Linearity

Problem 201

The percent of births to teenage mothers that are out-of-wedlock can be approximated by a linear function of the number of years after 1954. The percent was 19 in 1974 and 76 in 2010. Complete parts (a) through (c). (a) What is the slope of the line joining the points $(20,19)$ and $(56,76)$ ?
The slope of the line is $\square$ . (Simplify your answer. Round to two decimal places as needed.)

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Problem 202

The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 375 square meters, find the dimensions.

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Problem 203

Solve the equation. $5.62 t=1.38 t-8.48$
The solution is $t=$ $\square$ $\square$ . (Simplify your answer.)

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Problem 204

In one town the annual consumption, $b$ , of beef (in pounds per person) can be estimated by $b=32-0.5$ , where $t$ is the number of years since 1975. What is the slope of the graph of this function? Write a sentence interpreting this value. A. The slope is 32 which means that the average consumption of beef in this town is decreasing by 32 pounds per person per year. B. The slope is -0.5 which means that the average consumption of beef in this town is decreasing by 0.5 pounds per person per year. C. The slope is 32 which means that the average consumption of beef in this town is increasing by 32 pounds per person per year. D. The slope is -0.5 which means that the average consumption of beef in this town is increasing by 0.5 pounds per person per year.

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Problem 205

Apply elimination and back substitution to solve: $\begin{array}{r} 2 x-2 y-1 z=3 \\ -4 x+2 y+3 z=-5 \\ 2 x+2 y-4 z=2 \end{array}$
The three pivots are: $\square$ $\square$ $\square$ . The three multipliers are: $\ell_{21}=$ $\square$ , $\ell_{31}=$ $\square$ , $\ell_{32}=$ $\square$ . The solution is $(x, y, z)=($ $\square$ , $\square$ , $\square$ ).

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Problem 206

$\frac{-x+10}{3}=\frac{-3 x+18}{5}$

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Problem 207

$\frac{x}{2}+4=-36$

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Problem 208

Two linear functions, $y_{1}$ and $y_{2}$ are graphed in a viewing window with the point of intersection of the graphs given in the display at the bottom. Use the intersection method to solve the equation $\mathrm{y}_{1}=\mathrm{y}_{2}$ . A. -1 B. $-\frac{5}{2}$ C. 1 D. -2

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Problem 209

ons list Determine the slope, if it exists, of the graph of the linear equation. $y=2-x$
Select the correct choice below and fill in any answer boxes within your choice. 11 A. The slope is $\square$ (Type an integer or a decimal.)

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Problem 210

Solve the compound inequality: $6 \leq 2 x-8<16$ .
Enter the exact answer in interval notation.
To enter $\infty$ , type infinity. To enter $\cup$ , type $U$ .

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Problem 211

Solve for $y$ . $\begin{array}{l} \frac{6}{11}=\frac{y}{3} \\ y= \end{array}$ $\square$

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Problem 212

6 erasers cost $\$ 6.60$ . Which equation would help determine the cost of 3 erasers? Choose 1 answer: (A) $\frac{3}{x}=\frac{\$ 6.60}{6}$ (B) $\frac{3}{6}=\frac{\$ 6.60}{x}$ (C) $\frac{x}{3}=\frac{6}{\$ 6.60}$ (D) $\frac{x}{3}=\frac{\$ 6.60}{6}$ (E) None of the above

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Problem 213

4 markers cost $\$ 7.04$ .
Which equation would help determine the cost of 7 markers? Choose 1 answer: (A) $\frac{4}{7}=\frac{\$ 7.04}{x}$ (B) $\frac{x}{7}=\frac{4}{\$ 7.04}$ (C) $\frac{7}{x}=\frac{\$ 7.04}{4}$ (D) $\frac{4}{7}=\frac{x}{\$ 7.04}$ (E) None of the above

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Problem 214

The following table shows a proportional relationship between $w$ and $z$ . \begin{tabular}{ll} $w$ & $z$ \\ \hline 18 & 2 \\ 45 & 5 \\ 81 & 9 \end{tabular}
Write an equation to describe the relationship between $w$ and $z$ . Equations may include exact decimals, proper fractions, or improper fractions. Please do NOT round or use mixed numbers. $\square$

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Problem 215

A total of 560 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold? adult tickets

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Problem 216

Alexandra paid $\$ 7$ to park her car for 3 hours at the parking garage. The garage charges a constant hourly parking rate.
Write an equation that shows the relationship between $p$ , the number of hours parked, and $c$ , the cost in dollars. Do NOT use a mixed number. $\square$

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Problem 217

Justin runs at a constant rate, traveling 17 km in 2 hours. Write an equation that shows the relationship between $d$ , the distance he runs in kilometers, and $h$ , the time he spends running in hours. Do NOT ise a mixed number. $\square$

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Problem 218

Wangari plants trees at a constant rate of 12 trees every 3 hours. Write an equation that relates $p$ , the number of trees Wangari plants, and $h$ , the time she spends planting them in hours. $\square$

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Problem 219

Solve for $v$ . $\frac{v}{6}=\frac{4}{8}$
Simplify your answer as much as possible. $v=$

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Problem 220

Alice can wash and wax her car in 3 hour and 30 minutes. If Bernice helped her, Alice could do the job in 2 hours. How long would it take Bernice working alone?

