Linearity

Problem 1001

Vox Pop
Une voiture sport accélère du repos jusqu'à 50 km/h50 \mathrm{~km} / \mathrm{h} en 1,5 s1,5 \mathrm{~s}. Combien lui faut-il de temps pour accélérer du repos jusqu'à 100.km/h100 . \mathrm{km} / \mathrm{h} ? (On suppose que la puissance du moteur est constante et indépendante de la vitesse et qu'on néglige le frottement.) A. 2 s B. 3 s C. 4,5 s4,5 \mathrm{~s} D. 6 s

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Problem 1002

It takes two scoops of detergent for every three scoops of fabric softener. If there are 28 scoops of detergent remaining, how many scoops of fabric softener will be needed? (CManeuvering the Middle LLC, 2015

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Problem 1003

Jack and Jill are saving for their first car. Jack saves $7\$ 7 for every $10\$ 10 Jill saves. If Jill has $350\$ 350 in her savings account, then how much money has Jack saved? OManeuvering the Midele LCC 25

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Problem 1004

Ivanna is saving money to buy a bike. She has $63\$ 63 and is going to save an additional $9\$ 9 each week. The bike costs $198\$ 198. In how many weeks will she have enough money to buy the bike? (a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 63,9, and 198. Let ww represent the number of weeks.
\square \square \square
\square w=w-\square= \square w+w+ \square (b) Solve the equation in part (a) to find the number of weeks. w=w=\square

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Problem 1005

Jane is saving money to buy a bike. She has $42\$ 42 and is going to save an additional $7\$ 7 each week. The bike costs $133\$ 133. In how many weeks will she have enough money to buy the bike? (a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 42, 7, and 133. Let ww represent the number of weeks. w+=\square w+\square=\square
\square \square ww == (b) Solve the equation in part (a) to find the number of weeks. w=w=\square

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Problem 1006

Solve the system with the addition method: {6x+4y=424x16y=16\left\{\begin{array}{lll} 6 x+4 y & = & -4 \\ -24 x-16 y & = & 16 \end{array}\right.
Answer: \square \square Enter your answers as integers or as reduced fraction(s) in the form A/B. If there is no solution, type "DNE" in each blank. If there are an infinite number of solutions, specify their form in the blanks in terms of xx (eg. (x, 2x-3)).

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Problem 1007

Choose the statement(s) that correctly describe the system. {2x+z=06x+yz=64x+y+z=0\left\{\begin{array}{rr} 2 x+z= & 0 \\ 6 x+y-z= & -6 \\ 4 x+y+z= & 0 \end{array}\right.
Select all that apply. The system's complete solutian can be written as (5+3a3,3a3,a)\left(\frac{5+3 a}{3}, \frac{3-a}{3}, a\right), where aa is any real number. The system has a unique solution. The system has no solution. The system has infinitely many solutions. The system is consistent. One solution is (1,2,2)(-1,2,2). The system is dependent. The system's complete solution can be written as (2+6a,2a,a)(2+6 a, 2-a, a) where aa is any real number.

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Problem 1008

Solve: 2<3x+61-2<3 x+6 \leq-1
The answer is \square <x<x \leq \square

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Problem 1009

Solve: 1<5x821<5 x-8 \leq 2 The answer is \square <x<x \leq \square

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Problem 1010

Use Gauss-Jordan elimination to solve the system. {x+y=02x+y+z=1y+2z=11\left\{\begin{array}{rlr} x+y & =0 \\ 2 x+y+z & = & -1 \\ y+2 z & = & -11 \end{array}\right.

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Problem 1011

Choose the statement(s) that correctly describe the system. {3x+z=212x+yz=1912x+y+z=17\left\{\begin{array}{rr} 3 x+z= & 2 \\ 12 x+y-z= & 19 \\ 12 x+y+z= & 17 \end{array}\right.

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Problem 1012

14x+3>5x+21 OR 13+6x13x614 x+3>5 x+21 \text { OR }-13+6 x \geq 13 x-6
Clear All Draw: \square

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Problem 1013

Question Show Examples
Which of the relationships below represents a function with a greater slope than the function y=2x2y=-2 x-2 ?
A
C \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-1 & -3 \\ \hline 2 & -9 \\ \hline 5 & -15 \\ \hline 8 & -21 \\ \hline \end{tabular}
B
D \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-4 & -13 \\ \hline 0 & -5 \\ \hline 4 & 3 \\ \hline 8 & 11 \\ \hline \end{tabular}
Answer A B Submit Answer C D

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Problem 1014

Write the linear equation that gives the rule for this table. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 3 & 15 \\ \hline 4 & 31 \\ \hline 5 & 47 \\ \hline 6 & 63 \\ \hline \end{tabular}
Write your answer as an equation with y first, followed by an equals sign.

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Problem 1015

Write the linear equation that gives the rule for this table. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 37 & 42 \\ \hline 41 & 46 \\ \hline 65 & 70 \\ \hline 72 & 77 \\ \hline \end{tabular}
Write your answer as an equation with y first, followed by an equals sign.

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Problem 1016

Write the linear equation that gives the rule for this table. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-78 & 78 \\ \hline-40 & 40 \\ \hline-2 & 2 \\ \hline 36 & -36 \\ \hline \end{tabular}
Write your answer as an equation with y first, followed by an equals sign.

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Problem 1017

Homework Part 1 of 2
Solve by the elimination method. Also determine whether the system is consistent or inconsistent and whether the equations are dependent or independent. 3x6y=152x4y=10\begin{array}{l} 3 x-6 y=15 \\ 2 x-4 y=10 \end{array}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is only one solution. The solution of the system is \square (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions of the form ( xx. \square ). (Simplify your answer.) C. There is no solution.

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Problem 1018

Function AA and Function B are linear functions. Function AA Function B y=2x1y=2 x-1 \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-7 & -21 \\ \hline 4 & 12 \\ \hline 6 & 18 \\ \hline \end{tabular}
Which statement is true?
The slope of Function A is greater than the slope of Function B.
The slope of Function AA is less than the slope of Function B.

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Problem 1019

Function AA and Function BB are linear functions.
Function A
Function B \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-4 & -9 \\ \hline 4 & 7 \\ \hline 8 & 15 \\ \hline \end{tabular}
Which statement is true?
The slope of Function AA is greater than the slope of Function B.
The slope of Function AA is less than the slope of Function B.

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Problem 1020

Function AA and Function BB are linear functions.
Function A
Function B y=5x2y=5 x-2
Which statement is true?
The yy-intercept of Function A is greater than the yy-intercept of Function B.
The yy-intercept of Function A is less than the yy-intercept of Function B .

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Problem 1021

Function AA and Function BB are linear functions. Function A Function B \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-4 & -25 \\ \hline 3 & 10 \\ \hline 4 & 15 \\ \hline \end{tabular} y=x1y=x-1
Which statement is true?
The yy-intercept of Function A is greater than the yy-intercept of Function B .
The yy-intercept of Function A is less than the yy-intercept of Function B.

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Problem 1022

BOOKMARK T4HWi QUESTIONS
19 Which equations represent linear functions? Select all that apply. Item 1 (A) x=y-x=y Item 2 Item 3 Item 4 B y=14x2+4y=\frac{1}{4} x^{2}+4 Item 5 c. 6x3y=126 x-3 y=12 Item 6 Item 7 Item 8 Item 9

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Problem 1023

Listen
USING TOOLS Use technology to solve the system of linear equation 1.6x3.2y=242.6x+2.6y=26\begin{array}{l} -1.6 x-3.2 y=-24 \\ 2.6 x+2.6 y=26 \end{array}

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Problem 1024

Solve the following system of equations. 4x+7y=118x4z=246y4z=22\begin{aligned} 4 x+7 y & =-11 \\ 8 x-4 z & =-24 \\ 6 y-4 z & =-22 \end{aligned}
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution is \square . \square D) \square (Type integers or simplified fractions.) B. There are infinitely many solutions. The solutions are \square , z) (Type integers or simplified fractions.) C. There is no solution.

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Problem 1025

Devon invested $8500\$ 8500 in three different mutual funds. A fund containing large cap stocks made 7.3%7.3 \% return in 1 yr. A real estate fund lost 13.2%13.2 \% in 1 yr, and a bond fund made 5.4%5.4 \% in 1 yr . The amount invested in the large cap stock fund was twice the amount invested in the real estate fund. If Devon had a net return of $163\$ 163 across all investments, how much was invested in each fund?

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Problem 1026

Find the equation of a straight line that passes through (3,5)&(7,1)(3,-5) \&(7,1)

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Problem 1027

Got II? 3. The length of the ball court at La Venta is 14 times the height of its walls. Write an equation that can be used to find the height of a model that has a length of 49 cm .

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Problem 1028

Solve using the substitution method. 5x7y=415x+53=y\begin{array}{l} 5 x-7 y=-41 \\ 5 x+53=y \end{array}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution of the system is \square . (Type an ordered pair.) B. There are infinitely many solutions in the form ( xx, \square ). C. There is no solution.

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Problem 1029

Find f+g,fg,fg\mathrm{f}+\mathrm{g}, \mathrm{f}-\mathrm{g}, \mathrm{fg} and fg\frac{\mathrm{f}}{\mathrm{g}}. Determine the domain for each function. f(x)=6x+1,g(x)=x+6f(x)=6 x+1, g(x)=x+6 (f+g)(x)=7x+7(\mathrm{f}+\mathrm{g})(\mathrm{x})=7 \mathrm{x}+7 (Simplify your answer.) What is the domain of f+gf+g ? A. The domain of f+gf+g is {\{\quad. (Use a comma to separate answers as needed.) B. The domain of f+gf+g is (,)(-\infty, \infty). (Type your answer in interval notation.) C. The domain of f+gf+g is \varnothing. (fg)(x)=(f-g)(x)= \square (Simylify your answer.)

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Problem 1030

13x=1\frac{1}{3} \cdot x=1

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Problem 1031

Graph the function rule. y=2x+1y=2 x+1

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Problem 1032

Solve the system by substitution. 3x6y=455y=x\begin{array}{r} -3 x-6 y=45 \\ -5 y=x \end{array}

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Problem 1033

Гурван оронтой тоо 5-аар гогсене. Эн цифрийг эхэнд нь шилжүүлэхэд анхны тоог 4 дахин авәад, 12-ыг нэмсэнтзй тэнцүү тоо гарна Өгегдсен гурван оронтой тоог ол.

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Problem 1034

5 Determina, em graus, 0 valor arredondado às décimas da inclinação de cada uma das retas de equação: 5.1. (x,y)=(1,1)+k(2,3)(x, y)=(1,1)+k(2,3); kRk \in \mathbb{R} 5.2. y=2x+1y=-2 x+1 5.3. 2yx+3=02 y-x+3=0 5.4. (x,y)=(0,3)+k(2,π)(x, y)=(0,3)+k(-2, \pi); kRk \in \mathbb{R} 5.5. y=πx2y=\pi x-2

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Problem 1035

5 Determina, em graus, 0 valor arredondado às décimas da inclinação de cada uma das retas de equação: 5.1. (x,y)=(1,1)+k(2,3)(x, y)=(1,1)+k(2,3); kRk \in \mathbb{R} 5.2. y=2x+1y=-2 x+1 5.3. 2yx+3=02 y-x+3=0 5.4. (x,y)=(0,3)+k(2,π)(x, y)=(0,3)+k(-2, \pi); kRk \in \mathbb{R} 5.5. y=πx2y=\pi x-2

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Problem 1036

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Problem 1037

\$7ow My Work (Optional) Submit Answer [-/14 Points] DETAILS MY NOTES TANFIN12 3.4.014. PRACTICE ANOTHER
Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: a type A,x\mathrm{A}, x, vessel has 60 deluxe cabins and 160 standard cabins, whereas a type B vessel, yy, has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with the Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their 15-day cruise in May. It costs $56,000\$ 56,000 to operate a type A vessel and \54,000tooperateatypeBvesselforthatperiod.(a)Howmanyofeachtypeofvesselshouldbeusedtokeeptheoperatingcosts54,000 to operate a type B vessel for that period. (a) How many of each type of vessel should be used to keep the operating costs Ctoaminimum? to a minimum?  The minimum is C= at (x,y)=()\text { The minimum is } C=\square \text { at }(x, y)=(\square) \text {. }(b)Suppose (b) Suppose C=c x+54,000 y.FindtherangeofvaluesthatthecostofoperatingatypeAvessel,thecoefficient. Find the range of values that the cost of operating a type A vessel, the coefficient cof of x,canassumewithoutchangingtheoptimalsolution., can assume without changing the optimal solution. \square c\leq c \leq \square(c)FindtherangeofvaluesthatRequirement1fordeluxecabinscanassume.(Requirement1pertainstothedeluxecabinrequirement.) (c) Find the range of values that Requirement 1 for deluxe cabins can assume. (Requirement 1 pertains to the deluxe cabin requirement.) \square \leq(Requirement1 Requirement 1) \leq \square(d)FindtheshadowpriceforRequirement1fordeluxecabins.(Roundyouranswertothenearestcent.)$ (d) Find the shadow price for Requirement 1 for deluxe cabins. (Round your answer to the nearest cent.) \$ \square$
S+ow My Work (Optional) \square

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Problem 1038

Solve the inequality and write your answer in interval notation. Use "U" between the two intervals. Use "oo" (two lower case o's) for \infty. 10x+1719+6x10 x+17 \leq-19+6 x

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Problem 1039

4. A miniature golf course charges different prices for adults and children. On Saturday, 50 adults and 50 children played, and the golf course earned $800\$ 800. On Sunday, 65 adults and 75 children played, and the golf course earned $1,100\$ 1,100. How much does the golf course charge for adults? A. \$6

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Problem 1040

7. Nolan is buying a season pass to a performing arts center. - One performing art center charges $100\$ 100 for the pass, plus $15.00\$ 15.00 to park each visit. - Another performing arts center charges $75\$ 75 for the pass, plus $20.00\$ 20.00 to park each visit. How many times would Nolan need to visit the two performing arts centers for the cost to be the same?
A 4 B. 5 C. 6 D. 7

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Problem 1041

Practice and Problem-Solving Exercises MATHEMATICAL PRACTICES See Problem 1. (A) Practice Tell whether each equation is true, false, or open. Explain.
7. 85+(10)=9585+(-10)=95
8. 225÷t4=6.4225 \div t-4=6.4
9. 2934=529-34=-5
10. 8(2)7=145-8(-2)-7=14-5
11. 4(4)÷(8)6=3+5(3)4(-4) \div(-8) 6=-3+5(3)
12. 91÷(7)5=35÷7+391 \div(-7)-5=35 \div 7+3
13. 4a3b=214 a-3 b=21
14. 14+7+(1)=2114+7+(-1)=21
15. 5x+7=175 x+7=17

Tell whether the given number is a solution of each equation.
16. 8x+5=29;38 x+5=29 ; 3
17. 5b+1=16;35 b+1=16 ;-3
18. 6=2n8;76=2 n-8 ; 7
19. 2=104y;22=10-4 y ; 2
20. 9a(72)=0;89 a-(-72)=0 ;-8
21. 6b+5=1;12-6 b+5=1 ; \frac{1}{2}
22. 7+16y=11;147+16 y=11 ; \frac{1}{4}
23. 14=13x+5;2714=\frac{1}{3} x+5 ; 27
24. 32t+2=4;23\frac{3}{2} t+2=4 ; \frac{2}{3}

Write an equation for each sentence.
25. The sum of 4x4 x and -3 is 8 .
26. The product of 9 and the sum of 6 and xx is 1 .
27. Training An athlete trains for 115 min each day for as many days as possible. Write an equation that relates the number of days dd that the athlete spends training when the athlete trains for 690 min .
28. Salary The manager of a restaurant earns $2.25\$ 2.25 more each hour than the host of the restaurant. Write an equation that relates the amount hh that the host earns each hour when the manager earns $11.50\$ 11.50 each hour.

