Answer:
7
Step-by-step explanation:
f(x) = 2^(x + 3)
Shifted 10 units to the right:
f(x) = 2^(x + 3 − 10)
f(x) = 2^(x − 7)
Therefore, k = 7.
Answer:
The dimensions of the wall are 100 ft x 100 ft
Step-by-step explanation:
we know that
The perimeter of a rectangular wall is
where
x is the length
y is the width
we have
so
simplify
----> equation A
The area of a rectangular wall is equal to
----> equation B
substitute equation A in equation B
This is the equation of a vertical parabola open downward (because the leading coefficient is negative)
The vertex represent a maximum
Convert the quadratic equation in vertex form
Factor -1
Complete the square
Rewrite as perfect squares
----> equation in vertex form
The vertex is the point (100,10,000)
The x-coordinate of the vertex represent the length of the wall for a maximum area
so
Find the value of y
equation A
therefore
The dimensions of the wall are 100 ft x 100 ft
Answer:
22.56
Step-by-step explanation:
1. We assume, that the number 94 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 94 is 100%, so we can write it down as 94=100%.
4. We know, that x is 24% of the output value, so we can write it down as x=24%.
5. Now we have two simple equations:
1) 94=100%
2) x=24%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
94/x=100%/24%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 24% of 94
94/x=100/24
(94/x)*x=(100/24)*x - we multiply both sides of the equation by x
94=4.1666666666667*x - we divide both sides of the equation by (4.1666666666667) to get x
94/4.1666666666667=x
22.56=x
x=22.56
Answer:
A 22
D 36
E 17
F 2
Step-by-step explanation:
sqrt(x) ≤6
Square each side
(sqrt(x))^2 ≤(6)^2
x ≤36
But we also know that x ≥ 0 from the square root
0≤x≤36
Answer:
The cost of a chair is $100
The cost of a table is $150
Step-by-step explanation:
