Linearity

Problem 3001

Determine the ratios from the points (2,3), (4,6), (6,9), (8,12). For every \_\_\_ cup(s) of water, \_\_\_ cup(s) of flour. When 8 cups of water, \_\_\_ cups of flour needed.

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Problem 3002

Which double number line helps find calories burned by Raul if he runs 7 miles after burning 342 Calories for 3 miles?

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Problem 3003

Alejandro spent \$ 18.82 on snacks: \$ 2.80 for apples and the rest on juice bottles. Find the cost per juice bottle.

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Problem 3004

Jamal's phone plan costs \$65.50/month plus \$3/GB. How many GB can he use if he wants to keep his bill at \$74.20?

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Problem 3005

A lacrosse team raised \$1365.75, spent \$774.50, and budgeted \$53.75 per player for meals. How many players can go?

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Problem 3006

A group has \$ 349.50 for parking (\$ 19.50) and tickets (\$ 30 each). How many can attend the amusement park?

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Problem 3007

Solve for $x$ in the equation $3 x + 4 = 25$ .

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Problem 3008

A sandwich is $0.20 more than a salad. Six sandwiches equal seven salads in cost. Find their prices.

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Problem 3009

Aria starts with 80 points and earns 13.5 points per visit. How many visits does she need to reach 188 points?

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Problem 3010

Let the beat length be $x$ . Write the inequality $x > 17 + 9$ . Find three possible values for $x$ .

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Problem 3011

Kevin works 3 times Karen's hours. If both add 6 hours, Kevin works twice as much. Find their current hours.

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Problem 3012

Find Kim's age when Tom is $a$ years old, based on the pattern: Tom's age $n$ corresponds to Kim's age $n + 3$ .

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Problem 3013

The height of a plant is 1.6 times its age. Create an equation with $h$ for height and $y$ for age.

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Problem 3014

Aaron, Betsy, and Charita work part-time at the library. If their total hours is $45$ and Betsy works $4$ more than Aaron, find their hours.

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Problem 3015

Aaron, Betsy, and Charita work a total of 45 hours. If $B = A + 4$ and $A + B = \frac{1}{2}C$ , find $A$ , $B$ , and $C$ .

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Problem 3016

Find an equivalent expression for the total cost of gift cards: $14 \ell + 42 a$ .

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Problem 3017

Jason started with \ $80 and adds \$15 monthly. Find the expression for his savings after$ m$ months and calculate it for 12 months.

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Problem 3018

Solve for $s$ in the equation $s + 2.8 = 6.59$ .

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Problem 3019

Aaron, Betsy, and Charita work a total of 45 h. If Betsy works 4 h more than Aaron, how many hours does each work?

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Problem 3020

Natalie's monthly cost at Pete's Pottery Place is based on a \$9 entry fee and \$3 per bowl.
A: Write an expression for her total cost if she makes $b$ bowls over 5 days. B: Calculate her total cost if she makes 4 bowls each visit.

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Problem 3021

If $AB \cong CD$ , find $AB$ when $AB = 2x + 5$ and $CD = 4x - 3$ .

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Problem 3022

A 20% price drop in sugar allows buying 2 kg more for Rs. 80. Find the new price per kg: (a) Rs. 10 (b) Rs. 8 (c) Rs. 6 (d) Rs. 7 (e) None.

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Problem 3023

Find the 2006 employment of sheet metal workers if 2016 is 201,000, a $6.3\%$ increase from 2006. Options: a. 214,000 b. 187,000 c. 195,000 d. 189,000

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Problem 3024

Solve for $y$ in the equation: $-2y - 6 = -3x$ .

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Problem 3025

Solve the equation $3 x - \frac{1}{5} - \frac{2}{9} x = \frac{124}{5}$ . Simplify by combining like terms.

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Problem 3026

Find the input value where $f(x)=1.8x-10$ equals $g(x)=-4$ . Choose the correct equation and solve for $x$ .

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Problem 3027

Solve the equation $3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}$ . Combine like terms and isolate $x$ .

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Problem 3028

Solve the equation $3.4+2(9.7-4.8 x)=61.2$ . Which steps apply? Distribute, combine, divide, or subtract?

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Problem 3029

Find the slope-intercept form of the line through the points: 7) $(2,5)$ and $(0,3)$ 8) $(3,3)$ and $(0,5)$ .

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Problem 3030

Find the line equations for the points: 1) $(-5,-1)$ and $(-3,-5)$ , 2) $(3,-2)$ and $(0,-3)$ using $y = mx + b$ .

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Problem 3031

Solve for $x$ in the equation $10 x - 1 = 15 - 6 x$ .

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Problem 3032

Express $a$ in terms of $y$ , $z$ , and $x$ from the equation $a x + y = z$ .

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Problem 3033

Determine the slope and y-intercept of the equation $y=2x-3$ .

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Problem 3034

Solve for $x$ and $y$ in the equation $2x + 4y = 12$ by isolating the variables.

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Problem 3035

Solve the equation: $(y+3)=-2(x-5)$ .

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Problem 3036

How many pitchers of lemonade does Molly need to fill 16 large glasses and 12 small glasses without leftovers?

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Problem 3037

Find the value of $\mathrm{c}$ for the function $f(\chi)=2 \chi+3 \mathrm{c}^{3}$ that passes through the origin.

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Problem 3038

Find the point where the line $f(\chi)=2 \chi-1$ intersects the $\mathrm{y}$ -axis from these options: (0,1), (0,-1), (1,0), (-1,0).

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Problem 3039

Find the value of $\mathrm{a}$ if the point $(\mathrm{a}, 3)$ is on the line $f(\chi)=4 \chi-5$ .

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Problem 3040

Which expression equals $11 y-5$ ? Choose Yes or No for each option: A. $\frac{1}{8}(88 y-40)$ B. $\frac{1}{2}(22 y-10)$ C. $3(33 y-15)$ D. $5-11 y$

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Problem 3041

Which equation is equivalent to $2x + 2 = 14$ ?

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Problem 3042

Is $x=6$ a solution to $3x + 8 = 56$ ? If $x$ changes to $9$ , what must the right side change to?

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Problem 3043

At 1:00, both towns had the same temperature. By 3:00, Jonestown's temp dropped 18 degrees and Cooperville's dropped 8 degrees. a. Model Jonestown's temp change with an equation. b. Model Cooperville's temp change with an equation. c. Which town was colder at 3:00?

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Problem 3044

Find the inequality for the shaded region to the right of the line $x = -\frac{1}{8}$ . Is the line included?

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Problem 3045

Solve the system of equations: $-5y + 3z = -13$ , $4x - z = -2$ , $-7x + 9y = 5$ .

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Problem 3046

Find the intersection of the lines defined by $y=x-4$ and $y=-x+6$ .

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Problem 3047

Solve for $x$ in the equation $2 x + 1 = 9$ .

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Problem 3048

A bag costs 4 times a dress. If the bag costs \$276, how much does Anna spend on the bag and 3 dresses?

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Problem 3049

Find the sum of $5x - 2 + 3x$ and $5(7 - x)$ .

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Problem 3050

Solve for $h$ : $6 h + 7 - 10 h = 2 h - 23$

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Problem 3051

Find three numbers where their sum is 61, the first is 7 less than the second, and the third is 2 times the second.

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Problem 3052

Determine which equation fits the pairs of $(x, y)$ : (1, 5), (2, 7), (3, 9), (4, 11). Options: A) $y=2x+3$ , B) $y=3x-2$ , C) $y=4x-1$ , D) $y=5x$ .

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Problem 3053

Find the system of equations for tickets sold: $x + y = 120$ and $90x + 250y = 27,600$ . Options: A, B, C, D.

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Problem 3054

Solve the equation: $4c - 7c + 5 = 9c + 6 - 8c$

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Problem 3055

Solve. $\frac{5 r+10}{15}=\frac{2 r-8}{2}$
The solution is $\mathrm{r}=$ $\square$ (Simplify your answer.)

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Problem 3056

41. $\frac{3 a+b}{2}=a+3 b$ бол $b$ нь $a$ -аас хэд дахин бага вэ?

