Answer:
Step-by-step explanation:
We know that the length is four times the width, so:
We also know the area, which is 324 m². The formula for area:
Insert the known values:
Solve for w. Simplify by removing parentheses:
Divide 4 from both sides to isolate the variable:
Find the square root of both sides:
The width is 9 m.
We know the width. Now find the length by using the area formula and inserting known values:
Solve for l. Divide both sides by 9:
The length of the rectangle is 36. (You can check: 4 times 9 is 36)
Now find the perimeter:
Insert values:
The perimeter is 90 m.
Answer:
The second term of the sequence is 8 False ⇒ B
The third term of the sequence is 3 True ⇒ A
The fourth term of the sequence is -3 True ⇒ A
Step-by-step explanation:
The form of the recursive rule is:
f(1) = first term; f(n) = f(n - 1) + d, where
- f(n - 1) is the term before the nth term
- d is the common difference
∵ f(1) = 15, f(n) = f(n - 1) - 6 for n ≥ 2
∴ The first term = 15
∴ d = -6
let us find the 2nd, 3rd, and 4th terms
∵ n = 2
∴ f(2) = f(1) - 6
∵ f(1) = 15
∴ f(2) = 15 - 6 = 9
∴ The second term is 9
∴ The second term of the sequence is 8 False
∵ n = 3
∴ f(3) = f(2) - 6
∵ f(2) = 9
∴ f(3) = 9 - 6 = 3
∴ The third term is 3
∴ The third term of the sequence is 3 True
∵ n = 4
∴ f(4) = f(3) - 6
∵ f(3) = 3
∴ f(4) = 3 - 6 = -3
∴ The fourth term is -3
∴ The fourth term of the sequence is -3 True
Answer:
Step-by-step explanation:
f(x) = x^2 + 4x + 4
f(x + a) = (x + a)^2 + 4(x + a) + 4
f(x + a) = x^2 + 2ax + a^2 + 4x + 4a + 4 Now combine like terms and use the distributive property.
f(x + a) = x^2 + (2a + 4)x + a^2 + 4a + 4
We are told that f(x + a) = x^2 - 6x + 9
So that means that
2a + 4 = - 6 Subtract 4 from both sides.
2a = - 6 - 4
2a = - 10 Divide by 2
a = - 10/2
a = - 5.
But you are not finished. You have to check the last part.
a^2 + 4x + 4 = 9
(a + 2)^2 = 9
Take the square root of both sides
sqrt(a+ 2)^2 = +/- 3
a+2 = 3
a = 1.
Does this work or is it extraneous? It is extraneous because it will not work for 2(a) + 4 = - 6
You get 6 = - 6 which is not correct. But you did give the second best answer.
a + 2 = - 3
a = - 3 - 2
a = - 5 which agrees with your previous answer.
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This is an extremely hard or tricky or sneaky problem. It takes a lot of conniving to get the right answer and 1 is not a left field answer. It just does not happen to be correct.
I’m pretty sure you multiply the sides your you find the formulas for the hight and width
Answer:
$8.8 per hour
Step-by-step explanation:
Well, the equation is simple.
Time (hours) * Money (per hour) = Total
We know the time he worked for and the total amount he earned, so just replace in this equation and find the unknown number
12.5 * money = 110
To find the money he earns per hour we should just simply divide the total amount he earned by the hours he spent working
money = 110/12.5
money = 8.8$
You can also check it out to make sure it's correct.
If he earns 8.8$ per hour and worked for 12.5 hours how much he'll earn? Let's find out
8.8 * 12.5 =?
8.8 * 12.5 = 110, the same total amount so our solution must be correct.
