32) Identify the turning point of the function f(x)= x^2-2x+8 by writing its equation in vertex form. Show your work.

Answers

Answer 1

Answer: (1,7)

Working;
Start by finding the derivative of the function f(x);
$f^(') (x)$ =2x-2
Turning points occur when the derivative function=0;
Thus
2x-2=0
x=1
when x=1 then
f(1)= $1^(2) -2(1)+8$
=7
Turning point then is (1,7)

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The fountain contains 20 pennies and 9 dimes. A coin is randomly taken and not replaced. A second coin is randomly taken. What is the probability that both coins are pennies?

Answers

Well, the first coin has chance $(20)/(29)$ to be a penny. When it is a penny, the only valid case (the other case gives 0 for the multiplications later, so it is ignored) gives $(19)/(28)$ chance for the second one to be a penny. The result is $(20*19)/(29*28)$ , which is $(95)/(203)$ , or about 46.80% (rounded to the first 2 decimals)

Answer:

9 dimes

Step-by-step explanation:

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Rewrite the rational exponent as a radical by extending the properties of integers exponents.2^3/4 / 2^1/2

Answers

$\frac{2 ^{(3)/(4)} }{2^(1)/(2)}=2 ^{(3)/(4)-(1)/(2)}=2 ^{(3)/(4)-(2)/(4)}=2 ^{(1)/(4) }=\sqrt[4]{2}$

What is the distance between points (3,8) and (-9,-8)5
10
15
20

what is the distance between points (2,6) and (5,2)
3
4
5

what is the distance between points (21,16) and (9,11)
13
12
22
24

Answers

It is better to graph these points, to easily understand that the distance of the two points form the hypotenuse of the right triangle. We need to use the Pythagorean theorem to solve for the distance of the two points.

a² + b² = c² ; a = x value ; b = y value

1) (3,8) and (-9,-8)
a = 3 - (-9) = 3 + 9 = 12 ⇒ 12² = 144
b = 8 - (-8) = 8 + 8 = 16 ⇒ 16² = 256 ⇒⇒ 144 + 256 = 400 ; c = √400 = 20

2) (2,6) and (5,2)
a = 2 - 5 = 3 ⇒ 3² = 9
b = 6 - 2 = 4 ⇒ 4² = 16 ⇒⇒ 9 + 16 = 25 ; c = √25 = 5

3) (21,16) and (9,11)
a = 21 - 9 = 12 ⇒ 12² = 144
b = 16 - 11 = 5 ⇒ 5² = 25 ⇒⇒ 144 + 25 = 169 ; c = √169 = 13

Find the solution of 3 times the square root of the quantity of x plus 5 equals negative 9, and determine if it is an extraneous solution.