Use mental math to find the solution of each equation. See Problem 3.
29. x3=10x-3=10
30. 4=7y4=7-y
31. 18+d=2418+d=24
32. 2x=52-x=-5
33. m3=4\frac{m}{3}=4
34. x7=5\frac{x}{7}=5
35. 6t=366 t=36
36. 20a=10020 a=100
37. 13c=2613 c=26

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Problem 1042

Nathan and Jackson are each saving money. - Nathan has $15\$ 15 saved and plans to save $5\$ 5 more each week. - Jackson has $25\$ 25 saved and plans to save $4\$ 4 more each week.
How many weeks will it be before both boys have saved the same amount of money?

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Problem 1043

Fill in the table using this function rule. y=4x+1y=-4 x+1 \begin{tabular}{|c|c|} \hline As & yy \\ \hline-2 & \square \\ \hline 0 & \square \\ \hline 2 & \square \\ \hline 4 & \square \\ \hline \end{tabular} Explanation Check

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Problem 1044

Fill in the table using this function rule. y=2x+3y=2 x+3 \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-4 & \square \\ \hline-2 & \square \\ \hline 0 & \square \\ \hline 2 & \square \\ \hline \end{tabular}

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Problem 1045

Labour planning
Labour information
Standard rate £17.00/hr£ 17.00 / \mathrm{hr} Overtime rate £22.50/hr£ 22.50 / \mathrm{hr} Targeted labour cost £11,050/wk Labour hours needed 650/wk Any hour worked over 40 hrs/wk must be paid at the overtime rate
For a 12-person team, how many extra workers should be hired to meet the labour hours needed without overtime? 5 17 55 170 921

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Problem 1046

Josh rented a truck for one day. There was a base fee of $19.95\$ 19.95, and there was an additional charge of 77 cents for each mile driven. Josh had to pay $133.14\$ 133.14 when he returned the truck. For how many miles did he drive the truck? \square miles

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Problem 1047

David will spend at most $30\$ 30 on gifts. So far, he has spent $21\$ 21. What are the possible additional amounts he will spend? Use cc for the additional amount (in dollars) David will spend. Write your answer as an inequality solved for cc.

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Problem 1048

Equations and Inequalities Solving a word problem using a one-step linear inequality
Bob runs each lap in 7 minutes. He will run at least 77 minutes today. What are the possible numbers of laps he will run today? Use n\boldsymbol{n} for the number of laps he will run today. Write your answer as an inequality solved for nn.

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Problem 1049

Solve for uu. 13=u7.68+713=\frac{u}{7.68}+7

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Problem 1050

Translate the sentence into an equation. Twice the difference of a number and 6 equals 5 . Use the variable xx for the unknown number. \square

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Problem 1051

Translate the sentence into an equation. Two less than the product of 3 and a number is 5 . Use the variable yy for the unknown number.

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Problem 1052

Translate the sentence into an equation. Seven times the sum of a number and 9 equals 2. Use the variable xx for the unknown number. \square

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Problem 1053

For each given value of xx, determine the value of yy that gives a solution to the given linear equations in two unknowns. 3x2y=18;x=4,x=53 x-2 y=18 ; \quad x=4, x=-5
If x=4x=4 what is yy ? \square

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Problem 1054

You are choosing between two health clubs. Club AA offers membership for a fee of $11\$ 11 plus a monthly fee of $20\$ 20. Club B offers membership for a fee of $23\$ 23 plus a monthly fee of $18\$ 18. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
In \square months the total cost of each health club will be the same.

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Problem 1055

The bus fare in a city is $1.50\$ 1.50. People who use the bus have the option of purchasing a monthly coupon book for $25.00\$ 25.00. With the coupon book, the fare is reduced to $0.50\$ 0.50. Determine the number of times in a month the bus mus be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.
The bus must be used \square times.

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Problem 1056

19. 3(2b)<103(b6)3(2-b)<10-3(b-6)

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Problem 1057

 Solve 274r=5rr=\begin{array}{c}\text { Solve } 27-4 r=5 r \\ r=\ldots\end{array}

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Problem 1058

Work out the value of uu in the equation below. 6u=225u6 u=22-5 u

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Problem 1059

(1)) 新, How many solutions does this equation have? 8u7(2u+2)=6u14-8 u-7(-2 u+2)=6 u-14 1)) 㸚 \square one solution infinitely many solutions