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Problem 221

1. The equation of a demand function is given by $Q=85-5 P$ where $Q$ is the number of buses demand to travel to Monze daily. $P$ is the price per Bus fare in K. a) What is the change in demand $Q$ when the $P$ increases by 1 unit? b) What is the demand when $P=0$ ? c) What is the price P when $Q=0$ ?

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Problem 222

Tell whether the order pair is a solution to the given equation
38. $y=-3 x ;(4,-13)$
39. $y=3 x-2 ;(-1,-5)$

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Problem 223

3. Given the supply function, $P=500+2 Q$ , where $P$ is the price of a bottle of a perfume, $Q$ is the number of litres supplied. a) What is the value of $Q$ when $P=K 750$ ? b) What is the value of P when $Q=35$ ?

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Problem 224

$\text{Find the slope and } y\text{-intercept of the equation } y = \frac{3}{5} x - 7.$

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Problem 225

6. At the corner's pasta restaurant it is expected that 350 dishes will be sold at a price of K200 each. For each k 4 reduction in price, 20 more dishes will be sold. The restaurant is willing to supply 325 pasta dishes at K100 each, and 475 dishes at K220 each. a) Find the linear demand equation of the pasta dish. b) Find the linear supply equation of the pasta dish. c) Find the equilibrium price and the quantity of the pasta dish.

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Problem 226

Gustaf wants to earn $\$ 3,000$ simple interest on a $\$ 9,000$ investment with an annual simple interest rate of $2.5 \%$ . How long should Gustaf plan to invest his money?

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Problem 227

1 point A $\$ 27,000$ car has a resale value of $\$ 18,000$ five years after it was purchased. Assuming the value of this car depreciates linearly, estimate the value of the car 8 years after it was purchased. Enter your answer rounded to the nearest whole number. Do not enter the $\$$ symbol. Type your answer...
Previous

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Problem 228

6) Elijah went to the store and bought a pair of shoes for $\$ 44$ and seven pairs of pants. He spent $\$ 96$ in total. A) Write an equation to represent this scenario.
Equation: $\qquad$ B) How much did each t-shirt cost? inswer: $\qquad$

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Problem 229

$\frac{2}{5}(x-2)=x+4$

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Problem 230

Charlotte is driving at $71.5 \mathrm{mi} / \mathrm{h}$ and receives a text message. She looks down at her phone and takes her eyes off the road for 3.92 s . How far has Charlotte traveled in feet during this time? distance: $\square$ ft

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Problem 231

A one-year membership to a gym costs $\$ 725$ . The registration fee is $\$ 125, * 1$ point and the remaining amount is paid monthly. Create an equation for the situation. Solve for the variable.
Your answer

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Problem 232

(3) Rajah menunjukklan kadar Sewaan bagikal di Sebuah taman. Dewasa: Rm10/jam kanak-kahak (umner 12 tahn ke bawah):Rm7//gmm Diskaun km2 Gasi cetiap karak"" puda har bekerya.
En. Rahman membawa keluargamya untule berbasikal pada han vabu. Rilongan ahli Keluarganye Lalah 7 orores tidak teumosk divinga. Diamembayar Rm 130 untuk riam untule Semia ahli Keluorganya. Nyatakan blogan arak En. Rahmenan yof berumur bowch 12 tahurs. $(4 m)$

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Problem 233

Solve the following system of equations. $\begin{array}{l} -2 x-3 y=15 \\ -3 x-4 y=19 \end{array}$ $x=$ $\square$ $\square$ $y=$ $\square$

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Problem 234

$\frac{x}{3}+10=15$

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Problem 235

11. The stylists in a hair salon cut hair for women and men. - The salon books at least four women's appointments for every man's appointment. - Usually there are 90 or more appointments, in total, during a week. - The salon is trying to reduce the number of hours the stylists work. - A woman's cut takes about 75 min , and a man's cut takes about 30 min . What combination of women's and men's appointments would minimize the number of hours the stylists work? How many hours would this be?

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Problem 236

Given that $\angle ADB = (6x + 10)^\circ$ and $\angle BDC = 4x^\circ$ , and knowing that these angles are complementary, find the measures of $\angle ADB$ and $\angle BDC$ .

