Answer: ![30](https://tex.z-dn.net/?f=30)
Step-by-step explanation:
Given
![k(x)=2x+3](https://tex.z-dn.net/?f=k%28x%29%3D2x%2B3)
![M(x)=3x^2+7x-10](https://tex.z-dn.net/?f=M%28x%29%3D3x%5E2%2B7x-10)
is given by replacing the
by
from the ![M(x)](https://tex.z-dn.net/?f=M%28x%29)
![\Rightarrow M\left(k(x)\right)=3(2x+3)^2+7(2x+3)-10\\\Rightarrow M\left(k(x)\right)=3(4x^2+9+12x)+14x+21-10\\\Rightarrow M\left(k(x)\right)=12x^2+50x+38](https://tex.z-dn.net/?f=%5CRightarrow%20M%5Cleft%28k%28x%29%5Cright%29%3D3%282x%2B3%29%5E2%2B7%282x%2B3%29-10%5C%5C%5CRightarrow%20M%5Cleft%28k%28x%29%5Cright%29%3D3%284x%5E2%2B9%2B12x%29%2B14x%2B21-10%5C%5C%5CRightarrow%20M%5Cleft%28k%28x%29%5Cright%29%3D12x%5E2%2B50x%2B38)
Now,
is
![\Rightarrow M\left(k(-4)\right)=12(-4)^2+50(-4)+38\\\Rightarrow M\left(k(-4)\right)=192-200+38\\\Rightarrow M\left(k(-4)\right)=30](https://tex.z-dn.net/?f=%5CRightarrow%20M%5Cleft%28k%28-4%29%5Cright%29%3D12%28-4%29%5E2%2B50%28-4%29%2B38%5C%5C%5CRightarrow%20M%5Cleft%28k%28-4%29%5Cright%29%3D192-200%2B38%5C%5C%5CRightarrow%20M%5Cleft%28k%28-4%29%5Cright%29%3D30)
Surface area of the cylinder = 816.4 sq. ft.
Solution:
Height of the cylinder = 21 ft
Diameter of the cylinder = 10 ft
Radius of the cylinder = 10 ÷ 2 = 5 ft
Use the value of
= 3.14
Surface area of the cylinder = ![2 \pi r h+2 \pi r^{2}](https://tex.z-dn.net/?f=2%20%5Cpi%20r%20h%2B2%20%5Cpi%20r%5E%7B2%7D)
Substitute the given values in the surface area formula, we get
Surface area of the cylinder ![$=2\times3.14\times 5\times 21+2 \times3.14\times 5^2](https://tex.z-dn.net/?f=%24%3D2%5Ctimes3.14%5Ctimes%205%5Ctimes%2021%2B2%20%5Ctimes3.14%5Ctimes%205%5E2)
![=659.4+157](https://tex.z-dn.net/?f=%3D659.4%2B157)
ft²
Hence the surface area of the cylinder is 816.4 sq. ft.
Step-by-step explanation:
X + 9= 7
get x by itself you -9 on both sides
X + 9 = 7
- 9. -9
X = -2
Step-by-step explanation:
last week there were
62 + 60 + 2 = 124 customers.
that means that the fraction of the customers, who paid by credit card, was
2/124 = 1/62
in situations like that, when we use history data and try to predict future behavior, we use that past experience and extrapolate to a predicted result.
we simply say that we expect the same fraction, 1/62, if customers to use credit cards.
for the absolute number of predicted credit card customers we multiply the predicted number of customers by the expected fraction
1000 × 1/62 = 500/31 = 16.12903226... ≈ 16
so, he expects 16 credit card customers.
Answer:
d-2 and d cannot = 8
Step-by-step explanation:
d^2 -10d+16
-----------------------
d-8
Factor the numerator
( d-8)(d-2)
-------------------
d-8
The undefined values occur when the denominator is equal to zero
d-8 = 0
d= 8
This means d cannot equal 8
Now cancel like terms in the equation ( d-8)
This yields d-2