solving system using subsitution
question
a shopper purchased 8 t-shirts and 5 pairs of pants for $220.The next day he purh pair of purchased 5 tshirts and 1 pair of pants for $112.How much does each tshirt and each pair of pants cost? ...?

Answers

Answer 1
Below is the solution:

8t + 5p = 220
5t + p = 112
 
From the second equation:
p = 112 - 5t
 
Replace into first:
8t + 5(112 - 5t) = 220
t = 20


 p = 112 - 5t = 112 - 100 = 12

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Related Questions

Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b.

A. –7
B. 7
C. 14
D. 32

Answers

The best and most correct answer among the choices provided by your question is the third choice or letter C.

If ST = 21, SP = 3b – 11, and PT = b + 4, the value of b would be 14.


I hope my answer has come to your help. God bless and have a nice day ahead!

As a salesperson at Roaring Waves Beach Supplies, Carissa receives a monthly base pay plus commission on all that she sells. If she sells $500 worth of merchandise in one month, she is paid $385. If she sells $1,000 of merchandise in one month, she is paid $470.

Find Carissa's salary when she sells $1,900 worth of merchandise. ...?

Answers

Carissa receives 17$ for each 100$ of merchandise she sells.This is on top of the traditional rate of 300 dollars a month.She will make 623$ for 1900$ worth of merchandise.

Answer:

$623

Step-by-step explanation:

Let us suppose that the

Earning = y

Fixed payment = c

Commission paid = m per unit

Case 1.

When 500 units are sold, Earning y = $385

Earning = Fixed Payment + Commission paid per unit * Number of units

385=c+m*500

385=c+500m   ________(a)

Case 2.

When 1000 units are sold  earning y = $470

Earning = c+m*1000

470=c+1000m _________(b)

Subtracting (a) from (b) we get

85=500m

[tex]m=\frac{85}{500}\\=0.17[/tex]

Putting this value of m in (a)

[tex]385=c+\frac{85}{500} * 500[/tex]

385=c+85

c=300

Hence the fixed payment is $300 and the commission given is $0.17 per unit

Case 3 :

Number of Units sold = 1900

Earning = 300+0.17*1900

Earning = 300+323

Earning = 623

Hence The earning will be $623

What is the maximum number of turns in the graph of f(x)=2x^3-2x^2+7x-25 ?

Answers

maximum number of turns in a cubic equation is always 2

the maximum number of turns will always be equal to one less degree of the poly
hope this helps

Answer:

The maximum number of turns in the graph of f(x) is:

                                2

Step-by-step explanation:

Turning Point of a graph--

The turning point of a graph is a point where the graph changes it's behavior i.e. it changes from increasing to decreasing and from decreasing to increasing.

The polynomial of degree n has atmost " n-1 " turning points.

Here we are given a polynomial f(x) as:

[tex]f(x)=2x^3-2x^2+7x-25[/tex]

The polynomial is of degree 3.

Hence, the maximum number of turning points of the function f(x) is: 3-1=2

6 1/2 as an improper fraction

Answers

6 1/2 as an improper fraction is 13/2

Which of the four triangles was formed by a translation of triangle XYZ?

A
B
C
D

Answers

I believe it's B, since your just sliding it 

Answer:

Options A & B

Step-by-step explanation:

Given is a triangle XYZ in the I quadrant.  There are four more triangles A, B,C and D given.

We have to find that which one is the translation of XYZ

We know that by translation we must get a congruent triangle as XYZ.

By simply seeing we can say that C and D are not congruent with XYZ.

So these two are eliminated

Remaining are A and B.

Both A and B are right

This is because XYZ is transformed into B by shifting 7 units horizontal to the left.

A is the reflection of B about x=-5.5

Thus both A and B are right

What is the conclusion of the following statement?
A number is even if the number is divisible by 6.

A. A number is even if the number is divisible by 6.

B. A number is divisible by 6 if the number is even.

C. A number is divisible by 6.

D. The number is even.

Answers

D. The number is even. Is the conclusion

Answer: Hello mate! The correct answer is D.

the statement is "A number is even if the number is divisible by 6."

Here the hipotesis is "the number is divisible by 6", and this hipotesis implies the conclussion, wich is "a number is even". This is because the statement implies that te first thing we check is if the number is divisible by 6, and then we can know if the number is even or not.

this can be written as

"if a number is divisible by 6, then the number is even"

where is more easy to see wich one is the conclussion of the statement.

Then you can see that the right answer is D "the number is even"

Given 4x-8y=8, transform the equation into slope intercept form

Answers

4x - 8y = 8
Subtract 4x from each side.

-8y = 8 - 4x
Divide -8 to each.

y = -1 + 1/2x

So, the answer is y = 1/2x - 1
subtract 4x and divide by negative 8 to isolate Y
Y=-.5x-1 

The range of f(x) = logb x is the set of all negative real numbers.
a.true
b.false

Answers

Answer:

Statement is false .

Step-by-step explanation:

Given : The range of f(x) = [tex]log_{b}(x)[/tex] is the set of all negative real numbers.

To find : Statement is true or false.

Solution : We have given that function f(x) = [tex]log_{b}(x)[/tex].

Range :  range of logarithm function is all real numbers (-∞, ∞)

Therefore, Statement is false .

archie earns 4$ each week for doing his chores.how much money will archie earn in 2 months if there are 4 weeks in each month?

Answers

4$×4=16$ 16$+16$=32$.
archie earns 32$ in 2 minths

Answer:

can we skip to the good part? oh oh oh ohhhhh mhhhmhmhmhhhhhhhmh

Step-by-step explanation:

drink some coco juice and add some keyboard and it will be HAPSOD

hapsod is the one who absorb the hapsod

you roll two dice what is the probability that the sum of the dice is less than 5 and one dice shows a 2? ...?

Answers

Lets say the 1st die rolled a 2 - there would be 2 combinations for which the sum of dice being < 5 : 2,1 2,2 Now say the 2nd die rolled a 2 - there would be 2 combinations for which the sum of dice being < 5 : 1,2 2,2 Now we want to count all cases where either dice showed a 2 and sum of the dice was < 5. However note above that the roll (2,2) is counted twice. So there are three unique dice roll combinations which answer the criteria of at least one die showing 2, and sum of dice < 5: 1,2 2,1 2,2 The total number of unique outcomes for two dice is 6*6=36 . So, the probability you are looking for is 3/36 = 1/12

A copy machine makes 114 copies in 4 minutes and 45 seconds. How many copies does it make per minute?

Answers

I would assume on how to answer this would be to shift the 4 minutes and 45 seconds into a fraction.
Since 45/60 seconds is basically 3/4ths you can deduce that it takes 4.75 minutes.
With that said I then believe you just divide 114 by 4.75 to get your answer.

To determine the number of copies made per minute, the total time of 4 minutes and 45 seconds is first converted to 4.75 minutes. Dividing the total copies (114) by the total time in minutes (4.75) gives us 24 copies per minute.

Calculating Copies Per Minute

To find out how many copies the machine makes per minute, we need to convert the total time into minutes. There are 4 minutes and 45 seconds. Since there are 60 seconds in a minute, we can convert 45 seconds into minutes by dividing by 60, which gives us 0.75 minutes. Therefore, the total time in minutes is 4 + 0.75 = 4.75 minutes.

Now, we use the given information that the copy machine makes 114 copies in 4.75 minutes to calculate the number of copies it makes per minute:

Copies per minute = Total copies / Total time in minutes

Copies per minute = 114 copies / 4.75 minutes

Copies per minute = 24 copies per minute (rounded to the nearest whole number)

It takes carl 2/3 of an hour to clean his room every day. How many hours did he spend cleaning his room in the month of May?

Answers

So 2/3 of an hour is 40. And there is 31 days in May. Multiply 40 by 31 and you will get 1,240. Divide this by an hour so 1240/60 will equal 20.6666667 which is roughly 21 hours. Approximately 21 hours is your answer.

Find the mode.19, 1, 17, 19, 3, 20, 5, 2

Answers

The mode of this set is 19.

1. **List the Numbers**: Start by listing out all the numbers in the set.

  [tex]\[ 19, 1, 17, 19, 3, 20, 5, 2 \][/tex]

2. **Count Frequency**: Count how many times each number appears in the list.

  - 19 appears twice.

  - 1 appears once.

  - 17 appears once.

  - 3 appears once.

  - 20 appears once.

  - 5 appears once.

  - 2 appears once.

3. **Identify the Most Frequent Number**: The mode is the number that appears most frequently. In this case, 19 appears twice, which is more than any other number in the set. Therefore, the mode of this set is 19.

for the normal (perpendicular) line to the curve y= square root of 8-x^2 at (-2,2) would the slope be 1/2? ...?

