Answer:
#15) B. 30 mn^5
#17) B. 1/2
Step-by-step explanation:
<h2>#15:</h2>
The area of a trapezoid is given in the formula: 1/2(a + b) * h, where a is the length of the top of the trapezoid, b is the length of the bottom of the trapezoid, and h is the height of the trapezoid.
All of these measurements are given so all that you need to do is to substitute these values into the formula.
Substitute 3 for a, 9 for b, and 5 for h.
Solve inside the parentheses first. Add 3 and 9.
Multiply 12 and 1/2 together.
Multiply 6 and 5.
We need to figure out if the area is to the 5th or 6th power. When we added 3 and 9 together, we combined like terms so the exponent stayed to the 3rd power.
After multiplying this ^3 by the 5mn^2, the exponent becomes to the 5th power because you add exponents when multiplying.
Therefore the final answer is B. 30 mn^5.
<h2>#17:</h2>
When going down from 32 to 8 to 2, you can see that each number is being divided by 4.
32 / 4 = 8...
8 / 4 = 2...
So to find the next number in this sequence you would divide 2 by 4.
The answer is B. 1/2.
Answer:
Part A)
The equation in the point-slope form is:
![y-11=\frac{4}{3}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-11%3D%5Cfrac%7B4%7D%7B3%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
Part B)
The graph of the equation is attached below.
Step-by-step explanation:
Part A)
Given
The point-slope form of the line equation is
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
Here, m is the slope and (x₁, y₁) is the point
substituting the values m = 4/3 and the point (-2, 11) in the point-slope form of the line equation
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
![y-11=\frac{4}{3}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-11%3D%5Cfrac%7B4%7D%7B3%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
Thus, the equation in the point-slope form is:
![y-11=\frac{4}{3}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-11%3D%5Cfrac%7B4%7D%7B3%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
Part B)
As we have determined the point-slope form which passes through the point (-2, 11) and has a slope m = 4/3
The graph of the equation is attached below.
In the given figure we can determine the coordinate of point M from the graph, we get:
![M=(\frac{d}{2},\frac{c}{2})](https://tex.z-dn.net/?f=M%3D%28%5Cfrac%7Bd%7D%7B2%7D%2C%5Cfrac%7Bc%7D%7B2%7D%29)
We can also determine the coordinates of point N as:
![N=(\frac{a+b}{2},\frac{c}{2})](https://tex.z-dn.net/?f=N%3D%28%5Cfrac%7Ba%2Bb%7D%7B2%7D%2C%5Cfrac%7Bc%7D%7B2%7D%29)
Now, to determine the length of segment MN, we need to subtract the x-coordinate of M from the coordinates of N, we get:
![MN=\frac{a+b}{2}-\frac{d}{2}](https://tex.z-dn.net/?f=MN%3D%5Cfrac%7Ba%2Bb%7D%7B2%7D-%5Cfrac%7Bd%7D%7B2%7D)
Subtracting the fractions we get:
![MN=\frac{a+b-d}{2}](https://tex.z-dn.net/?f=MN%3D%5Cfrac%7Ba%2Bb-d%7D%7B2%7D)
Now, to obtain the length of AB we need to subtract the x-coordinate of A from the x-coordinate of B.
The coordinates of A are determined from the graph:
![A=(0,0)](https://tex.z-dn.net/?f=A%3D%280%2C0%29)
The coordinates of B are:
![B=(a,0)](https://tex.z-dn.net/?f=B%3D%28a%2C0%29)
Therefore, the length of segment AB is:
![AB=a](https://tex.z-dn.net/?f=AB%3Da)
Now we do the same procedure to determine the segment of CD. The coordinates of C are:
![C=(b,c)](https://tex.z-dn.net/?f=C%3D%28b%2Cc%29)
The coordinates of D are:
![D=(d,c)](https://tex.z-dn.net/?f=D%3D%28d%2Cc%29)
Therefore, CD is:
![CD=b-d](https://tex.z-dn.net/?f=CD%3Db-d)
Now, we determine MN as half the sum of the bases. The bases are AB and CD, therefore:
![MN=\frac{1}{2}(a+b-d)](https://tex.z-dn.net/?f=MN%3D%5Cfrac%7B1%7D%7B2%7D%28a%2Bb-d%29)
Therefore, we have proven that the median of a trapezoid equals half the sum of its bases.
![f(t) = 80(4^t)](https://tex.z-dn.net/?f=f%28t%29%20%3D%2080%284%5Et%29)
For each time period, each time "t" increases by one, the population will be multiplied by 4.