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Problem 237

$3x + 4y = 8$

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Problem 238

Recall the Formula: To find the equation of a tangent line to a function $f$ at a given point $\left(x_{1}, y_{1}\right)$ , calculate the tangent slope $m$ , then plug $x_{1}, y_{1}$ , and $m$ into the point-slope form of the equation of a line.
Give the point-slope form of the equation of a line.

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Problem 239

What are $m$ and $b$ in the linear equation, using the common meanings of $m$ and $b$ ? $1+4 x+6-x=y$ (A) $m$ is $3, b$ is 7 (B) $m$ is $4, b$ is 6 (C) $m$ is $6, b$ is 4 (D) $m$ is $7, b$ is 3

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Problem 240

If: $\begin{array}{l} 2 x+y+z=52 \\ x+2 y+z=49 \\ 2 x+2 z=50 \end{array}$
Fhen solve $2 x+3 y+z=$

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Problem 241

A number increased by 24 is 89 . Find the number.

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Problem 242

How old is Tyrone if twice his age increased by 17 is 53 ?

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Problem 243

This question: 10 point(s) possible Submit quiz Graph the function. $f(x)=\frac{1}{2} x+8$
Use the graphing tool on the right to graph the function. $\square$

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Problem 244

tu point(S) possible Submit quiz Suppose the sales of a particular brand of appliance satisfy the relationship $S=160 x+4,800$ , where $S$ represents the number of sales in year $x$ , with $x=0$ corresponding to 1982. Find the number of sales in 1994. A. 6,560 B. 13,280 C. 13,440 D. 6,720

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Problem 245

3. A table and 8 chairs weigh 235.68 lb together. If the table weighs 157.84 lb , what is the weight of one chair in pounds?

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Problem 246

Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
Let $y$ represent the area (in square meters) left to paint after $x$ hours.
Complete the equation for the relationship between the area and number of hours. $y=$ $\square$
Show Calculator $\square$
Related content
Constructing linear equations from context

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Problem 247

A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets, they were still at a net loss of $\$ 800$ (due to the production costs). They sold each ticket for $\$ 70$ .
Let $y$ represent the net profit (in dollars) when they have sold $x$ tickets. Complete the equation for the relationship between the net profit and number of tickets sold. $y=\square$

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Problem 248

Linear equations word probiems
Mr. Mole left his burrow and started digging his way down. $A$ represents Mr. Mole's altitude relative to the ground (in meters) after $t$ minutes. $A=-2.3 t-7$
How fast did Mr. Mole descend? $\qquad$ meters per minute
Related content
Linear equation word problems Report a proble

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Problem 249

Shryia read a book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 out of the total 480 pages left to read.
Let $y$ represent the number of pages left to read after $x$ hours.
Complete the equation for the relationship between the number of pages left and number of hours. $y=$ $\square$
Show Calculator Related content

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Problem 250

(20) Shane used 25 gallons of gas traveling 350 miles. How much gas will he use in 462 miles?

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Problem 251

Suraj took a slice of pizza from the freezer and put it in the oven. The oven heated the pizza at a rate of $7.5^{\circ}$ Celsius per minute, and it reached the desired temperature of $80^{\circ}$ Celsius after 12 minutes.
Graph the relationship between the pizza's temperature (in degrees Celsius) and time (in minutes).

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Problem 252

\begin{tabular}{|c|c|c|c|c|c|} \hline teen & 0 & 2 & 4 & 5 & 7 \\ \hline & & & & & \\ \hline (in) & 150 & 190 & 230 & 250 & 290 \\ \hline \end{tabular}

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Problem 253

\begin{align} 2y + 2 &= 5 \\ \end{align}

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Problem 254

Find the solution set. $\frac{m}{3}-3>\frac{4}{3}-\frac{m}{4}$
The solution set is $m>\frac{52}{7}$ . (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in interval notation.)

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Problem 255

$6(x+2)-7 x \geq 8$

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Problem 256

$\begin{array}{l}0.8 x-2.1 y=10.8 \\ 1.6 x-0.7 y=7.6\end{array}$

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Problem 257

$\begin{array}{l}2 y+x=6 \\ 5 y-4 x=2\end{array}$

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Problem 258

7. Aline contains the point $(2,5)$ . As $x$ decreases by 3 units, y decreases by 1 unit. Find an equation for the line.
8. The quantity demanded of a certain brand of DVD player is 3000 per week when the unit price is K485. For each decrease in unit price of K20 below K485, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is K300 or lower. But at a unit price of K525, they are willing to make available 2500 units in the market. The supply equation is also known to be linear. a) Find the demand equation. b) Find the supply equation.

