An architect plans to make a drawing of the room of a house. The segment LM represents the ceiling of the room. He wants to construct a line passing through Q and perpendicular to side LM to represent a wall of the room. He uses a straightedge and compass to complete some steps of the construction, as shown below:
470 = 8.75(46 - c) + 11c
470 = 402.5 - 8.75c + 11c
67.5 = 2.25c
30 = c
If c = 30 and Soren worked 30 hours in the office, earning $11 per hour, he earns $330 from his office job. 46 - 30 = 16, which should be the remaining amount of hours Soren worked. 16 * 8.75 = 140. He earned $140 from his cashier job. $330 + $140 = $470.
The correct formula to solve this problem is A. 11c + 8.75(46 - c) = 470
Answer:
8.8%
Step-by-step explanation:
you have ( $150 / $1695 ) * 100 = 8.8
The slope-point form of a line:
![y-y_0=m(x-x_0)](https://tex.z-dn.net/?f=y-y_0%3Dm%28x-x_0%29)
The slope-intercept form of a line:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
1.
![m=6,\ (4,\ 1)\to x_0=4,\ y_0=1](https://tex.z-dn.net/?f=m%3D6%2C%5C%20%284%2C%5C%201%29%5Cto%20x_0%3D4%2C%5C%20y_0%3D1)
Substitute
![y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}](https://tex.z-dn.net/?f=y-1%3D6%28x-4%29%5Cqquad%7C%5Ctext%7Buse%20distributive%20property%7D%5C%5C%5C%5Cy-1%3D6x-24%5Cqquad%7C%5Ctext%7Badd%201%20to%20both%20sides%7D%5C%5C%5C%5C%5Cboxed%7By%3D6x-23%7D)
2.
![m=-5,\ (6,\ -3)](https://tex.z-dn.net/?f=m%3D-5%2C%5C%20%286%2C%5C%20-3%29)
Substitute
![y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}](https://tex.z-dn.net/?f=y-%28-3%29%3D-5%28x-6%29%5Cqquad%7C%5Ctext%7Buse%20distributive%20property%7D%5C%5C%5C%5Cy%2B3%3D-5x%2B30%5Cqquad%7C%5Ctext%7Bsubtract%205%20from%20both%20sides%7D%5C%5C%5C%5C%5Cboxed%7By%3D-5x%2B24%7D)
3.
![m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}](https://tex.z-dn.net/?f=m%3D-%5Cdfrac%7B1%7D%7B2%7D%2C%5C%20%28-8%2C%5C%202%29%5C%5C%5C%5Cy-2%3D-%5Cdfrac%7B1%7D%7B2%7D%28x-%28-8%29%29%5C%5C%5C%5Cy-2%3D-%5Cdfrac%7B1%7D%7B2%7D%28x%2B8%29%5C%5C%5C%5Cy-2%3D-%5Cdfrac%7B1%7D%7B2%7Dx-4%5Cqquad%7C%5Ctext%7Badd%202%20to%20both%20sides%7D%5C%5C%5C%5C%5Cboxed%7By%3D-%5Cdfrac%7B1%7D%7B2%7Dx-2%7D)
4.
![m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}](https://tex.z-dn.net/?f=m%3D0%2C%5C%20%28-7%2C%5C%20-1%29%5C%5C%5C%5Cy-%28-1%29%3D0%28x-%28-7%29%29%5C%5C%5C%5Cy%2B1%3D0%5Cqquad%7C%5Ctext%7Bsubtract%201%20from%20both%20sides%7D%5C%5C%5C%5C%5Cboxed%7By%3D-1%7D)
Answer:
The correct answer is 25.2 in.
Step-by-step explanation:
It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.
2 inches of the ribbon are frayed so actual length = 58 inches
Please refer to the attached image for the ribbon.
A is at 0
C is at 60
B is at 2
P is the point to divide the remaining ribbon in the ratio 2:3.
Part AB of the ribbon is frayed.
BP: PC = 2:3
Let BP = 2
and PC = 3![x](https://tex.z-dn.net/?f=x)
Now, BP + PC = BC = 58 = 2
+ 3
= 5![x](https://tex.z-dn.net/?f=x)
So,
![5x =58\\\Rightarrow x =11.6](https://tex.z-dn.net/?f=5x%20%3D58%5C%5C%5CRightarrow%20x%20%3D11.6)
BP = ![2\times x = 2 \times 11.6 = 23.2\ inches](https://tex.z-dn.net/?f=2%5Ctimes%20x%20%3D%202%20%5Ctimes%2011.6%20%3D%2023.2%5C%20inches)
Location of the Cut = 2 + 23.2 = <em>25.2 inches</em>
<em></em>
Alternatively, we can use the formula directly:
![x = \dfrac{m} {m + n } (x_2 - x_1) + x_1](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7Bm%7D%20%7Bm%20%2B%20n%20%7D%20%28x_2%20-%20x_1%29%20%2B%20x_1)
![x_1 = 2\\x_2 = 60](https://tex.z-dn.net/?f=x_1%20%3D%202%5C%5Cx_2%20%3D%2060)
m: n is the ratio 2:3
![x = \dfrac{2} {2 +3 } (60- 2) + 2\\\Rightarrow 0.4 (58 )+2\\\Rightarrow 23.2+2 \\\Rightarrow \bold{25.2\ inches}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B2%7D%20%7B2%20%2B3%20%7D%20%2860-%202%29%20%2B%202%5C%5C%5CRightarrow%200.4%20%2858%20%29%2B2%5C%5C%5CRightarrow%2023.2%2B2%20%5C%5C%5CRightarrow%20%5Cbold%7B25.2%5C%20inches%7D)