<h3><u>Solution</u></h3>
<u>Given </u><u>:</u><u>-</u>
- Paul is exactly 6yrs older than jane.
- jane.the ratio of their ages is5:3
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>:</u><u>-</u>
<h3><u>E</u><u>x</u><u>p</u><u>l</u><u>a</u><u>n</u><u>a</u><u>t</u><u>i</u><u>o</u><u>n</u></h3>
<u>Let,</u>
- Age of paul = x years
- Age of jane = y years
<u>A</u><u>c</u><u>c</u><u>o</u><u>r</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>to</u><u> question</u>
==> x = 6 + y
==> x - y = 6_____(1)
<u>And,</u>
==> x : y = 5:3
==> x/y = 5/3
==> 3x - 5y = 0______(2)
Multiply by 3 in equ(1)
==> 3x - 3y = 18_____(3)
<u>Subtract</u><u> </u><u>equ(</u><u>2</u><u>)</u><u> </u><u>&</u><u> </u><u>(</u><u>3</u><u>)</u>
==> -5y + 3y = -18
==> -2y = -18
==> y = 18/2
==> y = 9
<u>keep </u><u>in </u><u>equ(</u><u>2</u><u>)</u>
==> 3x - 5×9 = 0
==> 3x = 45
==> x = 45/3
==> x = 15
<h3><u>Hence</u></h3>
<h2><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u></h2>
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
The correct answer is B
The point (4,4) is a solution to both because the point lies on both of the lines that are graphed.
I think the answer is 245.14