9514 1404 393
Answer:
d. The triangles are not similar
Step-by-step explanation:
The angle between the given sides is the same, so we need to compare the side ratios. In ΔQRS, we have ...
QR/RS = 4/15
In ΔVTU, we have ...
VT/TU = 8/32 = 1/4 ≠ 4/15
The triangles are not similar because corresponding sides are not proportional.
Answer:
Value is x=8 and y=4
Step-by-step explanation:
Given : A right triangle 'A' hypotenuse length of x+4 and a leg of x,
and right triangle 'B' hypotenuse length of 3y and a leg length of y+4
To find : For what values of x and y are the triangles congruent by HL?
Solution :
Triangle A,
Hypotenuse: x+4
Leg: x
Triangle B,
Hypotenuse: 3y
Leg: y+4
Since the triangle A and B are congruent so, the sides of triangles are equal.
(Hypotenuse are equal) ..........[1]
and
(Legs are equal) ..........[2]
Solving the equation of system,
Put the value of x from [2] in [1],
![x+4=3y](https://tex.z-dn.net/?f=x%2B4%3D3y)
![y+4+4=3y](https://tex.z-dn.net/?f=y%2B4%2B4%3D3y)
![8=2y](https://tex.z-dn.net/?f=8%3D2y)
![y=4](https://tex.z-dn.net/?f=y%3D4)
Substitute y in [2],
Therefore, The value of x=8 and y=4
Verifying for the values of x and y:
Triangle A,
Hypotenuse: x+4=8+4=12
Leg: x=8
Triangle B,
Hypotenuse: 3y=3(4)=12
Leg: y+4=4+4=8
Both hypotenuses and both legs are equal hence they are congruent.
Answer:
∠DEK = 88°
Step-by-step explanation:
Well, I supposed that ∠DEF is equal to ∠KEF and that the sum of these angles equals 88°
44° + 44° = 88°
Answer: M=-3
Step-by-step explanation: sorry dont feel like typing
The solution for the variable y is
, if a given line passing through the point (12, -5) has a slope of
.
Step-by-step explanation:
The given is,
Point - (12, -5)
Slope - ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Step:1
Formula for slope of line,
...........................(1)
Where,
,
are points
m - Slope
From given,
(12, -5) - ![(x_{1} ,y_{1} )](https://tex.z-dn.net/?f=%28x_%7B1%7D%20%2Cy_%7B1%7D%20%29)
m = ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Let, (x,y ) =
Equation (1) becomes,
![\frac{1}{3} = \frac{(y - (-5))}{x-12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%3D%20%5Cfrac%7B%28y%20-%20%28-5%29%29%7D%7Bx-12%7D)
![\frac{1}{3} (x-12) = (y-(-5))](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%28x-12%29%20%3D%20%28y-%28-5%29%29)
![\frac{1}{3} (x-12) = (y+5)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%28x-12%29%20%3D%20%28y%2B5%29)
![(y+5) = \frac{1}{3} (x-12)](https://tex.z-dn.net/?f=%28y%2B5%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%28x-12%29)
![(y+5) = (\frac{1}{3} x ) -\frac{1}{3}(12))](https://tex.z-dn.net/?f=%28y%2B5%29%20%3D%20%28%5Cfrac%7B1%7D%7B3%7D%20x%20%29%20%20%20%20%20-%5Cfrac%7B1%7D%7B3%7D%2812%29%29)
![(y+5) = (\frac{1}{3} x ) -4](https://tex.z-dn.net/?f=%28y%2B5%29%20%3D%20%28%5Cfrac%7B1%7D%7B3%7D%20x%20%29%20%20%20%20%20-4)
![y = \frac{1}{3} x -4-5](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20x%20%20%20%20%20-4-5)
![y = \frac{1}{3} x -9](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20x%20%20%20%20%20-9)
Result:
The solution for the variable y is
, if a given line passing through the point (12, -5) has a slope of
.