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Problem 3057

Solve each equation. Check your answer.
38. $\frac{2+y}{3}=-1$
39. $-24=-10 t+3$
40. $10=0.3 x-9.1$
41. $\frac{1}{2}=\frac{1}{2} c-2$
42. $\frac{x-3}{3}=-4 \frac{1}{2}$
43. $9.4=-d+5.6$
44. $\frac{d+17}{2}=5 \frac{1}{3}$
45. $2.4+10 m=6.89$
46. $\frac{1}{5} t-3=-17$
Solve each equation. Justify each step.
47. $15=9-3 p$
48. $4-5 k=-16$
49. $9+\frac{c}{-5}=-5$
50. $\frac{9}{-3}+12=2$

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Problem 3058

Got It?
1. What is the solution of each equation? Check each answer. a. $11 m-8-6 m=22$ b. $-2 y+5+5 y=14$

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Problem 3059

The tables below show the values of four different functions for given values of $x$ . \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline 1 & 12 \\ \hline 2 & 19 \\ \hline 3 & 26 \\ \hline 4 & 33 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline 1 & -1 \\ \hline 2 & 1 \\ \hline 3 & 5 \\ \hline 4 & 13 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline $x$ & $h(x)$ \\ \hline 1 & 9 \\ \hline 2 & 12 \\ \hline 3 & 17 \\ \hline 4 & 24 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline $x$ & $k(x)$ \\ \hline 1 & -2 \\ \hline 2 & 4 \\ \hline 3 & 14 \\ \hline 4 & 28 \\ \hline \end{tabular}
Which table represents a linear finction? (1) $f(x)$ (3) $h(x)$ (2) $g(x)$ (4) $k(x)$

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Problem 3060

Solve the following system of equations using Gaussian elimination or Gauss-Jordan elimination. $\begin{aligned} 7 x-4 y+7 z & =-14 \\ 21 x-12 y+21 z & =-44 \\ -14 x+8 y-14 z & =31 \end{aligned}$

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Problem 3061

In a certain country people own a total of about 352 million fish, cats, and dogs as pets. The number of fish owned is 14 million more than the total number of cats and dogs owned, and 15 million more cats are owned than dogs. How many of each type of pet do people in this country own?
The number of fish owned by people in this country is $\square$ million, the number of cats owned by people is $\square$ million, the number of dogs owned by people is $\square$ million. (Type whole numbers.)

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Problem 3062

Michelle borrows a total of $\$ 6000$ in student loans from two lenders. One charges $3.6 \%$ simple interest and the other charges $5.6 \%$ simple interest. She is not required to pay off the principal or interest for 3 yr. However, at the end of 3 yr, she will owe a total of $\$ 738$ for the interest from both loans. How much did she borrow from each lender?
Part: $0 / 2$
Part 1 of 2
Michelle borrowed \\square $at$ 3.6 \%$.

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Problem 3063

Solve the system. If the system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. $\begin{aligned} -2 x-3 y & =23 \\ +3 y+3 z & =-2 \\ 2 x & -3 z \end{aligned}=14$ The system has one solution. The solution set is $\{$ $\square$ , $\square$ $\square$ \}. The system has no solution. $\square$ The system is inconsistent. The equations are dependent. The system has infinitely many solutions. The system is inconsistent. The equations are dependent.

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Problem 3064

The general solution is given for the system of linear equations. Find three individual solutions to the system. $\begin{array}{r} -x+4 y+2 z=4 \\ x-3 y-z=-2 \\ -x+y-z=-2 \end{array}$
Solution: $\{(-2 z+4,-z+2, z) \mid z$ is any real number $\}$
Three possible solutions are $\square$ . 1 $\square$ $\square$ ).( ■. $\square$ ). and ([:-5). $\square$ ！ $\square$

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Problem 3065

Question 9 of 15, Step 1 of 1 $7 / 15$ Correct
Use any convenient method to solve the following system of equations. If the system is dependent, express the solution set in terms of of of the variables. Leave all fractional answers in fraction form. $\left\{\begin{array}{rr} x+2 y= & 6 \\ y-6 z= & 17 \\ -4 x-7 y+2 z= & -15 \end{array}\right.$
Answer Keypa Keyboard Short
Selecting an option will display any text boxes needed to complete your answer. Only One Solution Inconsistent System Dependent System

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Problem 3066

Type the correct answer in each box. Use numerals instead of words.
The domain of this function is $\{-12,-6,3,15\}$ . $y=-\frac{2}{3} x+7$
Complete the table based on the given domain. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-6 & $\square I$ \\ \hline $\square$ & 5 \\ \hline 15 & $\square$ \\ \hline & 15 \\ \hline \end{tabular}

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Problem 3067

Question3. Solve the following linear program use Simplex method? $\begin{aligned} \operatorname{Min} Z= & 8 x_{1}+2 x_{2}+x_{3} \\ \mathrm{~s} / \mathrm{t} & \left\{\begin{aligned} 2 x_{1}-x_{2}+x_{3} \geq-3 \\ x_{1}+2 x_{3} \geq 1 \\ 3 x_{1}+x_{2}=5 \\ x_{1}, x_{2}, x_{3} \geq 0 \end{aligned}\right. \end{aligned}$

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Problem 3068

1. $\frac{x+7}{3}=\frac{3 x-1}{6}$ бол $x=?$
2. Үржигдэхүш". болгон задал.

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Problem 3069

Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. $\left\{\begin{array}{rr} 2 x+3 y+4 z= & -20 \\ 2 x-4 y-6 z= & 16 \\ x+y-z= & 4 \end{array}\right.$
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution set is $\{(\square, \square, \square)\}$ . $\square$ (Simplify your answers.) B. There are infinitely many solutions. The solution set is $\{(\square, \square, z)\}$ , where $z$ is any real number. $\square$ $\square$ (Type expressions using $z$ as the variable. Use integers or fractions for any numbers in the expressions.) C. There is no solution. The solution set is $\varnothing$ .

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Problem 3070

a) Given that the line joining the points $A(a, 5)$ and $B(-2, b)$ have a slope of 2 and that the gradient of the line joining the points B and $C(-b, a)$ is 2 , find the values of $a$ and $b$ . [9 marks] b) The interior angle of a regular polygon exceeds its exterior angle by $108^{\circ}$ . How many sides does the polygon have? [11 marks]

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Problem 3071

Felipe drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Felipe drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Felipe live from the mountains?
Do not do any rounding.

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Problem 3072

48. $a, b, c$ нь бүхэл тоонууд, $a=2 b, \frac{a}{4}=\frac{b}{c}$ бол $c=$ ?

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Problem 3073

$1 A$ 18 1C 1 D Summary Bookwork code: 1D Calculator not allowed
The day before a show, a theatre had sold adult and child tickets in $t$ ratio 9 : 4.
On the day of the show, the theatre sold 20 more adult tickets and nc more child tickets. The ratio of adult to child tickets sold became $8: 3$ . Work out how many adult tickets had been sold the day before the show. < Previous Watch video Answe

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Problem 3074

Fully simplify the following: a) $-2 t \times u \times 8$ b) $6 d \times-3 f$

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Problem 3075

$2 x+y=8 \quad 2 x+5 y=9$ 10. $\begin{array}{l} 2 x-y=-8 \\ x+2 y=6 \end{array}$
11. $4 x-y=10$
12. $4 x-y=-9$ $x-y=1$ $2 x-3 y=-7$

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Problem 3076

Solve the system of equations by using the substitution method. $\begin{array}{l} 2 x+y=-1 \\ 3 x+4 y=6 \end{array}$
The solution set is $\square$ \}.

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Problem 3077

Solve the system of equations by using the addition method. $\begin{array}{l} 3 x-2 y=-2 \\ 7 x+6 y=-26 \end{array}$
The solution set is $\square$ (ㅁ, ㅁ)

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Problem 3078

(a) Write the general solution. (b) Find three individual solutions. $\begin{aligned} -8 x-y & =12 \\ 24 x & =-3(y+12) \end{aligned}$
Part: $0 / 2$
Part 1 of 2
Instructor Note Write your answer in the form of $x, y$ where $y$ is an expression of an arbitrary variable $x$ .
A general solution to the system is $\{$ $\square$ | $x$ is any real number $\}.$

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Problem 3079

What kind of transformation converts the graph of $f(x)=-7 x-10$ into the graph of $g(x)=$ $x-10$ ? horizontal stretch horizontal shrink vertical shrink vertical stretch

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Problem 3080

Solve the system of equations. $\begin{aligned} x-3 y-z & =6 \\ -x+8 y-4 z & =-16 \\ 2 x-15 y+7 z & =30 \end{aligned}$

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Problem 3081

What kind of transformation converts the graph of $f(x)=6 x-1$ into the graph of $g(x)=x-$ 1 ? horizontal shrink vertical shrink horizontal stretch vertical stretch

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Problem 3082

Solve the following system of equations. $\begin{array}{l} 4 x+5 y=10 \\ 8 x+5 y=30 \end{array}$

