Answer:

Step-by-step explanation:
we have

we know that




Substitute the values in the expression


Answer:
The last one (x,y)->(x+3,y+5)
Step-by-step explanation:
Whenever you move the x coordinate it’s the opposite, for example translated 3 units the the left is +3 and translated 3 units to the right is -3.
Whenever you move the y coordinate it’s normal so up 5 units means +5 and down means -5.
Answer:
28 ft
Step-by-step explanation:
Let longer side of rectangle be
and the shorter side be
, thus we can write the ratio:

<em>Now putting 21 into S, we solve for L:</em>

Hence, length of longer side is 28 ft.
Answer:

Step-by-step explanation:
-For a known standard deviation, the sample size for a desired margin of error is calculated using the formula:

Where:
is the standard deviation
is the desired margin of error.
We substitute our given values to calculate the sample size:

Hence, the smallest desired sample size is 23
Answer:
The answer is 3 and (-4).
Step-by-step explanation:
We are given an equation 2x² + 2x – 24.
Let us assume that the equation is equal to zero.
2x² + 2x – 24 = 0
Now, divide whole equation by 2 we get,
x² + x – 12 = 0
x² + 4x – 3x – 12 = 0
x(x + 4) – 3(x + 4) = 0
(x – 3) (x + 4) = 0
x = 3, -4
Thus, The actual roots of f(x) are 3 and (-4).