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Problem 259

9. The supply and demand equations of a good are given by: $P=Q s+8 ; \quad P=-3 Q d+80$ a) Find the price and quantity at equilibrium. b) At a price of $P=5$ find the excess Demand. c) At a price of $P=50$ find the Surplus. d)
10. The supply and demand equations of a good are given by: $P=\frac{1}{2} Q s+25 ; \quad P=-2 Q d+50$ a) Find the price and quantity at equilibrium. b) At a price of $P=40$ find the excess Supply.
11. Suppose that the number $Q$ of bushels of apples a farmer is willing to sell is given by $Q=100 p-25$
Where $p$ is the price, in Kwacha, per bushel of apples. The number $Q$ of bushels of apples a grocer is willing to purchase is given by $Q=-150 p+655$
Where $p$ is the price per bushel of apples. Find the equilibrium price.

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Problem 260

Dianelys was offered a job after college earning a salary of $\$ 60,000$ . She will get a raise of $\$ 2,000$ after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.
Answer Attempt 1 out of 2
The independent variable, $x$ , represents the and the dependent variable is the $\qquad$ , because the depends on the $\square$ $\square$ ・.
A function relating these variables is $B(x)=$ $\square$ .
So $B(2)=$ $\square$ , meaning 2 $\square$

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Problem 261

2.) $3=5 x-\frac{2-x}{2}$

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Problem 262

56. What is the pattern rule?
Write an expression to represent the pattern. \begin{tabular}{|c|c|} \hline Input & Output \\ \hline 1 & 2 \\ \hline 2 & 5 \\ \hline 3 & 8 \\ \hline 4 & 11 \\ \hline \end{tabular}

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Problem 263

3. Ejah works in a diamond mine. When he works the late shift, $\$ 2 / \mathrm{h}$ is added to his regular hourly wage. Last week, he worked the late shift for a total o 40 h and made \$960. Write and solve and equation to determine Elijah's reguicer hourly wage.

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Problem 264

Entscheiden Sie durch Ankreuzen des zugehörigen Kästchens, welche Aussagen richtig und welche falsch sind. Begründen Sie Ihre Entscheidung bei allen Aussagen in Stichworten. \begin{tabular}{|c|c|c|c|c|c|} \hline & \multicolumn{2}{|l|}{ Die Gerade(n) der Funktionsgraphen zu... } & Richtig & Falsch & Begründung \\ \hline a) & $f(x)=\frac{1}{2} x-2$ & $a$ und $b$ sind parallel & $\square$ & $\square$ & \\ \hline b) & $f(x)=-0,5 x-1$ & c verläuft durch den & & & \\ \hline c) & $f(x)=0,3 x+5$ & Ursprung & $\square$ & $\square$ & \\ \hline d) & \begin{tabular}{l} $f(x)=\frac{1}{3} x$ \end{tabular} & \begin{tabular}{l} $c$ und $g$ haben dieselbe \\ Steigung \end{tabular} & $\square$ & $\square$ & \\ \hline e) & \begin{tabular}{l} $f(x)=\frac{1}{2} x+3$ \end{tabular} & \begin{tabular}{l} d verläuft steiler als \\ die Gerade e \end{tabular} & $\square$ & $\square$ & \\ \hline f) & $f(x)=5 x+1$ & fund $g$ schneiden sich & & & \\ \hline g) & \begin{tabular}{l} $f(x)=\frac{1}{3} x+1$ \end{tabular} & auf der $y$ -Achse & $\square$ & $\square$ & \\ \hline \end{tabular}

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Problem 265

$-5=6 d-7 d+4$

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Problem 266

10. $11-\frac{1}{2} y=3+6 x$

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Problem 267

Question Watch Video Show Examples
Under her cell phone plan, Arianna pays a flat cost of $\$ 54.50$ per month and $\$ 5$ per gigabyte. She wants to keep her bill under $\$ 75$ per month. Write and solve an inequality which can be used to determine $g$ , the number of gigabytes Arianna can use while staying within her budget.

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Problem 268

$\frac{m}{4} \rightarrow=-3$

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Problem 269

Question 7 of 15, Step 1 of 1 6/15 Correct 3
Solve the following linear equation using equivalent equations to isolate the variable. Express your answer as an integer, as a simplified fraction, or as a decimal number rounded to two places. $-12-2=4 u-6 u$ Answer Keypad

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Problem 270

Use the graph to derive the equation $y=m x$ for a line through the origin. Simplify the numerical coefficient, if needed. (1 point) $y=3 x$ $y=x$ $y=\frac{3}{3} x$ $y=8 x$