Answers

Final answer:

The slope of the normal line to the curve y = sqrt(8 - x^2) at the point (-2, 2) is -1/2.

Explanation:

The question asks for the slope of the normal line to the curve y = sqrt(8 - x^2) at the point (-2, 2). To find the slope of the normal line, we need to find the derivative of the given curve and evaluate it at the given point. The derivative of y with respect to x is d/dx [sqrt(8 - x^2)]. Using the chain rule, the derivative is -x / sqrt(8 - x^2).

To find the slope of the normal line, we take the negative reciprocal of the derivative. So the slope of the normal line is 1 / (x / sqrt(8 - x^2)). Evaluating this at x = -2, we get the slope of the normal line as -1/2.

Evaluate a + b ÷ 2, if we know a = 3 and b = 6. A. 4 B. 6 C. 1 D. 4.5

Answers

Your aswer would be "6"  :) 

Because→  3 ( 6 ÷ 2) which is reverse to: 3 + 3 which is equaling to "6" 


A rectangular piece of metal is twice as long as it is wide. Squares with sides 4 inches long are cut from the four corners and the flaps are folded upward to form a box. If the volume is 1536 inches cubed, what were the original dimensions of the piece of metal? ...?

Answers

Original rectangle has sides x and 2x.
 the box will have length 2x - 8
 width x - 8
 and height 4.
 So
 the volume is length x width x height:
(2x - 8)(x - 8)(4) = 15362x^2 - 24x + 64
= 384x^2 - 12x + 32
= 192x^2 - 12x - 160
= 0(x - 20)(x + 8)
 = 0x
 = 202x
= 40
check: 12 * 32 * 4
 = 1536

The slope of diagonal AB is , _ and its equation _ is .

Answers

Given two points (x₁,y₁) and (x₂,y₂) the slope of the line that passes through theses points will be:
m=(y₂-y₁)/(x₂-x₁)

We have two points A(-2,-2) and B(2,-2); therefore the slope will be:
m=(-2+2)/(2+2)=0/4=0

slope-intercept form:
y=mx +b
m=slope
b=y-intercept =-2

y=0x-2
y=-2

Answer: The slope of diagonal AB is 0 and its equation is y=-2

Slope = Rise/Run

Given: 
Rise = 0
Run = 5

Therefore,
Slope = 0/5
          = 0
The general form of a linear equation is : 
y = mx + b

m = slope 
b = y-intercept

Given:
Slope = 0
Y-intercept = -2

Hence,
Equation is : y = -2

Your cell phone company started a rewards club. For every three texts sent, you get 15 points. You need 1800 points for a prize. How many texts do you need to send to get that prize

Answers

Answer:

360 texts

Step-by-step explanation:

Given,

The points given for 3 texts = 15,

So, the points given for 1 text = [tex]\frac{15}{3}[/tex] = 5,

If x text are sent,

Then the number of points earned = x × points for 1 text

= 5x

According to the question,

5x = 1800

[tex]\impilies x = \frac{1800}{5} = 360[/tex]

Hence, 360 texts needs to send to get 1800 points.

Part A
Ling and $44 each week for six weeks mowing lawns in his neighborhood. His weekly expenses for supplies are d. Write an expression to show the amount of money ling have after paying his expenses.
Part B
If Ling's expenses are $13 each week, how much money will ling have?

Answers

I'm not sure because some months have a different amount of days so it will be hard to determine precisely. Without further due, lets begin...

Part B:
Lets say that each month has 4 weeks in it. That means go ahead and multiply 4 x 6 = 24, 24 is the amount of weeks total.
Then, do 13 x 24 which equals 312.

That means he earned 312 dollars.

WILL MARK BRAINLIEST Harry had $32. He spent all the money on buying 3 notebooks for $x each and 4 packs of index cards for $y each. If Harry had bought 5 notebooks and 5 packs of index cards, he would have run short of $18. A student concluded that the price of each notebook is $5 and the price of each pack of index cards is $1. Which statement best justifies whether the student's conclusion is correct or incorrect? The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2). The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (8, 2). The student's conclusion is correct because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (5, 1). The student's conclusion is correct because the solution to the system of equations 3x − 4y = 32 and 5x − 5y = 50 is (5, 1).

