Answer: 0
<u>Step-by-step explanation:</u>
g(x) = x² + 6x ; x ≥ -3
To find the inverse, swap the x's and y's and solve for "y":
x = y² + 6y
x + 9 = y² + 6y + 9 <em>add 9 to both sides to create a perfect square</em>
x + 9 = (y + 3)²
= y + 3 <em>take square root of both sides</em>
= y ; y ≥ -3
g⁻¹(0) = 
= 
= -3 ± 3
= -3 + 3 , -3 - 3
= 0 , -6
since the restriction is: y ≥ -3, then -6 is not valid
Answer: the initial deposit is $162.1
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
r = 7% = 7/100 = 0.07
t = 3 years
A= $200
Therefore,
200 = P x 2.7183^(0.07 x 3)
200 = P x 1.234
P = 200/1.234
P = $162.1 to the nearest cent
Answer:
She will pay $3,000 less if she pays a down payment of $3,000.
Step-by-step explanation:
Down-payments are just payments you make on the spot for the vehicle.
Answer:
x = 10, theta = 30 degrees
Step-by-step explanation:
i. 6^2 + 8^2 = x^2
36 + 64 = x^2
100 = x^2
10 = x
ii. the angle is 30 degrees, because the opposite side is 1/2 of the hypotenuse.
You could also solve it with the law of sines:
sin(90)/12 = sin(x)/6
Multiply each side by 6
6 * sin(90)/12 = sin(x)
0.5 = sin(x)
x = 30 degrees