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Problem 271

Save \& Exit Certify Lesson: 2.3b Solving Linear Equations Usin... HAYLEE MARTINSON 7/15 Question 8 of 15, Step 1 of 1 Correct 3
Solve the following linear equation using equivalent equations to isolate the variable. Express your answer as an integer, as a simplified fraction, or as a decimal number rounded to two places. $-5 y=\frac{-2}{7}$ Keypad Answer How to enter your answer (opens in new window) Keyboard Shortcuts

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Problem 272

What is the equation of the line, in standard form, that is parallel to the given line and passes through the point $(4,2)$ ? $3 x-y=2$ $3 x-y=10$ $3 x-y=-1$ $\frac{1}{3} x-y=\frac{2}{3}$

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Problem 273

Skill 2: Solving linear equations involving brackets Solve the following equations Show correct working out a. $3(x+1)=18$

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Problem 274

A table of values is shown. \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -8 & -4 & 2 & 5 \\ \hline $y$ & 8 & $\frac{11}{2}$ & $\frac{7}{4}$ & $-\frac{1}{8}$ \\ \hline \end{tabular}
Which equation models the relationship in the table? $y-8=-\frac{5}{8}(x+8)$ $y+8=-\frac{8}{5}(x-8)$ $y-8=-\frac{8}{5}(x+8)$ $y+8=-\frac{5}{8}(x-8)$

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Problem 275

$x+5=12 \quad 2 x=-48$

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Problem 276

Orly uses 3 cups of raisins for every 10 cups of trail mix she makes. How many cups of trail mix will she make if she uses 12 cups of raisins? 10 cups $2 \frac{1}{2}$ cups 40 cups $3 \frac{3}{5}$ cups

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Problem 277

Save \& Exit certily Lesson: b., the Cartestan coorimate syst... $0 / 16$ Question 1 of 4,5 Step 1 of 2 Correct
Conblef the following equmition: $3 x-4 y=7$ stap 1 of 2: the given ordered pair, $(-1,-3)$ , satisfies the given equation. Answer YES NO

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Problem 278

$5 s+16=s+20$

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Problem 279

Graph the solution set, and write the solution set in interval notation. $7 \leq 5 b-1<39$

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Problem 280

8. $\frac{(x-5)}{3}+4 x=7$

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Problem 281

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more than 2 times the width, what is the largest possible length? Write an equation and solve. $(2 w+3) 4=60 ; 15$

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Problem 282

$\frac{3+x}{-7}=0$

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Problem 283

nomework1.4: Prodiem 4 (1 point)
Write equations for each of the following three lines. a. The line given by the table of values \begin{tabular}{|l|l|l|} \hline $x=$ & 1 & 1 \\ \hline $y=$ & 2 & 4 \\ \hline \end{tabular} ? $\square$ b. The line given by the graph ? $\square$ c. The line for which the $y$ coordinate of every point is -3 . ? $\square$
Note: In order to get credit for this problem all answers must be correct.

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Problem 284

If the sum of three consecutive even integers is 90, what is the smallest of the three integers?

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Problem 285

Solve for $p$ . $3.5-p=18$ $-14.5$ $-21.5$ 21.5 14.5

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Problem 286

Explaining Linear Functions
Given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

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Problem 287

What value of $y$ is a solution to ais a $61=7 y-16$ $y=11$ $y=12$

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Problem 288

What is the equation of the line that passes through the point $(5,3)$ and has a slope of $\frac{3}{5}$ ?

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Problem 289

The table represents a linear function. The rate of change between the points $(-5,10)$ and $(-4,5)$ is -5 . What is the rate of change between the points $(-3,0)$ and $(-2,-5)$ ? \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-5 & 10 \\ \hline-4 & 5 \\ \hline-3 & 0 \\ \hline-2 & -5 \\ \hline \hline \end{tabular} $-5$ $-\frac{1}{5}$ $\frac{1}{5}$ 5 Mark this and return Save and Exit Next Submit

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Problem 290

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & -9 \\ \hline 2 & -13 \\ \hline 3 & -17 \\ \hline 4 & -21 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

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Problem 291

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & -3 \\ \hline 2 & -2 \\ \hline 3 & -1 \\ \hline 4 & 0 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

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Problem 292

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-1 & -5 \\ \hline 1 & -3 \\ \hline 3 & -1 \\ \hline 5 & 1 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

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Problem 293

Directions: Solve each system of equations by graphing. Clearly identify your solution.
1. $y=\frac{1}{4} x+1$ $y=-x-9$
3. $3 x+7 y=-63$ $x-y=-1$
5. $-6 y=36-x$ $4 x-3 y=-3$
4. $3 x-2 y=10$ $x=2$
6. $-12 x=30 y+60$ $2 x+5 y=20$

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Problem 294

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-3 & 17 \\ \hline 1 & -3 \\ \hline 5 & -23 \\ \hline 9 & -43 \\ \hline \end{tabular}
Answer $\square$ Submit Answer Forixey Policyl Permes of Sentice

