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maxonik [38]
2 years ago
14

Candice is an interior designer, and she is currently trying to change the look of a room. Candice found that the area of a room

could be given by the expression 3x2 + 2x. The aread of the rug she wants to spread on the floor is given by the expression x2 + 24x - 144. What expression represents the area of the room not covered by the rug?
Mathematics
1 answer:
german2 years ago
7 0

Answer:

A(x) = 2x^2-22x+144

Step-by-step explanation:

We are given the following in the question:

Area of room =

3x^2 + 2x

Area of rug =

x^2 + 24x - 144

We have to find the area of of the room not covered by the rug.

Area of of the room not covered by the rug =

Area of room - Area of rug

A(x)=(3x^2 + 2x) - ( x^2 + 24x - 144)\\A(x)=3x^2 + 2x-x^2  -24x + 144\\A(x)=(3x^2-x^2)+(2x -24x) + 144\\A(x)=2x^2-22x+144

is the required expression for the area of floor not covered by the rug.

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What is the sum of the expressions (2/3x −7)+(1/3 x+5)?
Anit [1.1K]
The answer is

Final result :

x - 2
Step by step solution :

Step 1 :

1
Simplify —
3
Equation at the end of step 1 :

2 1
((—•x)-7)+((—•x)+5)
3 3
Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 3 as the denominator :

5 5 • 3
5 = — = —————
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Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x + 5 • 3 x + 15
————————— = ——————
3 3
Equation at the end of step 2 :

2 (x + 15)
((— • x) - 7) + ————————
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Step 3 :

2
Simplify —
3
Equation at the end of step 3 :

2 (x + 15)
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3 3
Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

7 7 • 3
7 = — = —————
1 3
Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

2x - (7 • 3) 2x - 21
———————————— = ———————
3 3
Equation at the end of step 4 :

(2x - 21) (x + 15)
————————— + ————————
3 3
Step 5 :

Adding fractions which have a common denominator :

5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(2x-21) + (x+15) 3x - 6
———————————————— = ——————
3 3
Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

3x - 6 = 3 • (x - 2)

Final result :

x - 2

100% Verified!

Hope This Helps! :)
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Answer:

Step-by-step explanation:

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Answer:

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