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Problem 3083

12 Given that $x x+y=7$ and $3 x$ $-2 y=3$ by how much is $7 x$ greater th an 10 ? a> 1, b, 3 (c) 7 (d) 17

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Problem 3084

8-Two automobiles are 150 kilometers apart and traveling toward each other. One automobile is moving at $60 \mathrm{~km} / \mathrm{h}$ and the other is moving at $40 \mathrm{~km} / \mathrm{h} \mathrm{mph}$ . In how many hours will they meet? A. 2.5 B. 2.0

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Problem 3085

Solve the following system of equations. $\begin{array}{l} -8 x+3 y=2 \\ -2 x+9 y=-16 \end{array}$

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Problem 3086

Solve the following system. $\left\{\begin{aligned} -3 x+4 y+3 z & =10 \\ y & =4 \\ -5 x+6 y & =4 \end{aligned}\right.$

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Problem 3087

Linda, Pablo, and Ahmad have a total of $\$ 100$ in their wallets. Ahmad has 3 times what Linda has. Linda has $\$ 10$ less than Pablo. How much do they have in their wallets?

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Problem 3088

The ratio of red to blue marbles in a bowl is $7: 8$ . There are 30 marbles total. How many red and blue marbles are there? A. 7 red and 8 blue B. 8 red and 7 blue C. 10 red and 12 blue D. 14 red and 16 blue

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Problem 3089

32:10 Hide THIS IS A PRACTICE TEST 4 $\square$ Mark for Review $\Delta \mathrm{A}^{2}$
If $5(x+4)=4(x+4)+29$ , what is the value of $x+4$ ? (A) -4 (B) 25 (C) 29 (D) 33

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Problem 3090

Solve the system. $\begin{aligned} 2 x+y+z & =-3 \\ -2 x+y+2 z & =4 \\ -x+2 y+z & =5 \end{aligned}$ $\begin{array}{l} x= \\ y= \\ z= \end{array}$

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Problem 3091

3 3.1
Gaston bought two types of candies: red candies that cost $\$ 0.60$ each and green candies that each cost $z$ times as much as a red candy. If the cost of 3 red candies and 1 green candy was $\$ 3$ , what is the value of $z$ ?

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Problem 3092

Solve for $s$ . $\begin{array}{l} 3+3 s=15 \\ s=\square \end{array}$

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Problem 3093

Samir sold 4 of his old Star Leaper video games at Trading Post Game Shop. Before he left, he spent $\$ 23.65$ of his earnings on a controller. Samir had $\$ 6.35$ remaining.
Which equation can you use to find the amount of money, $v$ , Samir received for each video game? $23.65 v-4=6.35$ $4 v-23.65=6.35$ $4(v-23.65)=6.35$ $23.65(v-4)=6.35$
How much money did Samir receive for each video game? \$

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Problem 3094

Question Watch Video Show Examples
Gabriella is a high school basketball player. In a particular game, she made some two point shots and some three point shots. Gabriella scored a total of 32 points and made 4 more three point shots than two point shots. Determine the number of two point shots Gabriella made and the number of three point shots she made.
Answer
Gabriella made $\square$ two point shots and $\square$ three point shots. Submit Answer

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Problem 3095

Find the solution of the system of equations. $\begin{array}{l} -5 x-2 y=-1 \\ -6 x+4 y=-46 \end{array}$
Answer ( $\square$ $\square$ Submit Answer

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Problem 3096

$\begin{array}{c}2 x-y+3 z=-17 \\ 4 x \quad-6 z=-42 \\ 6 y+z=13\end{array}$

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Problem 3097

Determine if the ordered triple is a solution to the system of equations. $\begin{array}{l} 2 x+y-4 z=4 \\ x+3 y+2 z=16 \\ -x+y+2 z=4 \end{array}$
Part: 0 / 2
Part 1 of 2 (a) $(2,4,1)$ (Choose one) $\square$ a solution to the system of equations.

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Problem 3098

Determine if the ordered triple is a solution to the system of equations. $\begin{array}{r} x+y+z=2 \\ 3 x+3 y-2 z=11 \\ 4 x+5 y+2 z=10 \end{array}$
Part: $0 / 2$
Part 1 of 2 (a) $(3,0,-1)$ (Choose one) $\square$ a solution to the system of equations.

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Problem 3099

Solve the system. If the system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. $\begin{aligned} -2 x+2 y+3 z & =-5 \\ y-2 z & =1 \\ -2 x+7 z & =-7 \end{aligned}$ The system has one solution. $\square$ $\square$ $\square)\}$
The solution set is $\{$ $\square$ \} The system has no solution. The system is inconsistent. The equations are dependent. The system has infinitely many solutions. The system is inconsistent. The equations are dependent.

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Problem 3100

The general solution is given for the system of linear equations. Find three individual solutions to the system. $\begin{array}{rr} 2 x-3 y+ & z=1 \\ x+4 y- & z=3 \\ 5 x-2 y+ & z=5 \end{array}$
Solution: $\{(x,-3 x+4,-11 x+13) \mid x$ is any real number $\}$
Three possible solutions are $\square$ ， $\square$ $\square$ $),(\square$ $\square$ $\square$ ), and $\square$ , $\square$ ). , , $\square$ ，

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1 ...28 29 30 31 32 33 34 ...39

Linearity

Problem 3001

Determine the ratios from the points (2,3), (4,6), (6,9), (8,12). For every \_\_\_ cup(s) of water, \_\_\_ cup(s) of flour. When 8 cups of water, \_\_\_ cups of flour needed.

Problem 3002

Which double number line helps find calories burned by Raul if he runs 7 miles after burning 342 Calories for 3 miles?

Problem 3003

Alejandro spent \$ 18.82 on snacks: \$ 2.80 for apples and the rest on juice bottles. Find the cost per juice bottle.

Problem 3004

Jamal's phone plan costs \$65.50/month plus \$3/GB. How many GB can he use if he wants to keep his bill at \$74.20?

Problem 3005

A lacrosse team raised \$1365.75, spent \$774.50, and budgeted \$53.75 per player for meals. How many players can go?

Problem 3006

A group has \$ 349.50 for parking (\$ 19.50) and tickets (\$ 30 each). How many can attend the amusement park?

Problem 3007

Solve for xxx in the equation 3x+4=253 x + 4 = 253x+4=25.

Problem 3008

A sandwich is $0.20 more than a salad. Six sandwiches equal seven salads in cost. Find their prices.

Problem 3009

Aria starts with 80 points and earns 13.5 points per visit. How many visits does she need to reach 188 points?

Problem 3010

Let the beat length be xxx. Write the inequality x>17+9x > 17 + 9x>17+9. Find three possible values for xxx.

Problem 3011

Kevin works 3 times Karen's hours. If both add 6 hours, Kevin works twice as much. Find their current hours.

Problem 3012

Find Kim's age when Tom is aaa years old, based on the pattern: Tom's age nnn corresponds to Kim's age n+3n + 3n+3.

Problem 3013

The height of a plant is 1.6 times its age. Create an equation with hhh for height and yyy for age.

Problem 3014

Aaron, Betsy, and Charita work part-time at the library. If their total hours is 454545 and Betsy works 444 more than Aaron, find their hours.

Problem 3015

Aaron, Betsy, and Charita work a total of 45 hours. If B=A+4B = A + 4B=A+4 and A+B=12CA + B = \frac{1}{2}CA+B=21​C, find AAA, BBB, and CCC.

Problem 3016

Find an equivalent expression for the total cost of gift cards: 14ℓ+42a14 \ell + 42 a14ℓ+42a.

Problem 3017

Jason started with \80andadds$15monthly.Findtheexpressionforhissavingsafter80 and adds \$15 monthly. Find the expression for his savings after 80andadds$15monthly.Findtheexpressionforhissavingsafterm$ months and calculate it for 12 months.

Problem 3018

Solve for sss in the equation s+2.8=6.59s + 2.8 = 6.59s+2.8=6.59.

Problem 3019

Aaron, Betsy, and Charita work a total of 45 h. If Betsy works 4 h more than Aaron, how many hours does each work?

Problem 3020

Natalie's monthly cost at Pete's Pottery Place is based on a \$9 entry fee and \$3 per bowl. A: Write an expression for her total cost if she makes bbb bowls over 5 days. B: Calculate her total cost if she makes 4 bowls each visit.

Problem 3021

If AB≅CDAB \cong CDAB≅CD, find ABABAB when AB=2x+5AB = 2x + 5AB=2x+5 and CD=4x−3CD = 4x - 3CD=4x−3.

Problem 3022

A 20% price drop in sugar allows buying 2 kg more for Rs. 80. Find the new price per kg: (a) Rs. 10 (b) Rs. 8 (c) Rs. 6 (d) Rs. 7 (e) None.

