Answer:
27 Feet is the answer. Option C.
Answer:
f(x) = 2(x –3)²
Step-by-step explanation:
f(x) = 2x² – 12x + 18
The vertex form of the above expression can be obtained as follow:
f(x) = 2x² – 12x + 18
Factorise
f(x) = 2(x² – 6x + 9)
Next, we shall simplify x² – 6x + 9 by factorisation method.
This is illustrated below:
x² – 6x + 9
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, find two factors of 9x² such that their sum will result to the 2nd term i.e –6x in the expression above.
The factors are –3x and –3x
Next, replace –6x with –3x and –3x in the equation above as shown below:
x² – 6x + 9
x² – 3x –3x + 9
Factorise
x(x – 3) –3(x –3)
(x –3)(x –3)
(x –3)²
f(x) = 2x² – 12x + 18
f(x) = 2(x² – 6x + 9)
f(x) = 2(x –3)²
Therefore, the vertex form of the function f(x) = 2x² – 12x + 18 is
f(x) = 2(x –3)²
Answer:
1/8
Step-by-step explanation:
Leonard spent 1 fourth of his money on a sandwich.
Fraction of money spent on sandwich = 1/4
He spent 2 times as much on a gift for his brother as on some comic books.
= 1/4 × 2
= 2/8
Hence, Fraction of money spent on Comic books = 2/8
He had 3 over 8 of his money left.
Let us represent his total money has: 1
The fraction of his money that he spent on the comic books is calculated as:
= 1 -( 1/4 + 2/8+ 3/8)
Lowest Common Denominator = 8
= 1 - (2 +2 + 3/8)
= 1- 7/8
= 1/8
Therefore, the fraction of his money that he spent on the comic books is 1/8
Answer:-12r+20=-4(3r-5)
Step-by-step explanation:
Pls mark as brainliest
Answer:
0.375 feet-lb
Step-by-step explanation:
We have been given that the work required to stretch a spring 2 ft beyond its natural length is 6 ft-lb. We are asked to find the work needed to stretch the spring 6 in. beyond its natural length.
We can represent our given information as:
We will use Hooke's Law to solve our given problem.
Substituting this value in our integral, we will get:
Using power rule, we will get:
![6=\left[ \frac{kx^2}{2} \right ]^2_0](https://tex.z-dn.net/?f=6%3D%5Cleft%5B%20%5Cfrac%7Bkx%5E2%7D%7B2%7D%20%5Cright%20%5D%5E2_0)
We know that 6 inches is equal to 0.5 feet.
Work needed to stretch it beyond 6 inches beyond its natural length would be 
Using power rule, we will get:
![\int\limits^{0.5}_0 {3x} \, dx = \left [\frac{3x^2}{2}\right]^{0.5}_0](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B0.5%7D_0%20%7B3x%7D%20%5C%2C%20dx%20%3D%20%5Cleft%20%5B%5Cfrac%7B3x%5E2%7D%7B2%7D%5Cright%5D%5E%7B0.5%7D_0)
Therefore, 0.375 feet-lb work is needed to stretch it 6 in. beyond its natural length.
