<u>Answer:</u>
The correct answer options are A, B, C and D.
<u>Step-by-step explanation:</u>
A. Leg-angle (LA):
According to this theorem, if the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.
B. Hypotenuse-leg (HL):
If any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
C. Hypotenuse-angle (HA):
If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.
D. Leg-leg (LL):
If any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
Step-by-step explanation:
x+4y = 2
4y= -x+2
![y = \frac{ - 1}{4} x + \frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B%20-%201%7D%7B4%7D%20x%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20)
slope of the above line = -1/4
The slope of the required line which is perpendicular to this line = 4
And, the required line also passes through(-2,6)
![\frac{y - 6}{x - ( - 2)} = 4](https://tex.z-dn.net/?f=%20%5Cfrac%7By%20-%206%7D%7Bx%20-%20%28%20-%202%29%7D%20%20%3D%204)
![\frac{y - 6}{x + 2} = 4](https://tex.z-dn.net/?f=%20%5Cfrac%7By%20-%206%7D%7Bx%20%2B%202%7D%20%20%3D%204)
![y - 6 = 4(x + 2)](https://tex.z-dn.net/?f=y%20-%206%20%3D%204%28x%20%2B%202%29)
![y - 6 = 4x + 8](https://tex.z-dn.net/?f=y%20%20-%206%20%3D%204x%20%2B%208)
![4x + 8 - y + 6 = 0](https://tex.z-dn.net/?f=4x%20%2B%208%20-%20y%20%2B%206%20%3D%200)
![4x - y + 14 =0](https://tex.z-dn.net/?f=4x%20-%20y%20%2B%2014%20%3D0)
The equation of the line that is perpendicular to the line x+4y=2 and goes through the point (-2,6)
4x-y+14=0
Answer:
4/0
Step-by-step explanation:
The given equation is an equation of a circle where the number after the equal sing is the radius squared.
To find the radius take the square root.
Radius = SQRT(169)
Radius = 13 units.
Using linear functions, it is found that the sales price in Port Townsend is never double the Seattle price.
A linear function has the following format:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
In which:
- m is the slope, which is the rate of change.
- b is the y-intercept, which is the initial value.
For Seattle:
- Initial value of $38,000 in 1970, thus the y-intercept is
.
- Increased by $137,000 in 20 years, thus the slope is:
![m = \frac{137000}{20} = 6850](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B137000%7D%7B20%7D%20%3D%206850)
Thus, the <u>sales prince in n years after 1970</u> for Seattle is:
![S(n) = 38000 + 6850n](https://tex.z-dn.net/?f=S%28n%29%20%3D%2038000%20%2B%206850n)
For Port Townsend:
- Initial value of $8,400 in 1970, thus the y-intercept is
.
- Increased by $160,000 in 20 years, thus the slope is:
![m = \frac{160000}{20} = 8000](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B160000%7D%7B20%7D%20%3D%208000)
Thus, the <u>sales prince in n years after 1970</u> for Port Townsend is:
![P(n) = 8400 + 8000n](https://tex.z-dn.net/?f=P%28n%29%20%3D%208400%20%2B%208000n)
Port Townsend is double Seattle in n years after 1970, for which:
![P(n) = 2S(n)](https://tex.z-dn.net/?f=P%28n%29%20%3D%202S%28n%29)
Then
![8400 + 8000n = 2(38000 + 6850n)](https://tex.z-dn.net/?f=8400%20%2B%208000n%20%3D%202%2838000%20%2B%206850n%29)
![8400 + 8000n = 76000 + 13700n](https://tex.z-dn.net/?f=8400%20%2B%208000n%20%3D%2076000%20%2B%2013700n)
![7500n = -67600](https://tex.z-dn.net/?f=7500n%20%3D%20-67600)
Negative number, and we are working only with positive, thus, it is found that the sales price in Port Townsend is never double the Seattle price.
A similar problem is given at brainly.com/question/23861861