Answer:
7. parallel: k = 3
perpendicular: k = -4/3
8. $1300
Step-by-step explanation:
7.
Rewrite each equation as the slope-intercept form of a linear equation:
y = mx + b (where m is the slope and b is the y-intercept)
8y = 12x + 6
⇒ ![y=\dfrac32x+\dfrac34](https://tex.z-dn.net/?f=y%3D%5Cdfrac32x%2B%5Cdfrac34)
4y = k(2x + 10)
⇒ 4y = 2kx + 10k
⇒ ![y = \dfrac12kx + \dfrac52k](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac12kx%20%2B%20%5Cdfrac52k)
If the graphs are parallel their slopes will be the same.
![\implies \dfrac32=\dfrac12k](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac32%3D%5Cdfrac12k)
![\implies k=3](https://tex.z-dn.net/?f=%5Cimplies%20k%3D3)
If the graphs are perpendicular then the product of their slopes will be -1.
![\implies \dfrac32 \times \dfrac12k=-1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac32%20%5Ctimes%20%5Cdfrac12k%3D-1)
![\implies \dfrac12k=-\dfrac23](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac12k%3D-%5Cdfrac23)
![\implies k=-\dfrac43](https://tex.z-dn.net/?f=%5Cimplies%20k%3D-%5Cdfrac43)
8. Create a linear equation, where x is the number of coffee mugs and y is the total cost (in dollars).
Choose 2 ordered pairs from the table: (10, 110) and (20, 195)
Let
= (10, 110)
Let
= (20, 195)
Use the slope formula to find the slope m:
![\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{195-110}{20-10}=\dfrac{17}{2}](https://tex.z-dn.net/?f=%5Cimplies%20m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cdfrac%7B195-110%7D%7B20-10%7D%3D%5Cdfrac%7B17%7D%7B2%7D)
Now use the point-slope form of linear equation:
![\implies y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=%5Cimplies%20y-y_1%3Dm%28x-x_1%29)
![\implies y-110=\dfrac{17}{2}(x-10)](https://tex.z-dn.net/?f=%5Cimplies%20y-110%3D%5Cdfrac%7B17%7D%7B2%7D%28x-10%29)
![\implies y=\dfrac{17}{2}x+25](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Cdfrac%7B17%7D%7B2%7Dx%2B25)
Substitute x = 150 into the equation and solve for y:
![\implies y=\dfrac{17}{2}(150)+25=1300](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Cdfrac%7B17%7D%7B2%7D%28150%29%2B25%3D1300)
Therefore, the total cost of ordereing 150 mugs is $1300
Answer:
B.) as x --> -∞, f(x) --> ∞ and x --> ∞, f(x) --> ∞
Step-by-step explanation:
F(x) is another way of representing "y". That being said, the question is asking you the behavior of the graph in terms of the y-axis. On both sides of the function, there is an arrow pointing upwards, towards infinite, positive y-values. Therefore, as "x" approaches -∞ and ∞, f(x) is approaching ∞ (positive infinity).
Answer: jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj
Step-by-step explanation:
I think d because it's the longest side
Answer:
I dont know im slow sneaky step sis is the way to go
Step-by-step explanation: