Here,
let the longer piece be y and shorter piece be x
now,
according to the question,
x+y=19 .............................equation (1)
y=4+2x ...............................equation (2)
from equation 1
x+y=19
x+4+2x=19 substituting the value of y from equation 2
3x=19-4
x=(19-4)/3
x=5
now
substituting value of x in equation (2)
y=4+2(5)
y=4+10
y=14
so , the longer piece is 14 foot and the shorter piece is 5 foot
Answer:
The equation of the line is:
![y=(-\frac{1}{2})x+1](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B2%7D%29x%2B1)
Therefore, option a is the correct answer.
Step-by-step explanation:
Given the points
Finding the slope
![\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cquad%20%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(-2,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:-1\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-2%2C%5C%3A2%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%284%2C%5C%3A-1%5Cright%29)
![m=\frac{-1-2}{4-\left(-2\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1-2%7D%7B4-%5Cleft%28-2%5Cright%29%7D)
![m=-\frac{1}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B2%7D)
As the point-slope form of the equation of the line is
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
where m is the slope
substituting the values
and the point (-2, 2)
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
![y-2=\frac{-1}{2}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B-1%7D%7B2%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
![y-2=\frac{-1}{2}\left(x+2\right)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B-1%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29)
∵![\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7B-a%7D%7Bb%7D%3D-%5Cfrac%7Ba%7D%7Bb%7D)
Add 2 to both sides
![y-2+2=-\frac{1}{2}\left(x+2\right)+2](https://tex.z-dn.net/?f=y-2%2B2%3D-%5Cfrac%7B1%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29%2B2)
![y=(-\frac{1}{2})x+1](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B2%7D%29x%2B1)
Hence, the equation of the line is:
![y=(-\frac{1}{2})x+1](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B2%7D%29x%2B1)
Therefore, option a is the correct answer.
Answer:
False
Step-by-step explanation:
the answer is false because
year 1 to 2 is $18
year 2 to 3 is $17
year 3 to 4 is $18
year 4 to 5 is $17
false because simple interest always has the same money not a pattern
Answer:
Use the straightedge to draw GK−→−. Place the point of the compass on point H and draw an arc in the interior of the angle. Label the intersection of the arcs in the interior of the angle as point K. Place the point of the compass on point G and draw an arc that intersects the sides of ∠G.
Answer:
PS = 10 ![\sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D)
Step-by-step explanation: