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nata0808 [166]
3 years ago
5

A and B are vertical angles. If m A = (3x+3)° and m B= (4x-8)°, then find the value of x.

Mathematics
1 answer:
iogann1982 [59]3 years ago
6 0

Answer: x=11

Step-by-step explanation:

First, since angle A and angle B are vertical angles, that means that they are congruent. If they are congruent, then the m of angle A equals the measure of angle B. So, (3x+3)=(4x-8). Simplify using algebra so that in the end, you will find that x=11.

3x+3=4x-8

3=x-8

11=x

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20. Carmen can buy bottles of paint for $2.00 each and boxes of colored pencils for $3.50 each. She can spend no more than
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Answer:

(a) The equality that express many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy is  2 x + 3.5 y = 42

b)Three different solutions:

x  = 14, y = 4 is First Solution.

x  = 7, y = 8 is Second Solution.

x  = 21, y = 0 is Third Solution.

Step-by-step explanation:

Here, the cost of 1 bottle of paint = $2.00 each

The cost of 1 box of colored pencils  = $3.5 each

Let us assume the number of bottle of paints purchased = x

So, the cost of x bottle of paints   = x ( Cost of 1 bottle of paint)

= x ($2.00)  = 2 x

Also, assume the number of box of colored pencils purchased = y

So, the cost of y box of colored pencils = y ( Cost of 1 box)

= y ($3.50)  = 3.5 y

Also, the total amount to be spent on art supplies  = $42

So, the total amount spent on x paint bottles + y box of colored pencil

= $42

or,  2 x + 3.5 y = 42

a ) So, the equality that express many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy is  2 x + 3.5 y = 42

b)Three different solutions:

When y = 4 ,  equation is:   2 x + 3.5(4)  = 42

or,  2 x = 42 - 14  = 28, or x = 28/2  =  14

So, x  = 14, y = 4 is First Solution.

When y = 8 ,  equation is:   2 x + 3.5(8)  = 42

or,  2 x = 42 - 28  = 14, or x = 14/2  =  7

So, x  = 7, y = 8 is Second Solution.

When y = 0 ,  equation is:   2 x + 3.5(0)  = 42

or,  2 x = 42 , or x = 42/2  = 21

So, x  = 21, y = 0 is Third Solution.

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