Answer:
6) y = x^(5/3)
7) B
8) C
10) A
Step-by-step explanation:
6) The fifth root is the same as raising to the 1/5 power, so we can write this in exponent form as:
f(x) = (x^(1/5))³
f(x) = x^(3/5)
To find the inverse, switch x and y and solve for y.
x = y^(3/5)
y = x^(5/3)
7) f(x) = 2√(x − 4) + 8
Switch the x and y and solve for y:
x = 2√(y − 4) + 8
x − 8 = 2√(y − 4)
(x − 8) / 2 = √(y − 4)
(x − 8)² / 4 = y − 4
(x² − 16x + 64) / 4 = y − 4
¼x² − 4x + 16 = y − 4
y = ¼x² − 4x + 20
8) Find the inverse:
x = 5√(y + 3) − 2
x + 2 = 5√(y + 3)
(x + 2) / 5 = √(y + 3)
(x + 2)² / 25 = y + 3
y = -3 + (x + 2)² / 25
The inverse function is an upwards parabola with a vertex at (-2, -3). The best fit is C.
desmos.com/calculator/fbabg5wc8b
10) √(4x − 31) = x − 7
Square both sides:
4x − 31 = (x − 7)²
4x − 31 = x² − 14x + 49
Combine like terms:
0 = x² − 18x + 80
Factor:
0 = (x − 8) (x − 10)
x = 8 or 10
Check for extraneous solutions.
√(4×8 − 31) = 8 − 7
1 = 1
√(4×10 − 31) = 10 − 7
3 = 3
x = 8 and x = 10 are both solutions.
Answer:
<h2>-28
°</h2>
Step-by-step explanation:
It is given that ∠1 is a right angle that is ∠1 = 90°.
∠8 - ∠1 = ∠ 7 = 62° - 90° = - 28°.
Answer:
D.1440
Step-by-step explanation:
V=lxwxh
10x12x12
1440
A. We are going to form 7 digit numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
where the first digit cannot be 0 or 1.
so we have 8 choices for the 1. digit, and 10 choices for all the other 6 digits.
this means there are

possible numbers.
b.
consider the numbers which start with 911. There are

such numbers, since for the 4th, 5th, 6th and 7th digits we have 10 choices.
then we remove this number, from the one we found in a:
There are in total

numbers which don't start with 911.
Answer:
a.

b.7,990,000