The number of households in a local school district has been increasing linearly over the last ten years. In 2010, there were 985 households, and in 2020 there were 1579 households. Question
2/10 Use this information to create a linear model for the number of households in the school district. Let H represent the number of households at t represent the number of years since 2010.
The number of households in a local school district has been increasing linearly over the last ten years. In 2010, there were 985 households, and in 2020 there were 1579 households. Question
3/10 Let H represent the number of households at t represent the number of years since 2010. The linear model for the number of households in the school district is H=59.4t+985 Use the linear model to predict the number of households in 2025.
Question 12
You are offered two different sales jobs. The first company offers a straight commission of 5% of the sales. The second company offers a salary of $440 per week plus 3% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good?
Solve the system of linear equations using the elimination method.
31x−32y+z=21x−43y+z=−2x−y+z=−2x−y+4 The unique solution to the system is □□ , ).
(Type an exact answer in simplified form.)
Solve the system with the addition method:
{6x+6y=−33x−5y=−4 Answer: (x,y)=( ,
□ ) Preview x
Preview y
Enter your answers as integers or as reduced fraction(s) in the form A/B.
Solve by the elimination method.
2x=52+5y3x=2−2y Select the correct choice below and fill in any answer boxes in your choice.
A. There is one solution. The solution of the system is □ .
(Simplify your answer. Type an ordered pair.)
Incomplete
B. There are infinitely many solutions of the form ( x, □ ).
(Simplify your answer.)
C. There is no solution.
2. The cost of auto repairs at a dealership is $175 for the parts plus $25 per hour for labor. The cost of the same repairs at a neighborhood garage is $190 for the parts plus $22.50 per hour for labor. State your answers in context.
a) Create and solve an algebraic model to determine when the cost of repairs at the neighborhood garage is less than the cost of repairs at the dealership.
\text{Your sister tells you that she will do the whole job for \$300, parts included. How many hours of labor would be required at the neighborhood garage to make the cost at the garage exceed what your sister will charge for the job? (Use a model to answer this.)} \\ \text{The hourly labor rate at the neighborhood garage is \$6 per hour.} \\
Solve the system. If there is no solution or if there are infinitely many solutions and the system's equations are dependent, so state.
2x−10y+6z=x+2y−z=10x−y−z=−100−27 Select the correct choice below and fill in any answer boxes within your choice.
A. There is one solution. The solution set is \{( □ , □□ )\}.
(Simplify your answers.)
B. There are infinitely many solutions.
C. There is no solution.
There's a roughly linear relationship between the length of someone's femur (the long leg-bone in your thigh) and their expected height. Within a certain population, this relationship can be expressed using the formula h=62.6+2.35f, where h represents the expected height in centimeters and f represents the length of the femur in centimeters. What is the meaning of the h-value when f=49 ? Answer The expected height for someone with a femur length of 177.75 centimeters. The femur length for someone with an expected height of 49 centimeters. The change in expected height for every one additional centimeter of femur length. The expected height for someone with a femur length of 49 centimeters. Submit Answer
A person invested $8100 for 1 year, part at 7%, part at 11%, and the remainder at 13%. The total annual income from these investments was $915. The amount of money invested at 13% was $300 more than the amounts invested at 7% and 11% combined. Find the amount invested at each rate. The person invested $□ at 7$□ at 11 and \\squareat13 \%$.
13.
[-/1 Points]
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LARPCALC11 8.1.056.MI. Write a system of linear equations represented by the augmented matrix. (Use x,y, and z as you order as they appear in the augmented matrix. Do not perform any row operations.)
⎣⎡100210−211−111−3⎦⎤□□ Use back-substitution to solve the system.
(x,y,z)=(□)□
回 To solve the equation below, what is the correct first step? 10x+7−10x=15 Simplify the left side by combining the 10x and −10x.
Subtract 10x from both sides of the equation.
Simplify by combining the 7 and 15 .
Divide both sides by 10x.
Cost, Revenue \& Profit
For these problems, x will represent the number of items and y will represent the money.
The fixed costs for a certain item are $120 per week. The cost to produce each item is $8 per item.
