<u>Answer: </u>
Simplified form of given expression (2x – 9 )( x + 6 ) is ![2 \mathrm{x}^{2}+3 \mathrm{x}-54](https://tex.z-dn.net/?f=2%20%5Cmathrm%7Bx%7D%5E%7B2%7D%2B3%20%5Cmathrm%7Bx%7D-54)
<u> Solution:
</u>
We need to simplify following expression.
(2x – 9) ( x + 6)
For sake of simplicity lets first assume 2x – 9 = A
So expression becomes A(x+6)
= Ax + A6
Now replace A by 2x – 9
= (2x – 9 ) x + (2x – 9 ) 6
![=2 \mathrm{x}^{2}-9 \mathrm{x}+12 \mathrm{x}-54](https://tex.z-dn.net/?f=%3D2%20%5Cmathrm%7Bx%7D%5E%7B2%7D-9%20%5Cmathrm%7Bx%7D%2B12%20%5Cmathrm%7Bx%7D-54)
On simplification, we get
![=2 \mathrm{x}^{2}+3 \mathrm{x}-54](https://tex.z-dn.net/?f=%3D2%20%5Cmathrm%7Bx%7D%5E%7B2%7D%2B3%20%5Cmathrm%7Bx%7D-54)
Hence simplified form of given expression (2x – 9 )( x + 6 ) is ![= 2 \mathrm{x}^{2}+3 \mathrm{x}-54](https://tex.z-dn.net/?f=%3D%202%20%5Cmathrm%7Bx%7D%5E%7B2%7D%2B3%20%5Cmathrm%7Bx%7D-54)
Answer:
Number of full size cars = 900
Step-by-step explanation:
The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size cars is 8 to 9. Since compact cars are there in both ratios , we need to make the number in the ratio for compact cars to be the same.
![\frac{medium}{compact} = \frac{7}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Bmedium%7D%7Bcompact%7D%20%3D%20%5Cfrac%7B7%7D%7B5%7D)
Multiply by 8 on numerator and denominator
![\frac{medium}{compact} = \frac{56}{40}](https://tex.z-dn.net/?f=%5Cfrac%7Bmedium%7D%7Bcompact%7D%20%3D%20%5Cfrac%7B56%7D%7B40%7D)
![\frac{compact}{full size} = \frac{8}{9}](https://tex.z-dn.net/?f=%5Cfrac%7Bcompact%7D%7Bfull%20size%7D%20%3D%20%5Cfrac%7B8%7D%7B9%7D)
Multiply numerator and denominator by 5.
![\frac{compact}{full size} = \frac{40}{45}](https://tex.z-dn.net/?f=%5Cfrac%7Bcompact%7D%7Bfull%20size%7D%20%3D%20%5Cfrac%7B40%7D%7B45%7D)
Ratio of medium, compact and full size are in ratio 56,40,45.
Total number of cars =2820.
(56 + 40 + 45)x = 2820
x = ![\frac{2820}{141}](https://tex.z-dn.net/?f=%5Cfrac%7B2820%7D%7B141%7D)
x = 20
Number of full size cars =
=900
Answer:
x = ![\frac{z}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Bz%7D%7By%7D)
Step-by-step explanation:
Given
z = xy ( isolate x by dividing both sides by y )
= x
Answer:
176 feet per minute
Step-by-step explanation:
Answer:
8/8
Step-by-step explanation:
There are two pies, and each one was cut into fourths. There are four fourths in a whole, and since there are two wholes, there are two four fourths (I don't know if this makes sense).
Basically, multiply how many fourths (four per pie) by how many pies there are.
4 x 2 = 8
There are 8 pieces.