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madam [21]
3 years ago
11

A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $52. The total cost to re

nt 9 chairs and 7 tables is $86. What is the cost to rent each chair and each table?
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
3 0

Answer:

The cost for 1 chair is $2.75 and the cost for 1 table is $8.75

Step-by-step explanation:

Use the elimination method of linear equations to find your answer.

Our equations for this problem are:

3c+5t=52 and 9c+7t=86

1. Multiply the entire first equation by -3.

-3(3c+5t=52)

2. Simplify the equation from above:

-9c-15t=-156

3. Stack the two equations on top of each other and add/subtract:

-9c-15t=-156

9c+7t=86

4. You should be left with -8t=-70. Simplify this to find the value of t:

t=8.75

5. Plug the value of t into any of the original equations and solve for c.

3c+5(8.75)=52

6. Simplify the equation above:

3c+43.75=52

7. Subtract 43.75 from both sides of the equation:

3c=8.25

8. Divide both sides by 3 to get your c value:

c=2.75

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Answer:

y=\frac{1}{4} x-5

Step-by-step explanation:

Slope intercept from is represented as :

y = mx + b

So, plugging in the numbers it would look like this :

y=\frac{1}{4} x-5

Hope this helps. Please mark brainliest!

3 0
3 years ago
jaxon earned $90 at his job when he worked for 9 hours . what was his hourly pay rate in dollars per hour ?
user100 [1]

Answer:

$10 dollars

Step-by-step explanation:

10x9=90

3 0
3 years ago
Read 2 more answers
Which of these correctly explains the solution of the system of equations shown
borishaifa [10]

The solution of the system of equations is the point (-6, 6), so the correct option is B.

<h3>Which statements are correct about the system of equations?</h3>

Here we have the system of equations:

2x + 3y = 6

x + 3y = 12

First, let's write these two lines in the slope-intercept form:

y = (6 - 2x)/3 = 2 - (2/3)*x

y = (12 - x)/3 = 4 - (1/3)*x

Now, because "y" is the represents the same variable in both equations, we can write:

2 - (2/3)*x = y = 4 - (1/3)*x

Now we can solve that for x.

2 - (2/3)*x =  4 - (1/3)*x

2 - 4 = (2/3)*x - (1/3)*x

-2 = (1/3)*x

3*(-2) = x = -6

Now, to get the y-value of the solution we can evaluate any of the two lines in x = -6, evaluating the first we get:

y =  4 - (1/3)*x = 4 - (1/3)*(-6) = 4 + 2 = 6

Then the solution of the system is the point (-6, 6). Then the correct statement is B:

"The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is the solution."

If you want to learn more about systems of equations:

brainly.com/question/13729904

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8 0
2 years ago
What is function and how is it related to domain and range?​
const2013 [10]

Answer:

Function- a relationship or expression involving one or more variables.

A domain refers to the set of possible input values.

The range is the set of possible output values.

Step-by-step explanation:

4 0
3 years ago
We know that side NM is parallel to side XZ. If we consider side NY the transversal for these parallel lines, we create angle pa
Likurg_2 [28]
See the picture attached.

We know:
NM // XZ
NY = transversal line
∠YXZ ≡ ∠YNM

1) <span>We know that ∠XYZ is congruent to ∠NYM by the reflexive property.</span>

The reflexive property states that any shape is congruent to itself.
∠NYM is just a different way to call ∠XYZ using different vertexes, but the sides composing the two angles are the same.
Hence, ∠XYZ ≡ <span>∠NYM</span> by the reflexive property.

2) Δ<span>XYZ is similar to ΔNYM by the AA (angle-angle) similarity theorem

The AA similarity theorem states that if two triangles have a pair of corresponding angles congruent, then the two triangles are similar.
Consider </span>Δ<span>XYZ and ΔNYM:
</span>∠YXZ ≡ <span>∠YNM
</span>∠XYZ ≡ ∠NYM
Hence, ΔXYZ is similar to ΔNYM by the AA similarity theorem.


8 0
3 years ago
Read 2 more answers
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