Let the smaller number be x
The bigger number is 5x
5x(x) = 180
5x² = 180
x² = 180÷5
x²=36
x=√36
x = 6
x=6
5x = 6 x 5
5x = 30
So the two numbers are 6 and 30
Answer:
V=720ft³
Step-by-step explanation:
V=whl=4·20·9=720ft³
happy to help
Answer:
Step-by-step explanation:
Since we know that the two lines are parallel because of alternate interior angles (5x-20)=3x
then solve for x
5x-20=3x
-20=-2x
x=10°
Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!
You need to know three exponent rules to simplify these expressions:
1)
The
negative exponent rule says that when a
base has a negative exponent, flip the base onto the other side of the
fraction to make it into a positive exponent. For example,

.
2)
Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example,

.
3) The
zero exponent rule<span> says that any number
raised to zero is 1. For example,

.
</span>
Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is

. The x-values are:
<span>
1) x = 0</span>Plug this into

to find letter a:

<span>
2) x = 2</span>Plug this into

to find letter b:

<span>
3) x = 4</span>Plug this into

to find letter c:

<span>
Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is

. The x-values are:
<span>
1) x = 0</span>Plug this into

to find letter d:

<span>
2) x = 2
</span>Plug this into

to find letter e:

<span>
3) x = 4
</span>Plug this into

to find letter f:

<span>
-------
Answers: a = 1b = </span>

<span>
c = </span>
d = 1e =
f =
Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations is the point of intersection of the two lines. From inspection of the graph, the point of intersection is at (1, 5).
<u>Proof</u>
The solution to a system of equations is the point at which the two lines meet.
⇒ g(x) = f(x)
⇒ 3x + 2 = |x - 4| + 2
⇒ 3x = |x - 4|
⇒ 3x = x - 4 and 3x = -(x - 4)
⇒ 3x = x - 4
⇒ 2x = -4
⇒ x = -2
Inputting x = -2 into the 2 equations:
⇒ g(-2) = 3 · -2 + 2 = -4
⇒ f(-2) = |-2 - 4| + 2 = 8
Therefore, as the y-values are different, x = -2 is NOT a solution
⇒ 3x = -(x - 4)
⇒ 3x = 4 - x
⇒ 4x = 4
⇒ x = 1
Inputting x = 1 into the 2 equations:
⇒ g(1) = 3 · 1 + 2 = 5
⇒ f(1) = |1 - 4| + 2 = 5
Therefore, as the y-values are the same, x = 1 IS a solution
and the solution is (1, 5)