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Problem 1060

Solve 7y=5y+167 y=5 y+16 y=y=\ldots

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Problem 1061

Solve the system by graphing. y=x+3y=x1\begin{array}{l} y=x+3 \\ y=-x-1 \end{array}

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Problem 1062

Solve x23=8\frac{x}{2}-3=8 x=x=\ldots

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Problem 1063

Solve 29=5(2u3)29=5(2 u-3)

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Problem 1064

Which expression is equivalent to 4(4p+9)+p4(4 p+9)+p ? 17p+917p+365p+3636p+17\begin{array}{c} 17 p+9 \\ 17 p+36 \\ 5 p+36 \\ 36 p+17 \end{array}

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Problem 1065

For each ordered pair, determine whether it is a solution to the system of equations. {6x+7y=53x2y=8\left\{\begin{array}{l} 6 x+7 y=-5 \\ 3 x-2 y=-8 \end{array}\right. \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{(x,y)(x, y)} & \multicolumn{2}{|c|}{ Is it a solution? } \\ \cline { 2 - 3 } & Yes & No \\ \hline(5,5)(5,-5) & \bigcirc & \bigcirc \\ \hline(1,2)(-1,2) & \bigcirc & \bigcirc \\ \hline(4,2)(-4,-2) & \bigcirc & \bigcirc \\ \hline(7,3)(7,3) & \bigcirc & \bigcirc \\ \hline \end{tabular}

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Problem 1066

olve the given system of equations. 5 L+6 W9H=52 L7 W2H=43 L+W.7H=1\begin{aligned} 5 \mathrm{~L}+6 \mathrm{~W}-9 \mathrm{H} & =5 \\ 2 \mathrm{~L}-7 \mathrm{~W}-2 \mathrm{H} & =-4 \\ 3 \mathrm{~L}+W-.7 H & =1 \end{aligned}

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Problem 1067

For each ordered pair (x,y)(x, y), determine whether it is a solution to the inequality 6x3y>96 x-3 y>-9 \begin{tabular}{|c|cc|} \hline \multirow{2}{*}{(x,y)(x, y)} & \multicolumn{2}{|c|}{ Is it a solution? } \\ \cline { 2 - 3 } & Yes & No \\ \hline(7,8)(-7,-8) & 0 & 0 \\ \hline(3,4)(3,-4) & 0 & 0 \\ \hline(0,9)(0,-9) & 0 & 0 \\ \hline(2,7)(2,7) & 0 & 0 \\ \hline \end{tabular}

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Problem 1068

Solve the system by the addition method. 9x4y=954x+24y=55\begin{array}{r} 9 x-4 y=-9 \\ -54 x+24 y=55 \end{array}

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Problem 1069

The length of a rectangle is six inches more than two times the width. The perimeter is 30 inches. Find the length and width.
The length is \square inches, and the width is \square inches.

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Problem 1070

Write the matrix equation as a system of linear equations without matrices. [658041283][xyz]=[121]\left[\begin{array}{rrr} -6 & -5 & 8 \\ 0 & 4 & -1 \\ 2 & 8 & -3 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{r} -1 \\ 2 \\ 1 \end{array}\right]
Equation 16x5y+8z=11-6 x-5 y+8 z=-1
Equation 2 \square

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Problem 1071

Bookwork code: 3B Calculator not allowed
Solve 92x=59-2 x=-5 x=x=\ldots

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Problem 1072

Bookwork code: 3C Calculator not allowed
Solve 9=15+m39=15+\frac{m}{3} m=m=\ldots

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Problem 1073

Bookwork code: 3D Calculator not allowed
Work out the value of xx in the equation below. 2x73=5\frac{2 x-7}{3}=5

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Problem 1074

Determine whether the lines are parallel perpendicular or neither. Next, write the slope of each equation. y=abx+cdxmy=n\begin{array}{c} y=\frac{a}{b} x+c \\ d x-m y=n \end{array} a=4b=6c=10d=12 m=8n=5a=4 \quad b=6 \quad c=-10 \quad d=12 \mathrm{~m}=-8 \quad \mathrm{n}=-5 y=46x10y=\frac{4}{6} x-10 12x+8y=512 x+8 y=-5

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Problem 1075

8. If x2=5y212\frac{x}{2}=\frac{5 y}{2}-\frac{1}{2} and 0.02x+0.05y=0.320.02 x+0.05 y=-0.32 then what is the value of yy ? (a) -2 (b) -1 (c) 1 (d) 2 (e) None of these

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Problem 1076

Sistemi: a) {x=y+1{1+2x=y\begin{array}{l} \{x=y+1 \\ \{1+2 x=y \end{array}

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Problem 1077

b) {xy=3{x2y=0\begin{array}{l}\{x-y=3 \\ \{x-2 y=0\end{array}

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Problem 1078

Solve the equation. 2z+6=5zz=\begin{array}{c} 2 z+6=5 z \\ z=\square \end{array}

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Problem 1079

Complete parts (A)(A) and (B)(B) below for the minimization problem to the right. (A) Form the dual problem.
Maximize P=6y1+6y2P=6 y_{1}+6 y_{2} subject to 4y1+y23,y1+4y2214 y_{1}+y_{2} \leq 3, y_{1}+4 y_{2} \leq 21 and y1,y20y_{1}, y_{2} \geq 0 (Simplify your answers. Type'expressions using y1y_{1} and y2y_{2} as the variables. Use a comma to separate answers as needed.) (B) Find the solution to the original problem by applying the simplex method to the dual problem. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The minimum is C=\mathrm{C}= \square \square and x2=x_{2}= \square . (Simplify your answers.) B. The optimal solution does not exist.

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Problem 1080

Solve the inequality. Graph the solution. 3p+2103 p+2 \geq-10
The solution is p>4p>-4. \hookleftarrow \quad \leftrightarrow

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Problem 1081

Solve the inequality. Graph the solution. 825(k2)-8 \leq \frac{2}{5}(k-2)
The solution is \square 1.

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Problem 1082

Solve the inequality. Graph the solution. 14(d+1)<2-\frac{1}{4}(d+1)<2
The solution is \square .

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Problem 1083

Let u,w,v1,v2u, w, v_{1}, v_{2}, and v3v_{3} be the vectors in R4\mathbb{R}^{4} defined by u=[17121610]w=[29122914]v1=[72619]v2=[219118]v3=[68111]u=\left[\begin{array}{l} 17 \\ 12 \\ 16 \\ 10 \end{array}\right] \quad w=\left[\begin{array}{c} 29 \\ 12 \\ -29 \\ 14 \end{array}\right] \quad v_{1}=\left[\begin{array}{c} 7 \\ -2 \\ 6 \\ -19 \end{array}\right] \quad v_{2}=\left[\begin{array}{c} -2 \\ -19 \\ 1 \\ -18 \end{array}\right] \quad v_{3}=\left[\begin{array}{c} 6 \\ -8 \\ -11 \\ -1 \end{array}\right] (a) Is uspan{v1,v2,v3}u \in \operatorname{span}\left\{v_{1}, v_{2}, v_{3}\right\} ? Write all zeros if it is not in the span or write zero as a non-trivial (not all zero coefficients) linear combination of u1,v1,v2u_{1}, v_{1}, v_{2}, and v3v_{3} if uu is in the span. 0=u+v1+v2+v30=\square u+\square v_{1}+\square v_{2}+\square v_{3} (b) Is wspan{v1,v2,v3}w \in \operatorname{span}\left\{v_{1}, v_{2}, v_{3}\right\} ? Write all zeros if it is not or if it is in the span write zero as a non-trivial (not all zero coefficients) linear combination of ww, v1,v2v_{1}, v_{2}, and v3v_{3} if ww is in the span. 0=w+v1+v2+v30=\square w+\square v_{1}+\square v_{2}+\square v_{3} (c) Type the dimension of span{v1,v2,v3,u}\operatorname{span}\left\{v_{1}, v_{2}, v_{3}, u\right\} : \square

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Problem 1084

L. 6 Slope-intercept form: write an equation A42
A line has a slope of 2 and a yy-intercept of 58\frac{5}{8}. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest forn \square Submit

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Problem 1085

L. 6 Slope-intercept form: write an equation A42 You
A line has a slope of 6 and passes through the point (2,16)(-2,-16). Write its equation in slopeintercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form. \square

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Problem 1086

Solve the inequality. Graph the solution. 203.2(c4.3)20 \geq-3.2(c-4.3)
The solution is \square .

