning.

Graph the solution for the inequality $x \leq -1$ .

Factor the expression $2 x^{3}+6 x^{2}-8 x-24$ .

What interval does the inequality $x \leq -1$ represent?

A car's tank is $80\%$ full. After using $30\%$ of that fuel, it needs 19 gallons to fill up. Find the tank's full capacity.

Simplify the expression: $\sqrt{\frac{7 x^{3}}{3}}$

What interval does the inequality $x \geq 5$ represent?

Choose the correct verbal expression for $4s - 4$ , where $s$ is the side length of a square.

Solve the inequality $-5z + 6 \geq -3z - 4$ and express the solution in interval notation.

Find the linear cost function $C(x)$ given a fixed cost of \$300 and that producing 60 items costs \$3,300.

Find the average cost per item given the cost function $C(x)=18x+1400$ for producing 100 items. What is the average cost?

Decompose the function $1+x \cos (x)$ into its even and odd parts.

Decompose $\sin^{2}(y) - 8y^{4}\sin(y)$ into even and odd functions.

Calculate the specific heat of a liquid given that $47.1 \mathrm{~J}$ raises $13.8 \mathrm{~g}$ by $1.79^{\circ} \mathrm{C}$ .

Solve the inequality $x + 1 \geq 5$ and express the solution in interval notation.

Solve the inequality $x + 1 \geq 5$ and express the solution in interval notation.

4,860 people visited a fair on Saturday, which was $20\%$ more than Friday. Find Friday's visitor count.

Solve for $x$ : $\frac{220,000}{x+475}=0$

Simplify: $16 - 24 \div 4(-4)^{2} + 21 =$

Find values of $a$ and $b$ such that $3(2x+15)=ax+b$ has exactly one solution. Options for $a$ and $b$ are given.

Evaluate a) $(-8)^{2}$ , b) $-(-8)^{2}$ , and c) $-8^{2}$ . What are the results?

Evaluate these expressions for $x = -8$ : a) $x^{2}$ , b) $-x^{2}$ , c) $(-x)^{2}$ .

Convert the equation $x - 4y = -4$ to slope-intercept form ( $y = mx + b$ ).

Evaluate a) $x^{2}$ , b) $-x^{2}$ , and c) $(-x)^{2}$ for $x = -8$ . What are the results?

Evaluate $-9z - 6$ for $z = 3$ . What is the result?

Evaluate the piecewise function $f(x)$ where $f(-9)$ and find $f(4)$ .

Evaluate $r^{2}-s^{2}$ for $r=-6$ and $s=-7$ . What is $r^{2}-s^{2}=?$

Mix how many gallons of $80\%$ antifreeze with 60 gallons of $30\%$ antifreeze for a $70\%$ mixture? Use six steps.

In a jar, $30\%$ of the beads are red, and there are 500 more blue beads than red. Find the total number of beads.

Simplify: $6 - 18 \div 6(-5)^{2} + 8$

Solve the inequality $-4x > 8$ and express the solution in interval notation.

A moving company delivers to two sites. What is the probability of the shortest route using the factorial rule? Calculate $2!$ .

Solve the inequality $-5 x \leq 30$ and express the solution in interval notation.

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ for given functions $f(x)$ and $g(x)$ in three cases.

Evaluate $r^{2}-s^{2}$ for $r=-3$ and $s=-4$ . What is the result?

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ for $f(x)=3x+4$ and $g(x)=2x-1$ .

Evaluate a) $x^{2}$ , b) $-x^{2}$ , and c) $(-x)^{2}$ for $x = -8$ . Find values for a), b), and c).

What interval does the inequality $-3 \leq x < 6$ represent?

Given $f(x)=2x-5$ and $g(x)=4x^{2}$ , find: a. $f+g$ , b. $f-g$ , c. $fg$ , d. $\frac{f}{g}$ .

Find the following for $f(x)=2x-5$ and $g(x)=4x^{2}$ : a. $f+g$ , b. $f-g$ , c. $fg$ , d. $\frac{f}{g}$ .

Find prices $p_{1}$ and $p_{2}$ for Ultra Mini and Big Stack such that $q_{1}=0$ and $q_{2}=0$ using given demand functions.

Find expressions equivalent to $(5 g+3 h+4) \cdot 2$ . Choose all that apply: A $(5 g+3 h) \cdot 8$ , B $(5 g+3 h) \cdot 6$ , C None.

Solve the inequality $\frac{2 x+5}{4}>\frac{x-2}{3}+2$ and express the solution in interval notation.

A motorist traveled from Town A to B, averaging $54 \mathrm{~km/h}$ . If the first $\frac{1}{3}$ was at $45 \mathrm{~km/h}$ and he traveled 480 km after, find the speed for the last $\frac{2}{3}$ .

Find the sums, differences, products, and quotients of the following functions:
1. $f(x)=3x+4, g(x)=2x-1$
2. $f(x)=2x-5, g(x)=4x^2$
3. $f(x)=x-4, g(x)=\sqrt{x}$

Which expressions equal $x + 2y + x + 2$ ? Select all that apply: A $2(x+y+1)$ B $2x + 4y + 4$ C None.

Find expressions equivalent to $2(4 f+2 g)$ . Choose 3: A $8 f+2 g$ , B $2 f(4+2 g)$ , C $8 f+4 g$ , D $4(2 f+g)$ , E $4 f+4 f+4 g$ .

Identify expressions equivalent to $4 b$ : A) $b + 2(b + 2b)$ B) $3b + b$ C) $2(2b)$

Given matrix $A$ and vectors $u$ and $v$ , find $T(u)$ and $T(v)$ where $T(x) = A x$ .

Find the following for $f(x)=x-4$ and $g(x)=\sqrt{x}$ : a. $f+g$ , b. $f-g$ , c. $fg$ , d. $\frac{f}{g}$ .

Find $(f \circ g)(x)$ , $(g \circ f)(x)$ , and $(f \circ g)(3)$ for $f(x)=2x$ , $g(x)=x+5$ .

Given the matrix $A$ and vectors $u$ and $v$ , find $T(u)$ and $T(v)$ where $T(x)=Ax$ . Simplify your answers.

Kayla drew a tangent line to $f(x)$ at $(10, f(10))$ with slope 2 and $y$ -intercept -1. Find $f(10)$ .

Solve for $x$ in the equation $5 x=9 x-16$ .

What dimensions must matrix $A$ have to map $\mathbb{R}^{6}$ to $\mathbb{R}^{7}$ using $T(\mathbf{x})=A \mathbf{x}$ ? A. 6 rows, 7 columns B. 6 rows, 6 columns C. 7 rows, 6 columns D. 7 rows, 7 columns

Show that multiplication is commutative by proving $q \cdot c = c \cdot q$ for variables 'q' and 'c'.

Solve the inequality for $y$ . $-2-\frac{2}{5} y \geq-18$
Simplify your answer as much as possible.

Solve the inequality for $x$ . $\frac{1}{4} x+8 \leq 17$
Simplify your answer as much as possible.

Solve the inequality for $w$ . $13-\frac{8}{3} w>19$
Simplify your answer as much as possible.

(16) A $90 \%$ antifreeze solution is to be mixed with a $75 \%$ solution to make 120 liters of a $78 \%$ solution. How many liters of the $90 \%$ and $75 \%$ solutions will be used?

Graph the line. $y=2 x-6$ Explanation Check