Problem 3023

Find the 2006 employment of sheet metal workers if 2016 is 201,000, a 6.3%6.3\%6.3% increase from 2006. Options: a. 214,000 b. 187,000 c. 195,000 d. 189,000

Problem 3024

Solve for yyy in the equation: −2y−6=−3x-2y - 6 = -3x−2y−6=−3x.

Problem 3025

Solve the equation 3x−15−29x=12453 x - \frac{1}{5} - \frac{2}{9} x = \frac{124}{5}3x−51​−92​x=5124​. Simplify by combining like terms.

Problem 3026

Find the input value where f(x)=1.8x−10f(x)=1.8x-10f(x)=1.8x−10 equals g(x)=−4g(x)=-4g(x)=−4. Choose the correct equation and solve for xxx.

Problem 3027

Solve the equation 3x−15−29x=12453x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}3x−51​−92​x=5124​. Combine like terms and isolate xxx.

Problem 3028

Solve the equation 3.4+2(9.7−4.8x)=61.23.4+2(9.7-4.8 x)=61.23.4+2(9.7−4.8x)=61.2. Which steps apply? Distribute, combine, divide, or subtract?

Problem 3029

Find the slope-intercept form of the line through the points: 7) (2,5)(2,5)(2,5) and (0,3)(0,3)(0,3) 8) (3,3)(3,3)(3,3) and (0,5)(0,5)(0,5).

Problem 3030

Find the line equations for the points: 1) (−5,−1)(-5,-1)(−5,−1) and (−3,−5)(-3,-5)(−3,−5), 2) (3,−2)(3,-2)(3,−2) and (0,−3)(0,-3)(0,−3) using y=mx+by = mx + by=mx+b.

Problem 3031

Solve for xxx in the equation 10x−1=15−6x10 x - 1 = 15 - 6 x10x−1=15−6x.

Problem 3032

Express aaa in terms of yyy, zzz, and xxx from the equation ax+y=za x + y = zax+y=z.

Problem 3033

Determine the slope and y-intercept of the equation y=2x−3y=2x-3y=2x−3.

Problem 3034

Solve for xxx and yyy in the equation 2x+4y=122x + 4y = 122x+4y=12 by isolating the variables.

Problem 3035

Solve the equation: (y+3)=−2(x−5)(y+3)=-2(x-5)(y+3)=−2(x−5).

Problem 3036

How many pitchers of lemonade does Molly need to fill 16 large glasses and 12 small glasses without leftovers?

Problem 3037

Find the value of c\mathrm{c}c for the function f(χ)=2χ+3c3f(\chi)=2 \chi+3 \mathrm{c}^{3}f(χ)=2χ+3c3 that passes through the origin.

Problem 3038

Find the point where the line f(χ)=2χ−1f(\chi)=2 \chi-1f(χ)=2χ−1 intersects the y\mathrm{y}y-axis from these options: (0,1), (0,-1), (1,0), (-1,0).

Problem 3039

Find the value of a\mathrm{a}a if the point (a,3)(\mathrm{a}, 3)(a,3) is on the line f(χ)=4χ−5f(\chi)=4 \chi-5f(χ)=4χ−5.

Problem 3040

Solve for $x$ in the equation $3 x + 4 = 25$ .

Let the beat length be $x$ . Write the inequality $x > 17 + 9$ . Find three possible values for $x$ .

Find Kim's age when Tom is $a$ years old, based on the pattern: Tom's age $n$ corresponds to Kim's age $n + 3$ .

The height of a plant is 1.6 times its age. Create an equation with $h$ for height and $y$ for age.

Aaron, Betsy, and Charita work part-time at the library. If their total hours is $45$ and Betsy works $4$ more than Aaron, find their hours.

Aaron, Betsy, and Charita work a total of 45 hours. If $B = A + 4$ and $A + B = \frac{1}{2}C$ , find $A$ , $B$ , and $C$ .

Find an equivalent expression for the total cost of gift cards: $14 \ell + 42 a$ .

Jason started with \ $80 and adds \$15 monthly. Find the expression for his savings after$ m$ months and calculate it for 12 months.

Solve for $s$ in the equation $s + 2.8 = 6.59$ .

Natalie's monthly cost at Pete's Pottery Place is based on a \$9 entry fee and \$3 per bowl.
A: Write an expression for her total cost if she makes $b$ bowls over 5 days. B: Calculate her total cost if she makes 4 bowls each visit.

If $AB \cong CD$ , find $AB$ when $AB = 2x + 5$ and $CD = 4x - 3$ .

Find the 2006 employment of sheet metal workers if 2016 is 201,000, a $6.3\%$ increase from 2006. Options: a. 214,000 b. 187,000 c. 195,000 d. 189,000

Solve for $y$ in the equation: $-2y - 6 = -3x$ .

Solve the equation $3 x - \frac{1}{5} - \frac{2}{9} x = \frac{124}{5}$ . Simplify by combining like terms.

Find the input value where $f(x)=1.8x-10$ equals $g(x)=-4$ . Choose the correct equation and solve for $x$ .

Solve the equation $3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}$ . Combine like terms and isolate $x$ .

Solve the equation $3.4+2(9.7-4.8 x)=61.2$ . Which steps apply? Distribute, combine, divide, or subtract?

Find the slope-intercept form of the line through the points: 7) $(2,5)$ and $(0,3)$ 8) $(3,3)$ and $(0,5)$ .

Find the line equations for the points: 1) $(-5,-1)$ and $(-3,-5)$ , 2) $(3,-2)$ and $(0,-3)$ using $y = mx + b$ .

Solve for $x$ in the equation $10 x - 1 = 15 - 6 x$ .

Express $a$ in terms of $y$ , $z$ , and $x$ from the equation $a x + y = z$ .

Determine the slope and y-intercept of the equation $y=2x-3$ .

Solve for $x$ and $y$ in the equation $2x + 4y = 12$ by isolating the variables.

Solve the equation: $(y+3)=-2(x-5)$ .

Find the value of $\mathrm{c}$ for the function $f(\chi)=2 \chi+3 \mathrm{c}^{3}$ that passes through the origin.

Find the point where the line $f(\chi)=2 \chi-1$ intersects the $\mathrm{y}$ -axis from these options: (0,1), (0,-1), (1,0), (-1,0).

Find the value of $\mathrm{a}$ if the point $(\mathrm{a}, 3)$ is on the line $f(\chi)=4 \chi-5$ .

Which expression equals $11 y-5$ ? Choose Yes or No for each option: A. $\frac{1}{8}(88 y-40)$ B. $\frac{1}{2}(22 y-10)$ C. $3(33 y-15)$ D. $5-11 y$

Which equation is equivalent to $2x + 2 = 14$ ?

Is $x=6$ a solution to $3x + 8 = 56$ ? If $x$ changes to $9$ , what must the right side change to?

Find the inequality for the shaded region to the right of the line $x = -\frac{1}{8}$ . Is the line included?

Solve the system of equations: $-5y + 3z = -13$ , $4x - z = -2$ , $-7x + 9y = 5$ .

Find the intersection of the lines defined by $y=x-4$ and $y=-x+6$ .

Solve for $x$ in the equation $2 x + 1 = 9$ .

Find the sum of $5x - 2 + 3x$ and $5(7 - x)$ .

Solve for $h$ : $6 h + 7 - 10 h = 2 h - 23$

Determine which equation fits the pairs of $(x, y)$ : (1, 5), (2, 7), (3, 9), (4, 11). Options: A) $y=2x+3$ , B) $y=3x-2$ , C) $y=4x-1$ , D) $y=5x$ .

Find the system of equations for tickets sold: $x + y = 120$ and $90x + 250y = 27,600$ . Options: A, B, C, D.

Solve the equation: $4c - 7c + 5 = 9c + 6 - 8c$

Solve. $\frac{5 r+10}{15}=\frac{2 r-8}{2}$
The solution is $\mathrm{r}=$ $\square$ (Simplify your answer.)

41. $\frac{3 a+b}{2}=a+3 b$ бол $b$ нь $a$ -аас хэд дахин бага вэ?

Got It?
1. What is the solution of each equation? Check each answer. a. $11 m-8-6 m=22$ b. $-2 y+5+5 y=14$

1. $\frac{x+7}{3}=\frac{3 x-1}{6}$ бол $x=?$
2. Үржигдэхүш". болгон задал.

48. $a, b, c$ нь бүхэл тоонууд, $a=2 b, \frac{a}{4}=\frac{b}{c}$ бол $c=$ ?

Fully simplify the following: a) $-2 t \times u \times 8$ b) $6 d \times-3 f$