Answer:
We have the sentence:
"X by the power of 5 times y to the power of 6 over 2 by the power of -2 times x by the power of 0times x by the power of 9"
Let's break it into parts.
"X by the power of 5 times y to the power of 6..."
This can be written as:
x^5*y^6
"... 2 by the power of -2 times x by the power of 0times x by the power of 9"
This can be written as:
2^(-2)*x^(0)*x^(9)
And we have the quotient between the first thing and the second thing, then the equation is:

And any number by the power of 0 is equal to 1, then:
x^0 = 1, then we can rewrite the equation as:

We can keep simplifying this.
We know that:
a^(-n) = (1/a)^(n)
Then:
2^(-2) = (1/2)^2 = 1/4
Then we get:

And we also know that:
a^n/a^m = a^(n - m)
Then:

And we can't simplify this anymore.
There are 4 cups per 1 quart...
4/1 × 2/2 = 8/2
There are 8 cups in 2 quarts.
Answer: Explanation:First, let's call the number of 2 cent coins: tNext, let's call the number of 5 cent coins: fWe can then write to equations from the information in the problem.Equation 1: t+f=40Equation 2: 0.02t+0.05f=1.55Step 1) Solve the first equation for t:t+f=40t+f−f=40−ft+0=40−ft=40−fStep 2) Substitute (40−f) for t in the second equation and solve for f:0.02t+0.05f=1.55 becomes:0.02(40−f)+0.05f=1.55(0.02×40)−(0.02×f)+0.05f=1.550.80−0.02f+0.05f=1.550.80+(−0.02+0.05)f=1.550.80+0.03f=1.550.80−0.80+0.03f=1.55−0.800+0.03f=0.750.03f=0.750.03f0.03=0.750.030.03f0.03=25f=25Step 3) Substitute 25 for f in the solution to the first equation at the end of Step 1 and calculate t:t=40−f becomes:t=40−25t=15The Solution Is:There are:15 two cent coins25 five cent coins
Step-by-step explanation:
Answer:

Step-by-step explanation:
<em>Look at the picture.</em>
We have
square with side length a = 9
trapezoid with base lengths b₁ = 9 and b₂ = 6 and the height length h = 6
right triangle with legs lengths l₁ = 3 + 6 = 9 and l₂ = 6
The formula of an area of a square

Substitute:

The formula of an area of a trapezoid:

Substitute:

The formula of an area of a right triangle:

Substitute:

The area of the shape:
