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mixas84 [53]
3 years ago
6

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is $53. The total cost to re

nt 8 chairs and 3 tables is $42. What is the cost to rent each chair and each table?
Mathematics
1 answer:
DiKsa [7]3 years ago
6 0

Answer:

c=cost of one chair rental

t=cost of one table rental

8c+3t=42

2c+5t=53

multiply the second equation, each term on both sides, by -4

8c+3t=42

-8c-20t=-212

add the two equations

-17t=-170

divide both sides by -17

t=$10 to rent one table

substitute t=10 into either original equation

2c+5(10)=53

2c+50=53

2c=3

c=$1.50 to rent one chair

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the slope-intercept form of an equation of the line perpendicular to the graph of x – 3y = 5 and passing through (0, 6).
Leona [35]

Answer:

y = - 3x + 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x - 3y = 5 into this form

Subtract x from both sides

- 3y = - x + 5 ( divide all terms by - 3 )

y = \frac{1}{3} x - \frac{5}{3}  ← in slope- intercept form

with slope m = \frac{1}{3}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{1}{3} } = - 3

Note the line crosses the y- axis at (0, 6) ⇒ c = 6

y = - 3x + 6 ← equation of perpendicular line

3 0
3 years ago
Find the value of y and x in the figure
Fed [463]

First, find the interior angle missing:

180-135=45

Then, we know all the interior angles in a triangle add up to 180º. So, we add all the values for the interior angles and we equate them to 180. We solve the equation normally.

45+(4z+9)+(5y+5)=180\\45+4z+9+5y+5=180\\59+4z+5y=180\\4z+5y=180-59\\4z+5y=121

After that, we must add the two angles on a straight line on the right-hand side and equate them to 180.

(4z+9)+(9y-2)=180\\4z+9+9y-2=180\\7+4z+9y=180\\4z+9y=180-7\\4z+9y=173

We compare the equations:

4z+5y=121\\4z+9y=173

We simultaneously solve by isolating one of the variables (y) in one of the equations (4z+5y=121) and substituting into the other (4z+9y=173):

4z+5y=121\\4z+9y=173\\\\4z+5y=121 => 4z=121-5y\\\\4z+9y=173\\(121-5y)+9y=173\\121-5y+9y=173\\121+4y=173\\4y = 173-121\\4y=52\\y=52/4\\y=13

We substitute it back into the first formula, the one in which we isolated the variable (4z+5y=121):

y=13\\\\4z+5y=121\\4z+5(13)=121\\4z+65=121\\4z=121-65\\4z=56\\z=56/4\\z=14

We now check our answer using the formula we know about the internal angles of a triangle (a+b+c=180):

a+b+c=180\\a=45,b=(5y+5),c=(4z+9),y=13,z=14\\45+(5y+5)+(4z+9)=180\\45+5(13)+5+4(14)+9=180\\45+65+5+56+9=180\\180=180

Now, if 180=180, then we are correct!

So, in conclusion, y=13 and z = 14.

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3 years ago
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