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Problem 295

1) Find the slope of the line that passes through the following two points: $(-1,3) \quad 3(5,5)$

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Problem 296

PROBLEM I Solving a System of Equations by Graphing
What is the solution of the system? Use a graph. $y=x+2$ $y=3 x-2$
1. Graph both equations on Desmos.
2. How many solutions does this system have? (Choose one) a. One solution b. Infinitely many solutions c. No solution
3. If a solution exists, draw an arrow to the solution on your graph.
Draw graphs here: $c f b$

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Problem 297

Question Watch Video Show Examples
Moussa is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee is $\$ 25$ and the one-time joining fee is $\$ 100$ . Write an equation for $C$ , in terms of $t$ , representing the total cost of the gym membership over $t$ months.
Answer Attempt 1 out of 2 $C=$ $\square$ Submit Answer

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Problem 298

Solve the system using elimination. $\begin{aligned} 4 x+14 y & =32 \\ x-14 y & =-27 \end{aligned}$

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Problem 299

Your school's talent show will feature 12 solo acts and 2 ensemble acts. The show will last 92 minutes. The 6 solo performers judged best will give a repeat performance at a second 56 minute show, which will also feature the 2 ensemble acts. Each solo act lasts $x$ minutes, and each ensemble act lasts y minutes. Use this information to answer parts (a) and (b). b) Solve the system from part (a).

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Problem 300

1. Identify the slope and $y$ -intercept in the linear equation $y=3 x-13$ $Y=M x+b \quad M=3 \quad b=-13$

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1 2 3 4 5 6 ...76

Linearity

Problem 201

Problem 202

The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 375 square meters, find the dimensions.

Problem 203

Solve the equation. 5.62t=1.38t−8.485.62 t=1.38 t-8.485.62t=1.38t−8.48The solution is t=t=t= □\square□ □\square□. (Simplify your answer.)

Problem 204

Problem 205

Problem 206

−x+103=−3x+185\frac{-x+10}{3}=\frac{-3 x+18}{5}3−x+10​=5−3x+18​

Problem 207

x2+4=−36\frac{x}{2}+4=-362x​+4=−36

Problem 208

Problem 209

ons list Determine the slope, if it exists, of the graph of the linear equation. y=2−xy=2-xy=2−xSelect the correct choice below and fill in any answer boxes within your choice. 11 A. The slope is □\square□ (Type an integer or a decimal.)

Problem 210

Solve the compound inequality: 6≤2x−8<166 \leq 2 x-8<166≤2x−8<16.Enter the exact answer in interval notation.To enter ∞\infty∞, type infinity. To enter ∪\cup∪, type UUU.

Problem 211

Solve for yyy. 611=y3y=\begin{array}{l} \frac{6}{11}=\frac{y}{3} \\ y= \end{array}116​=3y​y=​ □\square□

Problem 212

Problem 213

Problem 214

Problem 215

A total of 560 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold? adult tickets

Problem 216

Alexandra paid $7\$ 7$7 to park her car for 3 hours at the parking garage. The garage charges a constant hourly parking rate.Write an equation that shows the relationship between ppp, the number of hours parked, and ccc, the cost in dollars. Do NOT use a mixed number. □\square□

Problem 217

Justin runs at a constant rate, traveling 17 km in 2 hours. Write an equation that shows the relationship between ddd, the distance he runs in kilometers, and hhh, the time he spends running in hours. Do NOT ise a mixed number. □\square□

Problem 218

Wangari plants trees at a constant rate of 12 trees every 3 hours. Write an equation that relates ppp, the number of trees Wangari plants, and hhh, the time she spends planting them in hours. □\square□

Problem 219

Solve for vvv. v6=48\frac{v}{6}=\frac{4}{8}6v​=84​Simplify your answer as much as possible. v=v=v=

Problem 220

Alice can wash and wax her car in 3 hour and 30 minutes. If Bernice helped her, Alice could do the job in 2 hours. How long would it take Bernice working alone?

Problem 221

Problem 222

Tell whether the order pair is a solution to the given equation38. y=−3x;(4,−13)y=-3 x ;(4,-13)y=−3x;(4,−13)39. y=3x−2;(−1,−5)y=3 x-2 ;(-1,-5)y=3x−2;(−1,−5)

Problem 223

3. Given the supply function, P=500+2QP=500+2 QP=500+2Q, where PPP is the price of a bottle of a perfume, QQQ is the number of litres supplied. a) What is the value of QQQ when P=K750P=K 750P=K750 ? b) What is the value of P when Q=35Q=35Q=35 ?

Problem 224

Find the slope and y-intercept of the equation y=35x−7.\text{Find the slope and } y\text{-intercept of the equation } y = \frac{3}{5} x - 7.Find the slope and y-intercept of the equation y=53​x−7.

Problem 225

Problem 226

Gustaf wants to earn $3,000\$ 3,000$3,000 simple interest on a $9,000\$ 9,000$9,000 investment with an annual simple interest rate of 2.5%2.5 \%2.5%. How long should Gustaf plan to invest his money?

Problem 227

Problem 228

6) Elijah went to the store and bought a pair of shoes for $44\$ 44$44 and seven pairs of pants. He spent $96\$ 96$96 in total. A) Write an equation to represent this scenario.Equation: \qquad B) How much did each t-shirt cost? inswer: \qquad

Problem 229

25(x−2)=x+4\frac{2}{5}(x-2)=x+452​(x−2)=x+4

Problem 230

Charlotte is driving at 71.5mi/h71.5 \mathrm{mi} / \mathrm{h}71.5mi/h and receives a text message. She looks down at her phone and takes her eyes off the road for 3.92 s . How far has Charlotte traveled in feet during this time? distance: □\square□ ft

Problem 231

A one-year membership to a gym costs $725\$ 725$725. The registration fee is $125,∗1\$ 125, * 1$125,∗1 point and the remaining amount is paid monthly. Create an equation for the situation. Solve for the variable.Your answer

Problem 232

Problem 233

Solve the following system of equations. −2x−3y=15−3x−4y=19\begin{array}{l} -2 x-3 y=15 \\ -3 x-4 y=19 \end{array}−2x−3y=15−3x−4y=19​ x=x=x= □\square□ □\square□ y=y=y= □\square□

Problem 234

x3+10=15\frac{x}{3}+10=153x​+10=15

Problem 235

Problem 236

Given that ∠ADB=(6x+10)∘\angle ADB = (6x + 10)^\circ∠ADB=(6x+10)∘ and ∠BDC=4x∘\angle BDC = 4x^\circ∠BDC=4x∘, and knowing that these angles are complementary, find the measures of ∠ADB\angle ADB∠ADB and ∠BDC\angle BDC∠BDC.

Problem 237

3x+4y=83x + 4y = 83x+4y=8

Problem 238

Problem 239

What are mmm and bbb in the linear equation, using the common meanings of mmm and bbb ? 1+4x+6−x=y1+4 x+6-x=y1+4x+6−x=y (A) mmm is 3,b3, b3,b is 7 (B) mmm is 4,b4, b4,b is 6 (C) mmm is 6,b6, b6,b is 4 (D) mmm is 7,b7, b7,b is 3

Problem 240

If: 2x+y+z=52x+2y+z=492x+2z=50\begin{array}{l} 2 x+y+z=52 \\ x+2 y+z=49 \\ 2 x+2 z=50 \end{array}2x+y+z=52x+2y+z=492x+2z=50​Fhen solve 2x+3y+z=2 x+3 y+z=2x+3y+z=

Problem 241

A number increased by 24 is 89 . Find the number.

Problem 242

How old is Tyrone if twice his age increased by 17 is 53 ?

Problem 243

This question: 10 point(s) possible Submit quiz Graph the function. f(x)=12x+8f(x)=\frac{1}{2} x+8f(x)=21​x+8Use the graphing tool on the right to graph the function. □\square□

Problem 244

Problem 245

3. A table and 8 chairs weigh 235.68 lb together. If the table weighs 157.84 lb , what is the weight of one chair in pounds?

Problem 246

Problem 247

Problem 248

Solve the equation. $5.62 t=1.38 t-8.48$
The solution is $t=$ $\square$ $\square$ . (Simplify your answer.)

$\frac{-x+10}{3}=\frac{-3 x+18}{5}$

$\frac{x}{2}+4=-36$

ons list Determine the slope, if it exists, of the graph of the linear equation. $y=2-x$
Select the correct choice below and fill in any answer boxes within your choice. 11 A. The slope is $\square$ (Type an integer or a decimal.)

Solve the compound inequality: $6 \leq 2 x-8<16$ .
Enter the exact answer in interval notation.
To enter $\infty$ , type infinity. To enter $\cup$ , type $U$ .

Solve for $y$ . $\begin{array}{l} \frac{6}{11}=\frac{y}{3} \\ y= \end{array}$ $\square$

Alexandra paid $\$ 7$ to park her car for 3 hours at the parking garage. The garage charges a constant hourly parking rate.
Write an equation that shows the relationship between $p$ , the number of hours parked, and $c$ , the cost in dollars. Do NOT use a mixed number. $\square$

Justin runs at a constant rate, traveling 17 km in 2 hours. Write an equation that shows the relationship between $d$ , the distance he runs in kilometers, and $h$ , the time he spends running in hours. Do NOT ise a mixed number. $\square$

Wangari plants trees at a constant rate of 12 trees every 3 hours. Write an equation that relates $p$ , the number of trees Wangari plants, and $h$ , the time she spends planting them in hours. $\square$

Solve for $v$ . $\frac{v}{6}=\frac{4}{8}$
Simplify your answer as much as possible. $v=$

Tell whether the order pair is a solution to the given equation
38. $y=-3 x ;(4,-13)$
39. $y=3 x-2 ;(-1,-5)$

3. Given the supply function, $P=500+2 Q$ , where $P$ is the price of a bottle of a perfume, $Q$ is the number of litres supplied. a) What is the value of $Q$ when $P=K 750$ ? b) What is the value of P when $Q=35$ ?

$\text{Find the slope and } y\text{-intercept of the equation } y = \frac{3}{5} x - 7.$

Gustaf wants to earn $\$ 3,000$ simple interest on a $\$ 9,000$ investment with an annual simple interest rate of $2.5 \%$ . How long should Gustaf plan to invest his money?

6) Elijah went to the store and bought a pair of shoes for $\$ 44$ and seven pairs of pants. He spent $\$ 96$ in total. A) Write an equation to represent this scenario.
Equation: $\qquad$ B) How much did each t-shirt cost? inswer: $\qquad$

$\frac{2}{5}(x-2)=x+4$

Charlotte is driving at $71.5 \mathrm{mi} / \mathrm{h}$ and receives a text message. She looks down at her phone and takes her eyes off the road for 3.92 s . How far has Charlotte traveled in feet during this time? distance: $\square$ ft

A one-year membership to a gym costs $\$ 725$ . The registration fee is $\$ 125, * 1$ point and the remaining amount is paid monthly. Create an equation for the situation. Solve for the variable.
Your answer

Solve the following system of equations. $\begin{array}{l} -2 x-3 y=15 \\ -3 x-4 y=19 \end{array}$ $x=$ $\square$ $\square$ $y=$ $\square$

$\frac{x}{3}+10=15$

Given that $\angle ADB = (6x + 10)^\circ$ and $\angle BDC = 4x^\circ$ , and knowing that these angles are complementary, find the measures of $\angle ADB$ and $\angle BDC$ .

$3x + 4y = 8$

What are $m$ and $b$ in the linear equation, using the common meanings of $m$ and $b$ ? $1+4 x+6-x=y$ (A) $m$ is $3, b$ is 7 (B) $m$ is $4, b$ is 6 (C) $m$ is $6, b$ is 4 (D) $m$ is $7, b$ is 3

If: $\begin{array}{l} 2 x+y+z=52 \\ x+2 y+z=49 \\ 2 x+2 z=50 \end{array}$
Fhen solve $2 x+3 y+z=$

This question: 10 point(s) possible Submit quiz Graph the function. $f(x)=\frac{1}{2} x+8$
Use the graphing tool on the right to graph the function. $\square$

\begin{align} 2y + 2 &= 5 \\ \end{align}

Find the solution set. $\frac{m}{3}-3>\frac{4}{3}-\frac{m}{4}$
The solution set is $m>\frac{52}{7}$ . (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in interval notation.)

$6(x+2)-7 x \geq 8$

$\begin{array}{l}0.8 x-2.1 y=10.8 \\ 1.6 x-0.7 y=7.6\end{array}$

$\begin{array}{l}2 y+x=6 \\ 5 y-4 x=2\end{array}$

2.) $3=5 x-\frac{2-x}{2}$

56. What is the pattern rule?
Write an expression to represent the pattern. \begin{tabular}{|c|c|} \hline Input & Output \\ \hline 1 & 2 \\ \hline 2 & 5 \\ \hline 3 & 8 \\ \hline 4 & 11 \\ \hline \end{tabular}

3. Ejah works in a diamond mine. When he works the late shift, $\$ 2 / \mathrm{h}$ is added to his regular hourly wage. Last week, he worked the late shift for a total o 40 h and made \$960. Write and solve and equation to determine Elijah's reguicer hourly wage.

$-5=6 d-7 d+4$

10. $11-\frac{1}{2} y=3+6 x$

$\frac{m}{4} \rightarrow=-3$

Use the graph to derive the equation $y=m x$ for a line through the origin. Simplify the numerical coefficient, if needed. (1 point) $y=3 x$ $y=x$ $y=\frac{3}{3} x$ $y=8 x$

What is the equation of the line, in standard form, that is parallel to the given line and passes through the point $(4,2)$ ? $3 x-y=2$ $3 x-y=10$ $3 x-y=-1$ $\frac{1}{3} x-y=\frac{2}{3}$

Skill 2: Solving linear equations involving brackets Solve the following equations Show correct working out a. $3(x+1)=18$