Evaluate each expression for g = -7 and h = 3 and match it to its value.

1 answer:

5 0

G=-7, h=3 so

1. -4 g+h = -4*(-7)+3 = 312. 2 g-h = 2*(-7) -3 = -17
3. 46 h-g = 46*3-(-7) = 145
4. -10 gh = -10*(-7)*3 = 210
5. -21 g+h^2 = -21*(-7)+3^2 = 159
6. 10 g^2 -h = 10*(-7)^2 - 3 = 487

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ICE Princess25 [194]

Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6

Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1

(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1

Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x

Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2

Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2

Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144

Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0

The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0

Divide both sides by -4:
(x - 9) (x - 4) = 0

Split into two equations:
x - 9 = 0 or x - 4 = 0

Add 9 to both sides:
x = 9 or x - 4 = 0

Add 4 to both sides:
x = 9 or x = 4

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct

The solution is:
Answer: x = 9

5 0

3 years ago

If f(x) and its inverse function, fx), are both plotted on the same coordinate plane, what is their point of intersection?

Lubov Fominskaja [6]

Answer: (3, 3)

Step-by-step explanation:

the graphs of $f$ and $f^{-1$ are flipped: if the point $(x, y)$ is on the graph of $f$ , then the point $(y, x)$ is on the graph of $f^{-1$ .

Any points of intersection will satisfy $(x, y) = (y, x)$ . A point that satisfies this property must have the same x and y coordinate. (Think about it.) The only point on $f$ like that is $(3, 3)$ , so that is the point of intersection.