Answer:
a. y = 8x + 7
b. 8y = -x-74
Step-by-step explanation:
Here, we want to write the equation of a line which is parallel to y = 8x + 7 and passes through the given point
Since the line we want to write the equation is parallel to y = 8x + 7, it means that they have the same slope
Mathematically we can write the equation of a line as y = mx + c where m is the slope. Comparing this with y = 8x + 7, our slope is therefore 8
Now, the slope of our new line is also 8
We now make use of the point slope method to write the equation
Mathematically the point slope method is;
y-y1 = m(x-x1)
where our (x1,y1) = (-2,-9)
y-(-9) = 8(x -(-2))
y + 9 = 8(x + 2)
y + 9 = 8x + 16
y = 8x + 16-9
y = 8x + 7
For the second line, it is perpendicular to y = 8x + 7
Here too, we have the slope as 8
Now since they are perpendicular, it means that the product of the slopes is equal to -1
m1 * m2 = -1
8 * m2 = -1
m2 = -1/8
Now;
y-y1 = m(x-x1)
our point still remains same (-2,-9)
y-(-9) = -1/8 (x -(-2))
y + 9 = -1/8(x + 2)
8(y + 9) = -1(x + 2)
8y + 72 = -x -2
8y = -x -2-72
8y = -x-74
Answer:
Step-by-step explanation:
The plot chart below best represents the relationship between stress and productivity in the workplace. As seen in the chart both high and low levels of stress equate to very low productivity levels for employees in the workplace. While just enough stress creates very productive employees. This tends to be because employees are worried about the possibility of losing their jobs so they work hard in order to keep the job but are not so worried that they think it will happen tomorrow and become burned out.
Option C: 
is the possible expressions for length, width and height of the prism.
Explanation:
The volume of the rectangular prism is 
To determine the length, width and height of the rectangular prism, let us factor the expression.
Thus, factoring 5x from the expression, we have,
Let us break the expression 
into two groups, we get,
![5x[\left(12 x^{2}+8 x\right)+(21 x+14)]](https://tex.z-dn.net/?f=5x%5B%5Cleft%2812%20x%5E%7B2%7D%2B8%20x%5Cright%29%2B%2821%20x%2B14%29%5D)
Factoring 4x from the term 
, we get,
![5x[4 x(3 x+2)+(21x+14)]](https://tex.z-dn.net/?f=5x%5B4%20x%283%20x%2B2%29%2B%2821x%2B14%29%5D)
Similarly, factoring 7x from the term 
, we get,
![5x[4 x(3 x+2)+7(3x+2)]](https://tex.z-dn.net/?f=5x%5B4%20x%283%20x%2B2%29%2B7%283x%2B2%29%5D)
Now, let us factor out 
, we get,
Hence, the possible expressions for length, width and height of the prism is
Therefore, Option C is the correct answer.
Answer: The cats cost more
also there is a typo
Step-by-step explanation:
I bought 1 dog and 3 cats a total cost of $7.75. the three cats cost more so in all the cats must cost 3.56$
Put it in an improper fraction by multiply the coefficient with the denominator and add the numerator.
5/2 , 14/3
Find a common denominator which would be 6.
5/2 = 15/6 , 28/6
Add those together.
15/6 + 28/6 = 43/6
Since it can't be simplified the answer is 43/6
