Answer: 15 inches is the height of Keisha's fish tank.
Step-by-step explanation: Basically, multiply your length x width, which is 12 x 10. 12 x 10 = 120.
Next, divide 1800 by 120.
1800 divided by 120 is 15.
So, 15 inches is the height of the fish tank.
Answer:
Step-by-step explanation:
Graph: f(x) = 1 - ex
You meant f(x) = 1 - e^x, where ^ represents exponentiation.
First, graph the parent function y = e^x. The y-intercept of this graph is (0, 1), and the x-axis is the horizontal intercept. The graph begins on the left in Quadrant 2 and continues upward in Quadrant 1.
Next, reflect this graph in the x-axis, due to the - sign in f(x) = 1 - e^x. The y-intercept is (0, -1) and the horizontal asymptote is the x-axis.
Finally, translate the whole graph upward by 1 unit.
The value of x is –7.
Solution:
Given expression:
![$\left(\frac{1}{x+3}+\frac{6}{x^{2}+4 x+3}\right) \cdot \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%24%5Cleft%28%5Cfrac%7B1%7D%7Bx%2B3%7D%2B%5Cfrac%7B6%7D%7Bx%5E%7B2%7D%2B4%20x%2B3%7D%5Cright%29%20%5Ccdot%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D)
Let us factor
.
![x^2+4x+3=(x+1)(x+3)](https://tex.z-dn.net/?f=x%5E2%2B4x%2B3%3D%28x%2B1%29%28x%2B3%29)
Substitute this in the fraction.
![$\left(\frac{1}{x+3}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%24%5Cleft%28%5Cfrac%7B1%7D%7Bx%2B3%7D%2B%5Cfrac%7B6%7D%7B%28x%2B1%29%28x%2B3%29%7D%5Cright%29%20%5Ccdot%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D)
To make the denominator same, multiply and divide the first term by (x +1).
![$\left(\frac{(x+1)}{(x+1)(x+3)}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%24%5Cleft%28%5Cfrac%7B%28x%2B1%29%7D%7B%28x%2B1%29%28x%2B3%29%7D%2B%5Cfrac%7B6%7D%7B%28x%2B1%29%28x%2B3%29%7D%5Cright%29%20%5Ccdot%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D)
Denominators are same, you can add the fractions.
![$\left(\frac{x+1+6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%24%5Cleft%28%5Cfrac%7Bx%2B1%2B6%7D%7B%28x%2B1%29%28x%2B3%29%7D%5Cright%29%20%5Ccdot%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D)
![$\frac{x+7}{(x+1)(x+3)} \cdot \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%2B7%7D%7B%28x%2B1%29%28x%2B3%29%7D%20%5Ccdot%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D)
Cancel the common term in the numerator and denominator.
![$\frac{x+7}{x+1} \cdot \frac{1}{x+1}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%2B7%7D%7Bx%2B1%7D%20%5Ccdot%20%5Cfrac%7B1%7D%7Bx%2B1%7D)
Multiply the fractions.
![$\frac{x+7}{(x+1)^2}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%2B7%7D%7B%28x%2B1%29%5E2%7D)
![$\frac{x+7}{x^2+2x+1}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%2B7%7D%7Bx%5E2%2B2x%2B1%7D)
The expression is simplified to one rational expression.
Suppose the expression is equal to 0.
![$\frac{x+7}{x^2+2x+1}=0](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%2B7%7D%7Bx%5E2%2B2x%2B1%7D%3D0)
Do cross multiplication.
![${x+7}=0\times (}{x^2+2x+1})](https://tex.z-dn.net/?f=%24%7Bx%2B7%7D%3D0%5Ctimes%20%28%7D%7Bx%5E2%2B2x%2B1%7D%29)
Any number or variable multiplied by 0 gives 0.
![${x+7}=0](https://tex.z-dn.net/?f=%24%7Bx%2B7%7D%3D0)
Subtract 7 from both sides of the equation.
![${x+7-7}=0-7](https://tex.z-dn.net/?f=%24%7Bx%2B7-7%7D%3D0-7)
x = –7
The value of x is –7.
Answer:
77
Step-by-step explanation:
Add the numbers together, then divide them to how much numbers are there.
74 + 75 + 80 + 76 + 75 + 81 + 78 = 539
Since there are 7 numbers, you divide 539 by 7.
539/7 = 77
To find relative frequency of no voters;
p(A)=favourable outcomes/total outcomes
p(A)=100/400
= 1/4 or 0.25
Therefore, the probability a person will respond with a no is 0.25.
Hope I helped :)