Using this information, what is the cost equation? Give your answer in slope-intercept form:
y=□ The retailer intends to sell each item for $10/ item.
Using this information, what is the revenue equation? Give your answer in slope-intercept form:
y=□ If in this week 84 items are made, and all items are sold in the week, what are the total costs to the retailer?
Cost =$□
What is the revenue from selling 84 items?
Revenue = \\squareFinally,whatistheprofitforthisretailer?Profit=\$$ $\square$
The given bar graph shows the number of rooms, bathrooms, fireplaces, and elevators in the building. Combined, there are 203 rooms, bathrooms, fireplaces, and elevators. The number of rooms exceeds the number of bathrooms and fireplaces by 72 . The difference between the number of fireplaces and elevators is 25 . If the number of bathrooms is tripled, it exceeds the number of fireplaces and elevators by 77 . Determine the number of rooms, bathrooms, fireplaces, and elevators in the building. The number of rooms is □ , the number of bathrooms is □ , the number of fireplaces is □ , and the number of elevators is □ in the building.
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality. This line runs through points (2,2),(4,4),(6,6), and (8,8).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k=x2−x1y2−y1 or k=4−24−2=22=1 The constant of proportionality for this line is 1. Find the constant of proportionality for each graph.
I.
k=
2.
k=
b
k=k=
Math
Examples 2 and 3
Find the inverse of each function. Then graph the function and its inverse. If necessary, restrict the domain of the inverse so that it is a function. 5. f(x)=x+2 6. g(x)=5x 7. f(x)=−2x+1 8. h(x)=3x−4 9. f(x)=−35x−8 10. g(x)=x+4 11. f(x)=4x 12. f(x)=−8x+9 13. f(x)=5x2 14. h(x)=x2+4
10/10 How can you check if an ordered pair is the solution to the system of equations? By ensuring the pair is on the graph By checking if the pair satisfies both equations By confirming the pair is not on the graph By checking if the pair satisfies at least one equation
Solve the following system of equations and fill in the values below:
40x+5y=−2015x−3y=1255x+2y=−8 The solution is x= Blank 1 and y= Blank 2 . Blank 1 Add your answer
Practice Test Content
Page 14 of 20 Question 14
5 Point Assume that the linear cost and revenue models apply and let x be the number of items.. An item costs $15 to make. If fixed costs are $3700 and profits are $4300 when 200 items are made and sold, find then the revenue equation is:
R(x)= Blank 1
(Please enter a simplified expression involving whole numbers and the variable x )
Blank 1 Add your answer
9:54 AM Mon Nov 25
Done
AA
myopenma Optional Module 7 Practice Test
Score: 163.5/270
Answered: 20/27 Question 18 Solve the system with the addition method:
{4x−3y=36x−4y=2 Answer: (x,y)=(□
Preview x
Preview y
Enter your answers as integers or as reduced fraction(s) in the form A/B.
Question Help:
Video
Submit Question
Practice Test
Answered: 22/27
Question 26 Solve the system with the addition method:
{−5x+y=233x−6y=24 Answer: (x,y)=1□□
Preview x
Preview y
Enter your answers as integers or as reduced fraction(s) in the form A/B.
Question Help: ■ Video
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Terrell arranges x roses at $3.50 each with 10 carnations at $2.25 each. He makes a bouquet of flowers that averages $3.00 per flower. Select the equation that models the situation.
A. 3.50x+2.25(10)=3(x+10)
B. 3.50x+2.25=0.75x
C. 3.50x+3=22.5(x+10)
D. 3.50x+2.50=0.75(x+10)
MTH1 W1, Unit 5- Solving Equations and Word Problems Lesson 1- Homework
Solve each equation in the space provided. Show work-properly, carefully, and neatly! !
a)
5x=37+8x=625x=5.
d)
g)
5x−2+x=9+3x+10
h)
b)
4x+9=−119x=−11.9x=4−20=−5
e)
e) f)
8−7x=−41−7x=−41−8−7x=−49x=−7−49x=7−7x=−41−8−7x=−49x=−7−49x=7−7x−7xxx=−41−8=−49=−49=7 c) −2x7x−5=6x+69x+4=8x−37x−6x+5
i)
5x+5−x=−7+x−2 Solutions a)5
b) -5
c) 7 d) -7
e) 11
f) -7
g)7
h) 3−14
i) 25
In a certain urban area, the relationship between the number of students, x, in thousands, and the number of schools, y, has an x-intercept of -4 and a slope of 43. Write an equation for this relationship in standard form.
□x−□y=□
Dwayne will spend $80 on video games. Used video games cost $10 each, and new video games cost $20 each.
Let x represent the number of used video games and let y represent he number of new video games he can buy. Which ordered pairs represent possible combinations of video games that Dwayne can buy?
A. (0,4)
B. (2,3)
C. (1,6)
D. (7,2)
E. (8,0)
Use the points shown on the graph to determine the slope of the line. Find the slope of the equation. Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a simplified fraction.)
A. The slope is undefined.
B. The slope of the line is -3 .
of games in a community center. They charge $8 per person for entry into the event. The group wol to earn at least $600, after paying for the cost of renting the space, which is $40 an hour. 1. If x represents the number of entry tickets sold and y the hours of space rental, which inequal represents the constraints in the situation?
a. 8x−40y<600
b. 8x−40y≤600
c. 8x−40y>600
d. 8x−40y≥600
Find the inverse of the function. Is the inverse a function?
f(x)=2x−8f−1(x)=□□
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Exercice n∘5 ( 5 pts ). (Relations binaires). Les questions suivantes sont indépendantes
1) On définit sur R2 la relation ≪ par: (x,y)≪(x′,y′)⇔∣x′−x∣≤y′−y. Vérifier qu'il s'agit d'ume relation d'ordre. Cet ordre est-il total ?
2) On définit sur R2 la relation S par: (x,y)S(x′,y)⇔x−5y′=x′−5y
a) Montrer que S est une relation d'équivalence.
b) Vérifier que la classe d'équivalence du couple (0,0) est une droite D à préciser.
Gegeben ist die lineare Funktion f mit der Gleichung y=0,5x−2
a) Übernehmen Sie die folgende Wertetabelle und vervollständigen Sie diese für die Funktion f.
\begin{tabular}{|c|c|c|c|c|}
\hlinex & -3 & 0 & 1 & 6 \\
\hliney & & & & \\
\hline
\end{tabular} Zeichnen Sie den Graphen der Funktion f in ein Koordinatensystem.
b) Geben Sie für y=−1 den zugehörigen Wert für x an.
c) Der Graph der Funktion f schneidet die x-Achse im Punkt S. Geben Sie die Koordinaten des Punktes S an.
d) Durch den Punkt P(1;1) verläuft der Graph der Funktion g parallel zum Graphen der Funktion f.
Zeichnen Sie den Graphen der Funktion g in dasselbe Koordinatensystem.
Für Aứgabe 2 erreichbare BE: 6
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My Drive - Google Dr.
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Library - EatremeMa Graph these equations:
y=2xy=2x Click to select points on the graph.
y=2xy=2x
Question 3 of 10, Step 1 of 1
WILLIAM BURRIS
1/10
Correct Use a system of equations to solve the following problem. An investor decides to invest some cash in an account paying 6% annual interest, and to put the rest in a stock fund that ends up earning 9% over the course of a year. The investor puts $800 more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1950. How much money was invested at each of the two rates? Round to the nearest integer. Answer
How to enter your answer (opens in new window)
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Keyboard Shortcuts
\\squareat6 \%$\squareat9 \%$
Submit Answer
Application: 5 Marks 7. A catering company charges $590 for 20 guests and $740 for 26 guests. What is the cost per person? Provide "let" statements and show all calculations. [2 Marks]
The cost of 2 rackets and 3 squash balls is £21.63. The cost of 5 rackets and 7 squash balls is £52.90. Work out the cost of
a) a racket.
b) a squash ball.
368. Mootorpaat sõitis jõel vastuvoolu 16 km ja pöördus siis tagasi, kulutades tagasiteel 40 minutit vähem aega kui liikumisel vastuvoolu. Leidke paadi kiirus seisvas vees, kui jõe voolu kiirus on 2km/h.
Iname: Jude Elsayed
Date: 2024-11-25 Official Time: 11:38:00 Question 3 [10 points]
Give a basis for span(S), where S is the set given below.
⎩⎨⎧⎣⎡001⎦⎤,⎣⎡−212⎦⎤,⎣⎡10−5−9⎦⎤,⎣⎡6−3−9⎦⎤⎭⎬⎫ Number of Vectors: 1
⎩⎨⎧⎣⎡0002⎭⎬⎫
Question 3 (1 point)
✓ Saved A homogeneous system of linear equations consists of eight equations in six variables (unknowns). Which of the following is true?
The system can have no solution.
The system has between 1 and 6 solutions.
The system always has infinitely many solutions.
The system has either the trivial solution only or infinitely many solutions.
The system has only the trivial solution.
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Show Examples Rashaad is the youngest of three siblings whose ages are consecutive odd integers. If the sum of their ages is 63, find Rashaad's age. Answer Attempt 1 out of 2
Submit Answer
A scaffold of mass 64 kg and length 7.9 m is supported in a horizontal position by a vertical cable at each end. A window washer of mass 88 kg stands at a point 2.8 m from one end. What is the tension in (a) the nearer (relative to the person) cable and (b) the farther (relative to the person) cable?
(a) Number Units □
(b) Number □ Units □
(Algebra 1, Unit 2, Lesson 2)
Kiran's family is having people over to watch a football game. They plan to serve sparkling water and pretzels. They are preparing 12 ounces of sparkling water and 3 ounces of pretzels per person. Including Kiran's family, there will be 10 people at the gathering. A bottle of sparkling water contains 22 ounces and costs $1.50. A package of pretzels contains 16 ounces and costs $2.99. Let n represent number of people watching the football game, s represent the ounces of sparkling water, p represent the ounces of pretzels, and b represent Kiran's budget in dollars. Which equation best represents Kiran's budget? Select the correct choice.
(A) 12s+3p=b
(B) 12⋅10+3⋅10=b
(C) 1.50s+2.99p=b
(D) 1.50⋅6+2.99⋅2=b
B Alg1.2.4 Practice B
(Algebra 1, Unit 2, Lesson 2)
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distance. An object travels 100 feet in 2.5 seconds. Let the speed. S, be measured in feet per second.
Write an equation to represent the relationship between the three quantities (speed, distance, and time).
Type the answer in the box below.
The system in the figure below is in equilibrium, with the string in the center exactly horizontal. Block A weighs 39.0 N , block B weighs 50.0 N , and angle φ is 36.0∘. What are Find (a) tension T1, (b) tension T2, (c) tension T3, and (d) angle θ.
(a) Number Units □
(b) Number □ Units □
(c) Number □ Units □
(d) Number □ Units □
Problem Situation: Alec buys tickets to an amusement park.
He buys one adult ticket for $45 and four youth tickets.
He pays a total of $137.
What is the cost of a youth ticket?
Complete the equation to represent this situation.
The letter t represents the cost of a youth ticket.
CLEAR
CHECK
□t+45=□
Lesson 6-4 HW
Name:
Date: 11/25/2024 Question 1 Helmut is making a mosaic with a total of 290 blue tiles and green tiles. He chooses these number
of tiles in three shades of green: 68, 64, and 72 . How many blue tiles does he need to finish his mosaic? Blue tiles
Problem Situation: Ike has $126 in his bank account. He gets $20 for his birthday. He also has a part-time job that pays $8 per hour. How many hours will he need to work to have $250 in his bank account? Choose the equation that correctly models the situation. The letter h represents the hours lke will need to work.
CleAR
CHECK
(250−126)h=20+8126+20+8h=250250+126+20+8+250=h120+8h
Part C: The basketballs Noah packed had two different prices. Of the total number of basketballs sold, 60% had a price that was $21 more than the price of the remaining basketballs. The total amount of the store's sales for all the basketballs was $8,967. What was the price for one of the more expensive basketballs?
Enter answer here: