Solution:
The grocery store is 1/6 miles far from her house.
Explanation:
We have been given that Sylvia walked 3/4 mi east from her house to the bank. Hence, the distance between the house and the bank is 3/4 miles.
Now, she walked 1/3 mi west to a gift shop. It means that she moved 1/3 miles towards her house.
Also, from the gift shop, she walked 1/4 mi west to a grocery store. It means she moved 1/3 miles plus 1/4 miles towards her house.
Hence, the distance between the grocery store and the house is
![\frac{3}{4}-\left ( \frac{1}{3}+\frac{1}{4} \right )\\\\=\frac{3}{4}-\frac{1}{3}-\frac{1}{4} \\\\ =\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D-%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B4%7D%20%5Cright%20%29%5C%5C%5C%5C%3D%5Cfrac%7B3%7D%7B4%7D-%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B1%7D%7B4%7D%20%5C%5C%5C%5C%20%3D%5Cfrac%7B1%7D%7B6%7D)
Answer:
(A)(10, –2)
Step-by-step explanation:
The image of the given triangle has points :
![A'(-2, 10)\\B'(-6, 4)\\C'(-10, 8)](https://tex.z-dn.net/?f=A%27%28-2%2C%2010%29%5C%5CB%27%28-6%2C%204%29%5C%5CC%27%28-10%2C%208%29)
When points are reflected across the line y = x, the x-coordinate and y-coordinate change places.
Therefore, the pre-image of the triangle has points:
![A(10,-2)\\B(4,-6)\\C(8,-10)](https://tex.z-dn.net/?f=A%2810%2C-2%29%5C%5CB%284%2C-6%29%5C%5CC%288%2C-10%29)
Therefore, the pre-image of vertex A' is (10,-2).
The correct option is A.
We need to convert this equation to slope-intercept form first.
We can do that by solving for y.
x - 5y = 15
<em><u>Add 5y to both sides.</u></em>
x = 5y + 15
<em><u>Subtract 15 from both sides.</u></em>
x - 15 = 5y
<em><u>Divide both sides by 5.</u></em>
y = 1/5x - 3
We now know the slope is 1/5.
The slope of the line perpendicular to the line with a slope of 1/5 is -5.
The slope of a perpendicular line is the negative reciprocal of the original slope.
Using a graphing calculator, we know the y-intercept of the line that is perpendicular to the original line must have a y-intercept of -6 to run through the points (-2, 5).
The equation of the new line is y = -5x - 6.
Im not sure but try
C. (x – 10)2 + (y + 6)2 = 36
standard form is (x-x1)^2 + (y-y1)^2=r^2.