Answer:
x=1.25, y=1.75
Step-by-step explanation:
The two triangles formed (one triangle with side lengths of 5, 7, 8 and another with sides 5+x, 10, and 7+y) are similar, because they share the same angle measures.
Now, 2 sides given that we can compare ratios with are the side with length 8, and the side with length 10. 10/8= 1.25, which is the ratio of the sides on these 2 triangles.
Now we want to find what the side '5+x' is equal to. To do that we can use our ratio, and multiply 5 by 1.25 to find '5+x'. This is 6.25. To find x, all we need to do is subtract 5 from 6.25, which is 1.25.
Let's find y now. Do the same thing that we did with the side '5+x'; find what '7+y' is by multiplying 7 by 1.25, which is 8.75. 8.75-7= 1.75.
Hope this helps! :)
<h3>
Answer: Slope = -2/3</h3>
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Explanation:
Let's compute the slope of the line through the two original points
m = (y2-y1)/(x2-x1)
m = (4-10)/(7-(-2))
m = (4-10)/(7+2)
m = -6/9
m = (-2*3)/(3*3)
m = -2/3
The slope is -2/3
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Now apply the scale factor.
We'll multiply each coordinate of each point by 2
(-2,10) becomes (-4,20) after multiplying each coordinate by 2
(7,4) becomes (14,8) after multiplying each coordinate by 2
Let's find the slope of the line through (-4,20) and (14,8)
m = (y2-y1)/(x2-x1)
m = (8-20)/(14-(-4))
m = (8-20)/(14+4)
m = -12/18
m = (-2*6)/(3*6)
m = -2/3
We get the same slope. This isn't a coincidence. Dilating a set of points will preserve the slope of the line through those points.
If A and B are the two original points, and A' and B' are the dilated counterparts, then the slope of line AB is the same as the slope of line A'B'.
The scale factor doesn't affect the answer.
Let us first find the hieght of the triangle:
= 16² = p² + 8²
= 256 = p² + 64
= 256 - 64 = p²
= √192 = p
= 13.85 = p
Area of equilateral trianglular prism:
= ⅓× l² × h
- Here, l = length of side and h is height
= ⅓ × 16² × 13.85
= 256 × 13.85 × ⅓
= 1181.86 cm³
= 1182 cm³ (approx)
Answer:
Parallel: extending in the same direction, everywhere equidistant.
Perpendicular: ar an angle of 90 to a givin line, plane or surface.
Answer:
15/17
Step-by-step explanation:
sin A = side opposite A/ hypotenuse
= a/ c
=15/17