Answer:
length of rectangle = 5
width of rectangle = 5
Area of rectangle = 25
Step-by-step explanation:
Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:
Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.
Recall that the formula for the x of the vertex of a quadratic of the form :
is given by the formula:
which in our case gives:
Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.
The area of the rectangle is therefore the product of these two values: 5 * 5 = 25
Which should coincide with the value we obtain when we replace x by 5 in the area formula:
4 hours for short or 4.333 hours
The money will be triple after 15 years and 303 days.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given:
Principle (P) = $10,000
The amount will be triple.
So, Amount (A) = $30,000
Rate (r) = 7% = 0.07
The interest is compounded quarterly.
n = 4
We have to find the value of t.
Let,
Apply logarithm on both sides,
Hence, the money will be triple after 15 years and 303 days.
To know more about compound interest, click on the link
brainly.com/question/24274034
#SPJ4
The cost of large pizza is $24.62, a small pizza has an 8-in. diameter a large pizza has a 15-in. diameter the pizzeria charges the same price per square inch for both pizzas and the small pizza cost $7.
Step-by-step explanation:
The given is,
A small pizza has an 8-inches in diameter
A large pizza has a 15-inches in Diameter
The small pizza cost $7
Step:1
Area of smaller pizza,
...................................(1)
Where, r - Radius of small pizza
From given, 
r = 4 inches
Equation (1),
( ∵ 
=3.14 )
Square inches
Step:2
Area of smaller pizza,
...................................(1)
Where, r - Radius of small pizza
From given,
r = 7.5 inches
Equation (1),
( ∵ =3.14 )
Square inches
Step:3
Cost of pizza per square meter,
= $ 0.1393 per square meter
× 
= $24.62
Result:
The cost of large pizza is $24.62, a small pizza has an 8-in. diameter a large pizza has a 15-in. diameter the pizzeria charges the same price per square inch for both pizzas and the small pizza cost $7.
The required composite value f(g(-8) is 28
A composite function is a function inside another function. Given the following functions
f(x) = x² - 3x - 12
g(x) = -x - 12
Required composite function is f(g(-8))
First we need to get f(g(x))
f(g(x)) = f(-x-12)
f(-x-12) = (-x-12)² - 3x - 12
Expand
f(-x-12) = x² +24x + 144 - 3x - 12
f(-x-12) = x² +21x + 132
f(g(x)) = x² +21x + 132
Substitute x = -8 into the result
f(g(-8)) = (-8)² +21(-8) + 132
f(g(-8)) = 64 - 168 + 132
f(g(-8)) = 28
Hence the required composite value f(g(-8) is 28
Learn more here : brainly.com/question/3256461
