Suppose you buy 3 shirts and 2 pairs of slacks on sale at a clothing store for 72. The next day, a friend buys 2 shirts and 4 pairs of slacks for 96. If the shirts you each bought were all the same price and the slacks were also all the same price, then what was the cost of each shirt and each pair of slacks?

Answers

Answer 1

Taking into account the definition of a system of linear equations, the cost of each shirt is 12 and the cost of each pair of slacks is 18.

System of linear equations

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be found and they must give the solution proposed in both equations.

This case

In this case, a system of linear equations must be proposed taking into account that:

"S" is the cost of each shirt."PS" the cost of each pair of slacks

You buy 3 shirts and 2 pairs of slacks on sale at a clothing store for 72. The next day, a friend buys 2 shirts and 4 pairs of slacks for 96.

So, the system of equations to be solved is

[tex]\left \{ {{3S + 2PS=72} \atop {2S + 4PS=96}} \right.[/tex]

To solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Isolating the variable S from the first equation, you obtain:

3S= 72 - 2PS

S= (72 - 2PS)÷3

S= 72÷3 - 2PS÷3

S=24- 2/3PS

Replacing this expression in the second equation:

2(24 - 2/3PS) + 4PS= 96

Solving:

2×24 - 2×2/3PS+ 4PS= 96

48 - 4/3PS + 4PS= 96

48 + 8/3PS= 96

8/3PS= 96 - 48

8/3PS= 48

PS= 48÷ 8/3

PS= 18

Replacing this value in the expression S=24- 2/3PS, you obtain:

S= 24 -2/3×18

S= 24 - 12

S= 12

Finally, the cost of each shirt is 12 and the cost of each pair of slacks is 18.

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Related Questions

Which is the solution set of the inequality 15y - 9 < 36?
A. y > 9/5
B. y < 9/5
C. y > 3
D. y < 3

Answers

Answer:

D

Step-by-step explanation:

y < 3

the solution set is y< 3 also known as D

round each decimal to the nearest whole number 10.76

Answers

Answer:

11

Step-by-step explanation:

Answer: 11

Step-by-step explanation: Hope this helps:)

293 + 8 will mark brainiest

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Answer:

301

Step-by-step explanation:

bro :(

Answer:

301

Step-by-step explanation:

What is the difference of 18 ‒ (‒8)?

Answers

Answer: 26

Step-by-step explanation:

Answer:

26 is the answer because we have to subtract when the signs of the number are diffrent and add when it is same . so +18 - (-8) = 26

Given y = x^2 - 4, what is the value of y when x = -5?​

Answers

Answer:

21

Step-by-step explanation:

y = [tex]x^{2}[/tex] -4  Substitute in -5 for x

y = [tex](5)^{2}[/tex] - 4

y = 25 - 4

y = 21

Answer:

y = 21

Step-by-step explanation:

Plug in -5 into the equation

(-5)² - 4
25 - 4 = 21

The length of a bacterial cell is about 5 x 10−6 m, and the length of an amoeba cell is about 3.5 x 10−4 m. how many times smaller is the bacterial cell than the amoeba cell? write the final answer in scientific notation with the correct number of significant digits. 1.4 x 101 7 x 101 143 x 101 7 x 103

Answers

The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

What are scientific notations?

Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.

Calculation of the amount by which a bacterial cell is smaller than the amoeba cell

Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)

The length of a bacterial cell in scientific notations is 5 × 10^(- 6)

To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.

= 3.5 × 10^(- 4) / 5 × 10^(- 6)

= 0.7 × 10^(2)

= 7 × 10^(1)

Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

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the sum of her test scores 88+80=168 also she took 2 tests. her average would be?

the answer should be written in the form of coordinates.

Asap pls

Answers

Answer: her average is 84

Step-by-step explanation:

88+80=168/2 =84

the square quilt block shown is used in a larger quilt. the four small squares in the block are congruent, and the four small vertical rectangles in the block that are not squares are also congruent. the total area of the shaded regions is what fraction of the total area of the block? express your answer as a common fraction.

Answers

The total area of the shaded regions in fraction of the total area of the block is 3/8 as the common fraction.

What is common fraction?

A common fraction, sometimes known as a common fraction, is a fraction with an integer numerator and denominator. A common fraction may be used to identify a portion of a larger whole or set.

What is the formula for calculating a common fraction?

Multiply each component of a fraction by both the denominator of another fraction to find the common denominator. To calculate the common denominator of 1/3 + 2/5, multiply the 1 through 3 by 5 and the 2 and 5 by 3. You should obtain a total of 5/15 + 6/15. The fractions can then be calculated.

According to the given data:

Let's divide each square across four equal sections, for a total of 16 sections..

Using symmetry, one of the four portions in the top left square is shaded, and the same is true for the bottom right square.

Furthermore, two of the four squares inside this top right and bottom left corners are darkened.

Consequently,

the shaded area is:

{1 + 1 + 2 + 2}/ 16

6 /16 =  3 / 8

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Please help with problem 27​

Answers

Answer:

Step-by-step explanation:

I have a tip for you have you ever used the website Desmos graphing calculatr if you havnt i can help you a lot thats how i passed that class

admission to a certain university is determined by an entrance exam. the scores of this test are normally distributed with a mean of 400 and a standard deviation of 60. only students who score in the top 30% will be offered admission. april scores 425 on the test. choose the most accurate statement.

Answers

Only students who score in the top 30% will be offered admission - this statement is accurate.

What is the mean and standard deviation of the entrance exam?

In insights, the standard deviation is a proportion of how much variety or scattering of a bunch of values. A low standard deviation shows that the qualities will generally be near the mean of the set, while an elevated expectation deviation demonstrates that the qualities are fanned out over a more extensive territory. The standard deviation can generally be determined considerably more effectively with a number cruncher, and this might be satisfactory in certain tests. On my adding machine, you go into the standard deviation mode. Consequently, the main distinction among change and standard deviation is the units. For instance, in the event that we took the hours of 50 individuals running a 100-meter race, we would catch their time like a flash. Standard deviation assumes a vital part in the realm of money. In finance standard deviation is a factual estimation, when it's applied to the yearly pace of return of a venture.

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Solve for X
I need help please

Answers

Answer:

x = 24.5

Step-by-step explanation:

First find angle G: 90 degrees

Then do 90 degrees minus 41: 49 degrees

Find 49 = 2x - 8

Do 49 + 8: 57

57/2 = x

X = 24.5

A football team must move the ball forward at least 10 yards from its starting point to make a first down if the team has 2 losses of 2 yards each and a gain of 12 yards does the tean make a first touchdown justify your answer

Answers

No ,the team will not make the first down.

The definition of a yard is an outdoor area of a house or other building. An example of a yard is the lawn in front of your house; a front yard. An example of a yard is the area around a train repair center where trains are stored; a rail yard.

the first of a series of usually four downs in which a football team must net a 10-yard gain to retain possession of the ball.

If the team with the ball can pick up one yard or more on the third-down play, then they will be given a first down, which means they get to start all over with a new set of four downs. A team can continue moving the football down the field as long as they continue to pick up first downs.

we have been given that -

the ball forward at least 10 yards from its starting point to make a first down if the team has 2 losses of 2 yards each and a gain of 12 yards

Here are the integers that are represented by the scenario.

-2 + -2  = -4

-4 + 12 =8 yard gain.

There are 2 yards less of the first down.

Hence, the team will not make the first down.

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|60| ___ |-60| = < >

Answers

Answer:

It is equal

Step-by-step explanation:

60 and -60 cancel each other out so the answer is equal.

Answer:    |60|=|-60|

Step-by-step explanation:

|-60| would turn into 60 and |60| would remain 60 so they are equals

cosec4A-1/cot4a=1+2tan2a​

Answers

Answer:

See image for answer.

if a deli offers 10 fillings, 9 types of bread, and 6 condiments, and each sandwich consists of a filling, a type of bread, and a condiment, how many different sandwiches can the sandwich shop create?

Answers

540 and 5760 sandwiches can the sandwich shop create

10 fillings, 9 bread, 6 condiments

= 10 possibilities × 9 possibilities × 6 possibilities

=540

10 fillings, 9 bread, 6 condiments

= 10 possibilities × 9 possibilities × 64 possibilities

=5760

sandwich can have any no.of condiments,

let say A,B,C are condiment  then possibilities are

A,B,C,AB,BC,AC,ABC , no condiment

i.e, [tex]2^{6}[/tex] = 64 possibilities.

What do you mean by possibilities?

likelihood that something will or won't occur or exist: the condition or reality of being possible There is a chance of rain today. A potential event or object that might exist It's possible that life exists on other worlds. More about potential from Merriam-Webster.

An example of a probability that you will attend a party is if there is a 50/50 chance that you might do so. The green dress is an example of a potential option you may select from when given the choice between wearing a red dress or a green dress.

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Which equation matches

Answers

Answer:

The first one

Step-by-step explanation:

The first one is going to be your answer

I can figure out the steps -X=35

Answers

Answer:

-35

Step-by-step explanation:

−X=35

Multiply both sides by −1.

X=−35

I hoped this helped! Contact me for more information if you need anything else!

3
Point 0 is on live segment NP.
If OP= 3 and NO=15, what is
length of NP.

Answers

According to the length, the length of the NP become 18.

According to the statement

We have to find that the length of the NP.

So, For this purpose, we know that the

The length of this line segment is the distance between its endpoints A and B.

From the given information:

Point O is on live segment NP.

If OP= 3 and NO=15,

Then

Let draw a diagram and after seeing it in image we know that the:

NO=15 and OP= 3

And

Np is the sum of the op and no.

Then

NP = OP + NO

NP = 3+ 15

NP = 18.

Then the length of the NP become 18.

So, According to the length, the length of the NP become 18.

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can i please have help

Answers

Answer:

Side 3 = 5cm

Step-by-step explanation:

135/9=15

15/3=5

auto pistons at wenming​ chung's plant in shanghai are produced in a forging​ process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each​ day, the mean and the range of this diameter have been as​ follows: day mean bold x overbar ​(mm) range r ​(mm) 1 156.9 4.4 2 155.2 4.4 3 155.6 4.1 4 155.5 5.2 5 154.6 4.3 part 2 ​a) what is the value of x double overbar ​? x double overbar equalsenter your response here mm ​(round your response to two decimal​ places).

Answers

The value of the x double bar (mean) of the given data is 155.16mm.

What is mean?

The mean (average) of a records set is observed with the aid of using including all numbers withinside the records set after which dividing with the aid of using the quantity of values withinside the set. The median is the center price while a records set is ordered from least to greatest. The mode is the quantity that takes place most customarily in a records set. Created with the aid of using Sal Khan

X bar = sum of all means / numbers of means

X bar = (156.9 + 153.2+153.6+155.5+156.6) / 5

X bar = 775.8 / 5

X Bar = 155.16mm

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20 points How do you write four x cubed and also two x squared with numbers? asap please

Answers

Answer:

this should be the answer 4x^3 & 2x^2

What's 960 divided by 40?

Answers

Answer:

24

Step-by-step explanation:

960/40 =

To make it simpler you could divide 10 by both digits to simplify them (as in fractions).

960/10 = 96

40/10=4

Now your have 96/4

Again this can be simplified by dividing both by 2

96/2 = 48

4/2 = 4

48/2

48 is definitely a multiple of 2, so dividing this your answer is 24

The expression 960 divided by 40 is 24.

We have,

Expression:

960 divided by 40

This can be written as,

960 ÷ 40

40 ) 960 (24

       80

          160

          160

               0

The quotient is 24 and the remainder is 0.

Thus,

The expression 960 divided by 40 is 24.

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Rewrite the equation 4 = -6x + 3y + 3x in slope intercept form. (y = mx + b)
a.) y = 4/3 x +1
b.) y = x + 4/3
c.) y = -x + 4/3
d.) y = - 4/3 x + 1

Answers

Answer:

the answer will be

b.)

4 = -6x+3y+3x

4 = -3x+3y

3y = 3x+4

y. = x+4/3

elijah says that 9.56556555 is a rational number.Donna disagrees and says the number is irrational. Decide who is correct and what might likely cause one of them to make the error.

Answers

Answer:

It is a rational number because it is a repeating number.

Step-by-step explanation:

One might think it isn't rational because it isn't just one number repeating. But because it has a consistent number, it is rational.

The area of the top face of a cube is 9 square centimeters. use 9 of these cubes to make a rectangular prism. What is the volume of the rectagular prism

Answers

The volume of the rectangular prism is 243 cm³

given that

The top face of the cube has an area of 9 cm²

since All the faces of the cube are squares

therefore The top face is a square

∵ Area of any square = L² , where L is the length of the side of

 the square

∵ Area of the top face is 9 cm²

∴ L² = 9 ⇒ take √ for both sides

∴ L = 3 cm

∵ The volume of any cube = L³

∵ L = 3 cm

∴ The volume of the cube = (3)³ = 27 cm³

- We will use 9 cubes to make a rectangle prism

∴ The volume of the rectangle prism is equal to the volume of

 the 9 cubes

∴ The volume of the prism = 9 × volume of a cube

∵ The volume of the cube is 27 cm³

∴ The volume of the prism = 9 × 27 = 243 cm³

* The volume of the rectangular prism is 243 cm³

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30. Which of the following choices shows the slope-intercept form of the equation below?
31. Which of the following choices shows the standard form of the equation below?

Answers

The equation of the lines in slope intercept form and standard form is y = -2x + 10 and 2y+3x = 10

Equation of a line in slope intercept form

The equation of a line in point slope form is y = mx + b.

Given the equation below:

y-7 =-5/2(x+4)

2(y-7) = -5(x+4)

2y-14 = -4x - 20

2y = -4x-20+40

2y = -4x + 20

y = -2x + 10

For the equation;

y = -3/2 x + 5

Multiply through by 2

2y = -3x + 2(5)

2y = -3x + 10

2y+3x = 10

Hence the equation of the lines in slope intercept form and standard form is y = -2x + 10 and 2y+3x = 10

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I need help please….

Answers

Answer:

Graph A shapes are not congruent.
Graph B Shapes are congruent.

Step-by-step explanation:

For Graph A, Shape EFGH is 1 unit longer than shape ABCD.

For Graph B, the are the same, but rotated 90 degrees.

An artist used 6 tubes of red paint, 2 tubes of yellow paint, 13 tubes of white paint, and 9 tubes of blue paint for a mural. what is the ratio of blue paint tubes to all the tubes of paint used?

Answers

The ratio of blue paint to all tubes of paint = 3:10

Number of tubes of red paint = 6 tubes

Number of tubes of yellow paint = 2 tubes

Number of tubes of white paint = 13 tubes

Number of tubes of blue paint = 9 tubes

Total no. of paint tubes = 6 red tubes + 2 yellow tubes+ 13 white tubes + 9 blue tubes = 30 tubes of paint

We use the following formula to find the required ratio:

The ratio of blue paint tubes to all tubes of paint = Number of blue paint tubes: Number of all tubes = 9:30 or 3:10

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There are 900 boys and 300 girls at eqinisweni secondary school. martha claims that 25% of the learners are girls. verify her claim by means of calculations

Answers

Martha's claim that the 25% of the learners are girls, is correct.

In this question,

There are 900 boys and 300 girls at Eqinisweni secondary school.

Martha claims that 25% of the learners are girls.

We need to verify her claim by means of calculations.

Based on the given conditions, we formulate:

300 / (900 + 300)

We simplify above expression.

= 300 / 1200

= 1/4               ..................(Cross out the common factor)

Now multiply a number 25 to both the numerator and the denominator:

= (1 × 25)/(4 × 25)

= 25/200

Now we rewrite a fraction with denominator equals 100 to a percentage: 25%

This means, Martha's claim that the 25% of the learners are girls, is correct.

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write a two-column proof to verity each conjecture. If -3r+1/2= 4 the r=-7/6

Answers

If -3r + 1/2 = 4, then it is true that r=-7/6

How to write a two-column proof to verity each conjecture?

The equation is given as:

-3r + 1/2 = 4

And the solution is given as

r=-7/6

The two-column proof is as follows:

-3r + 1/2 = 4 ---- Given-3r = 4 - 1/2 ----- Subtract property of equation-3r = 3 1/2 ----- Subtract property of equation-3r = 7/2 ----- Convert to improper fractionr = -7/6 ----- Division property of equation

Hence, if -3r + 1/2 = 4, then it is true that r=-7/6

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