It's going to be kind of crazy, but you need to use Pythagorean's Theorem for this. That will look like this:
. FOIL out the left side to get
. FOIL out the first of the 2 expressions on the right to get
, and the second of the 2 to get 4x. Our equation now looks like this:
. Combine like terms to get an equation that still has square roots in it that we have to deal with:
and
. We will square both sides to get rid of the square root sign.
. This is a polynomial now that can be factored to solve for x. Bring the 2x over by subtraction and set the polynomial equal to 0.
. Factor out an x, leaving us with x(x-2)=0. That means that x = 0 or x - 2 = 0 and x = 2. Of course if we are solving for the length of a side we know it can't have a side length of 0, so it must have a side length that is a multiple of 2. x = 2
The value of (f - g)(x) is -x² + 3x + 7.
<h3>What is Function?</h3>
The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given functions are;
f(x) = 3x + 1
g(x) = x² - 6
Now,
(f - g)(x) = f(x) - g(x)
= (3x + 1) - (x² - 6)
= 3x + 1 - x² + 6
(f - g)(x) = -x² + 3x + 7
Thus, the value of (f - g)(x) is -x² + 3x + 7.
Learn more about Function from:
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Answer:
Statement A is true.
Step-by-step explanation:
A. If the group sells 15 prints, they will lose $85.
B. If the group sells 12 prints, they will lose $204.
C. If the group sells 35 prints, they will make $935.
D. If the group sells 28 prints, they will lose $136.
f(p) = 17p - 340
p = prints
f(p) = profit
Let's check the statements to see which one is true.
A. 17.15 - 340 = - 85 OK!
B. 17.12 - 340 = -136 (false, they will lose $136)
C. 17.35 - 340 = 255 (false, they will make $255)
D. 17.28 - 340 = 136 (false, they will make $136)
Answer:
3.75 feet
Step-by-step explanation:
The length of the frame is 3 times the width.
Let the width be x.
The length will be 3x.
Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.
The perimeter of a rectangle is:
P = 2(L + W)
=> 10 = 2(3x + x)
=> 10/2 = 4x
5 = 4x
=> x = 5/4 = 1.25 feet
The width is 1.25 feet. The length is therefore:
1.25 * 3 = 3.75 feet
