Answer:
Step-by-step explanation:
The "ab" inside absolute value has to go out positive, such as |-2|=2
Since both the a and b values are positive, the value of |ab| should be "ab"
For example:
a=2
b=3
|ab| = |2*3| = |6| = 6
Answer:
-1/32
Step-by-step explanation:
Answer:
The monthly growth rate is 3.5%.
Step-by-step explanation:
The exponential growth function is given as follows:
![y=a(1+r)^{x}](https://tex.z-dn.net/?f=y%3Da%281%2Br%29%5E%7Bx%7D)
Here,
<em>y</em> = final value
<em>a</em> = initial value
<em>r</em> = growth rate
<em>x</em> = time taken
The provided expression for the monthly growth of membership in the new drama club at a school is:
![f(x) = 12\cdot(1.035)^{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%2012%5Ccdot%281.035%29%5E%7Bx%7D)
Comparing this function with the exponential growth function:
![a(1+r)^{x}=12(1.035)^{x}\\\\a(1+r)^{x}=12(1+0.035)^{x}](https://tex.z-dn.net/?f=a%281%2Br%29%5E%7Bx%7D%3D12%281.035%29%5E%7Bx%7D%5C%5C%5C%5Ca%281%2Br%29%5E%7Bx%7D%3D12%281%2B0.035%29%5E%7Bx%7D)
Then value of <em>r</em> is 0.035 or 3.5%.
Thus, the monthly growth rate is 3.5%.
Answer:
-363
Step-by-step explanation:
42-27*5
42-405
Answer: -363
We have been given that a line
passes through the point (10, 3) and is parallel to the line
. We are asked to find the y-intercept of the line.
First of all we will rewrite our given equation in slope-intercept form as:
![2x-2x+5y=12-2x](https://tex.z-dn.net/?f=2x-2x%2B5y%3D12-2x)
![5y=-2x+12](https://tex.z-dn.net/?f=5y%3D-2x%2B12)
![\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5y%7D%7B5%7D%3D-%5Cfrac%7B2%7D%7B5%7Dx%2B%5Cfrac%7B12%7D%7B5%7D)
![y=-\frac{2}{5}x+\frac{12}{5}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B5%7Dx%2B%5Cfrac%7B12%7D%7B5%7D)
We know that slope of parallel lines is equal, so slope of parallel line to our given line would be
.
Now we will use slope-intercept form of equation to find y-intercept.
, where,
m = Slope,
b = The y-intercept.
Let us substitute
and coordinates of point
in above equation as:
![3=-\frac{2}{5}(10)+b](https://tex.z-dn.net/?f=3%3D-%5Cfrac%7B2%7D%7B5%7D%2810%29%2Bb)
![3=-2(2)+b](https://tex.z-dn.net/?f=3%3D-2%282%29%2Bb)
![3=-4+b](https://tex.z-dn.net/?f=3%3D-4%2Bb)
![3+4=-4+4+b](https://tex.z-dn.net/?f=3%2B4%3D-4%2B4%2Bb)
![7=b](https://tex.z-dn.net/?f=7%3Db)
Therefore, the y-intercept is 7 and our required equation would be
.