Answers

The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).

Answer:

The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).

Step-by-step explanation:

To see if the answer to an equation is right, you just have to put the value of X and Y into the equation system, since we don´t have the equation system that the student used, we will make our own, so we will start by stating that Notebooks are represented by X and index cards are represented by Y.

Your equation would look like this:

3x+ 4y=34

The student said that the price of the notebook is $5 and the index card would be $1, now we put those values into the equation.

3(5)+4(1)=32

15+4=32

19=32

Since 19 is not equal to 32, the equation is wrong, therefore the student is wrong.

Now to solve it you get your other equation, since if he had bought 5 and 5 he would have needed 18 extra dollars that means that

5x+5y= 32 +18

5x+5y=50

With the two equations you just use elimination process to create a single equation:

(5x+5y=50)-3=  -15x-15y=-150

(3x+4y=32)5 =   15x+20y= 160

You eliminate the x from the equation and are left with:

-15y+20y= -150+160

5y=10

y=[tex]\frac{10}{2}[/tex]

y=2

Now that you have the value of Y you just put it into the equation to know the value of x:

5x + 5(2) = 50

5x+10=50

You clear the x and the result would look like this:

x= [tex]\frac{50-10}{8}[/tex]

x=8

Select all the statements that are true about the linear equation. y = 4x - 3

a. The point (1,1) is on the graph of the equation.
b. The point (0,3) is on the graph of the equation.
c. 4x - y = -3 has the same graph.
d. The graph of the equation is the set of all points that are solutions to the equation.
e. The graph of the equation is a single point, representing one solution to the
equation.

Think that be is an answer but not sure.
Need help asap! It's a multiple answer choice worth a lot of points.

Answers

The answer is B. Have a nice day

The correct statements for this question would be:

a) The point (1, 1) is on the graph of the equation."

d) The graph of the equation is the set of all points that are solutions to the equation.

Option (a) and (d) are true.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The linear equation;

y = 4x - 3

Now, By option a;

To check the point (1, 1) is on the graph of the equation.

We can substitute x = 1 and y = 1 in the equation of line as;

y = 4x - 3

1 = 4 × 1 - 3

1 = 4 - 3

1 = 1

Thus, The point (1,1) is on the graph of the equation.

For option b;

Since, The point (0, 3) is not satisfy the equation y = 4x - 3.

Hence, Option b is not true.

For option c;

Since, The y - intercept of the line 4x - y = -3 and line y = 4x - 3 is not same.

Hence, Both have different graph.

Clearly, By the graph of y = 4x - 3 is is the set of all points that are solutions to the equation.

So, Option d is true.

Thus, The correct statements for this question would be:

a) The point (1, 1) is on the graph of the equation."

d) The graph of the equation is the set of all points that are solutions to the equation.

Option (a) and (d) are true.

Learn more about the equation of line visit:

https://brainly.com/question/13763238

#SPJ2

A $5000 investment earns $550 annual simple interest in one year. What is the annual interest rate?

Answers

I = prt 1) nope: since she earned 1536, that is your interest (I) 1536 = p*0.04*8 1536 = 0.32p 1536/0.32 = 0.32p/0.32 p = $4800 2) 550 = 5000*r*1 550/5000 = 5000r/5000 0.11 = r = 11%
550=5000r,,r=0.11*100=11%

Write the equation of the line perpendicular to 3x + y = -8 that passes through (-3,1) . Write your answer in slope-intercept form. Show your work.

Answers

y = -3x-8 , m=-3
m•m1 = -1
-3•m1 = -1
m1 = 1/3
from y-y1 = m (x-x1)
y-1 = 1/3(x+3)
y-1 = 1/3x +1
y = 1/3x + 2

Which line segment is a chord of circle E in the diagram below?

a) DE
b) BC
c) AB
d) CD

Answers

the answer is D.  
A  chord is a line segment connecting two points on a curve

Answer

Find out the which line segment is a chord of circle E in the diagram below.

To prove

As given

Definition of a chord

 A chord is the striaght line  whose  endpoints are lies in the circle.

Now as shown in the diagram given in the question.

CD is the striaght line  whose endpoints lies in the circle E .

Therefore CD is a chord of circle E.

Option (d) is correct.


If 80 is 80 percent of a value what is that value

Answers

100 is the right answer

Describe the variation 3xy = 5.

A. y varies inversely as the square of x.
B. y varies inversely as x.
C. y varies directly as x.
D. y varies directly as the square of x.

Answers

is B.y varies inversely as x.

Answer:

The answer is the option B

y varies inversely as x.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]yx=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

[tex]3xy=5[/tex] -----> rewrite

[tex]xy=5/3[/tex]

The value of k is equal to [tex]k=\frac{5}{3}[/tex]

therefore

y varies inversely as x.

How many times does 41 go into 278?

Answers

It goes into it 6 times if you divide it.
It's 6.78 and repeats but all you have to do is simply divide

Jeremy baked 9 cakes for the bake sale. He sifted 2 cups of powdered sugar evenly on the tops of the cakes.    How much powdered sugar is on each cake?  

Answers

If you divide 2 cups by 9 you get .22 cups per cake.
2/9 cups. 2 cups divided by 9 cakes

a rectangle has an area of 16ft squared, every dimension is multiplied by a scale factor, and the new rectangle has an areaof 64 ft squared, what was the scale factor? ...?

Answers

The scale factor is
 =2(8)(2)
 = 16(8 (2))(2 (2))
=64

Answer:

Scale factor is 2

Step-by-step explanation:

A rectangle has an area of 16ft²

That is

            Length₁ x Breadth₁ =  16 ft²

Every dimension is multiplied by a scale factor, let the scale factor be s.

New dimensions are

                  Length₂ = s x Length₁

                  Breadth₂ = s x Breadth₁

New area is given by

                 Area = Length₂ x Breadth₂ = s x Length₁ x s x Breadth₁

                 Area = s² x Length₁ x Breadth₁

                 64 = s² x 16

                  s² = 4

                  s = 2

So scale factor is 2

to calculate a rewards program incentive, you?

Answers

Final answer:

Rewards program incentives are calculated by considering the alignment between the rewards offered and the needs and values of the participants. These incentives must balance the trade-off between work and compensation, adhering to principles of effort and fair compensation.

Explanation:

Understanding Rewards Program Incentives

To calculate a rewards program incentive, one must consider the various factors that influence both the likelihood and the extent to which individuals participate in the program. Such a program typically aims to increase desired behaviors - for example, increasing purchases or promoting consistent work performance - by offering some form of reward or compensation. The effectiveness of these incentives is often determined by how well they align with participants' values and needs.

In contexts where these incentives might impact work behavior, one must consider the trade-offs individuals face. If a program reduces government assistance dollar for dollar as earnings increase, this could diminish the incentive to work. Conversely, if the program allows individuals to maintain a level of government assistance even as they earn income, some might choose to work fewer hours (choice S) but still maintain or increase their total income. Others might continue to work the same number of hours (choice R) or even more, depending on how the incentives align with their personal circumstances and preferences.

There are also principles of effort and compensation to consider. Ideally, a well-designed incentive program rewards individuals according to the effort they put in and the costs they incur. However, the balance between maximizing efficiency for the program and providing adequate motivation for the participants can be complex and requires careful calibration.

Final answer:

To calculate a rewards program incentive, it's important to analyze the relationships among work hours, income, and effort. Changes in incentives may influence individuals to adjust their work hours to maximize benefits. The goal is to find the sweet spot where the incentive structure aligns with the desired behavior, whether that's working more, the same, or fewer hours for optimal compensation.

Explanation:

To calculate a rewards program incentive, you need to assess the different factors that influence choice and compensation. For instance, when a program provides financial incentives without reducing them entirely as earnings increase, individuals might alter their work hours to maximize overall income. This could mean choosing a point on the budget line, like S, where they work fewer hours but have greater income, or a point like R, maintaining the same work effort, or even increasing their hours, depending on the incentives.

The decision-making process regarding work hours and income can be complex, involving considerations of effort and compensation. These are guided by incentives and how individuals weigh the trade-offs between labor and leisure. Furthermore, such choices reflect the underlying principle that rewards should ideally align with the effort and costs involved in a person's work activity.

Changes in incentives can lead to different choices. If rewards or penalties for certain actions are adjusted, individuals may shift their decisions accordingly to maximize their benefits. For example, if a program becomes more generous without penalizing additional earnings, some may opt to work less, as they could still maintain or increase their income levels. Conversely, if the program became less generous or introduced greater penalization for earnings, individuals might be inclined to work more to achieve the same level of income.

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