Answer:
A
Step-by-step explanation:
12x6=72
Answer:
k = 12
Step-by-step explanation:
Given:
The equation ![Q(x)=2x^2-kx+18](https://tex.z-dn.net/?f=Q%28x%29%3D2x%5E2-kx%2B18)
To find:
Value of
for which the given equation has one distinct real solution.
Solution:
The given equation is a quadratic equation.
There are always two solutions of a quadratic equation.
For the equation:
to have one distinct solution:
![b^2 - 4ac = 0](https://tex.z-dn.net/?f=b%5E2%20-%204ac%20%3D%200)
Here,
a = 2,
b = -k and
c = 18
Putting the values, we get:
![(-k)^2 - 4\times 2\times 18 = 0\\\Rightarrow k^2 = 18\times 8\\\Rightarrow k^2 =144\\\Rightarrow k = 12](https://tex.z-dn.net/?f=%28-k%29%5E2%20-%204%5Ctimes%202%5Ctimes%2018%20%3D%200%5C%5C%5CRightarrow%20k%5E2%20%3D%2018%5Ctimes%208%5C%5C%5CRightarrow%20k%5E2%20%3D144%5C%5C%5CRightarrow%20k%20%3D%2012)
The equation becomes:
![Q(x)=2x^2-12x+18](https://tex.z-dn.net/?f=Q%28x%29%3D2x%5E2-12x%2B18)
And the one root is:
![2(x^2-6x+9 ) = 0\\\Rightarrow 2(x-3)^2=0\\\Rightarrow x = 3](https://tex.z-dn.net/?f=2%28x%5E2-6x%2B9%20%29%20%3D%200%5C%5C%5CRightarrow%202%28x-3%29%5E2%3D0%5C%5C%5CRightarrow%20x%20%3D%203)
I believe the correct answers are:
<span>UV = 14 ft and m∠TUV = 45°</span>
<span>ST = 20 ft, UV = 14 ft, and m∠UST = 98°
Or, in other words, Options A and D.
</span>
Answer:
20 grams
Step-by-step explanation:
Let x be the total allowance of fat
16 grams is 80% of his total allowance
x * 80% = 16
Change percent to a decimal
x *.8 = 16
Divide each side by .9
.8x/.8 = 16/.8
x = 20