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Problem 1087

```latex \begin{tabular}{l|l|l} \text{multi-step equation and explain.} & \\ \hline \text{A. 1} & \begin{tabular}{l} \text{I can solve linear equations with rational} \\ \text{coefficients} \end{tabular} & \text{8. EE. 7} \end{tabular}

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Problem 1088

L. 6 Slope-intercept form: write an equation A42 You
A line passes through the points (4,18)(4,18) and (9,18)(9,18). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. \square Submit

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Problem 1089

Solve the linear programming problem.  Maximize P=15x+25y Subject to 0.6x+1.2y9000.03x+0.04y360.3x+0.2y300x,y0\begin{aligned} & \text { Maximize } P=15 x+25 y \\ \text { Subject to } \quad 0.6 x+1.2 y & \leq 900 \\ 0.03 x+0.04 y & \leq 36 \\ 0.3 x+0.2 y & \leq 300 \\ x, y & \geq 0 \end{aligned}
What is the maximum value of P ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. P=P= \square (Simplify your answer. Type an integer or a fraction.) B. There is no maximum value of PP.

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Problem 1090

Algebra 1 L. 6 Slope-intercept form: write an equation A42
A line passes through the points (11,10)(-11,10) and (14,10)(14,-10). Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. \square Submit

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Problem 1091

A line has a slope of 0 and passes through the point (10,6)(10,6). Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. \square Submit

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Problem 1092

Buscar 5:22 p.m. Dom nov 17
Graph this line: y6=13(x+3)y-6=-\frac{1}{3}(x+3)
Click to select points on the graph. Submit

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Problem 1093

Graph this line: y+5=15(x+6)y+5=\frac{1}{5}(x+6)
Click to select points on the graph. Submit

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Problem 1094

Graph this line: y+2=2(x+4)y+2=2(x+4)
Click to select points on the graph.

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Problem 1095

2+25x+17=35-2+25 x+17=-35

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Problem 1096

13. Taxi fare is $1.00\$ 1.00 for the first 12\frac{1}{2} mile and $0.35\$ 0.35 for each additional 12\frac{1}{2} mile. How many miles can a passenger ride for $3.10\$ 3.10 ? (A) 3123 \frac{1}{2} (B) 4 (C) 6126 \frac{1}{2} (D) 7 (E) 7127 \frac{1}{2}

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Problem 1097

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

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Problem 1098

4 Which situation is best represented by the inequality 12x+7010x+8012 x+70 \geq 10 x+80 ? (F) Cell phone company A charges an $80\$ 80 deposit and $10\$ 10 each month for unlimited service. Cell phone company B charges a $70\$ 70 deposit and $12\$ 12 each month for unlimited service. After how many months, xx, will cell phone company A cost more than cell phone company B? G Caroline receives $80\$ 80 for her birthday and earns $10\$ 10 each time she babysits. Addison has saved $70\$ 70 and earns $12\$ 12 each time she babysits. How many times must the girls babysit, xx, so that Addison has at least as much money as Caroline? H The science club plans a field trîp. A trip to an observatory will cost $80\$ 80 for gas plus a $10\$ 10 entrance fee per member. A trip to a planetarium will cost $70\$ 70 for gas plus a $12\$ 12 entrance fee per member. How many miles, xx, can the science club travel so that the observatory trip is less expensive than the trip to the planetarium? J.Marco wants to rent a drum set. At Music World, the cost to rent drums is $12\$ 12 per month plus an $80\$ 80 deposit. Instrumental Music rents drums for $10\$ 10 per month with a $70\$ 70 deposit. How many months, xx, can Marco rent drums from Music World and pay less than he will at Instrumental Music?

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Problem 1099

Graph this line: y2=12(x+7)y-2=\frac{1}{2}(x+7)
Click to select points on the graph. Silhmit Practice in the app

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Problem 1100

ixl.com
Graph this line: y+6=27(x2)y+6=-\frac{2}{7}(x-2)
Click to select points on the graph. Submit Practice in the app

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