Step-by-step explanation:
![{4}^{ - n} = 32](https://tex.z-dn.net/?f=%20%7B4%7D%5E%7B%20-%20n%7D%20%20%3D%2032)
![{2}^{ -2 n} = {2}^{5}](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7B%20-2%20n%7D%20%20%3D%20%20%7B2%7D%5E%7B5%7D%20)
![- 2n = 5](https://tex.z-dn.net/?f=%20-%202n%20%3D%205)
![n = \frac{ - 5}{2}](https://tex.z-dn.net/?f=n%20%3D%20%20%20%5Cfrac%7B%20-%205%7D%7B2%7D%20)
Answer:
![B'(x,y) = (0,-2)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%280%2C-2%29)
Step-by-step explanation:
Given
The attached grid
Translation rule: ![(x,y) = (x + 5, y - 2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28x%20%2B%205%2C%20y%20-%202%29)
Required
Determine the coordinates of B'
First, we have to write out the coordinates of B
![B(x,y) = (-5,0)](https://tex.z-dn.net/?f=B%28x%2Cy%29%20%3D%20%28-5%2C0%29)
Next is to apply the translation rule ![(x,y) = (x + 5, y - 2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28x%20%2B%205%2C%20y%20-%202%29)
becomes
![B'(x,y) = B(x+5,y-2)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20B%28x%2B5%2Cy-2%29)
Substitute -5 for x and 0 for y
![B'(x,y) = (-5+5,0-2)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%28-5%2B5%2C0-2%29)
![B'(x,y) = (0,-2)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%280%2C-2%29)
Simplifying
a + 4b = 5b + -3a
Reorder the terms:
a + 4b = -3a + 5b
Solving
a + 4b = -3a + 5b
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '3a' to each side of the equation.
a + 3a + 4b = -3a + 3a + 5b
Combine like terms: a + 3a = 4a
4a + 4b = -3a + 3a + 5b
Combine like terms: -3a + 3a = 0
4a + 4b = 0 + 5b
4a + 4b = 5b
Add '-4b' to each side of the equation.
4a + 4b + -4b = 5b + -4b
Combine like terms: 4b + -4b = 0
4a + 0 = 5b + -4b
4a = 5b + -4b
Combine like terms: 5b + -4b = 1b
4a = 1b
Divide each side by '4'.
a = 0.25b
Simplifying
a = 0.25b
Answer: t = 5
Step-by-step explanation: step one cross multiply 4/t = 2/2.5
(4) * (2.5) = 2 * t so 10 = 2t / step two flip the equation 2t = 10
step three divide both sides by two 2t/2 = 10/2 t = 5
Could you stop with the wird pictures, I'm at home with my fam and... ya
so
complementary angles add to 90 degerss
let's say
ABC=x
ABD=y for easier
x+y=90
also
x is 20 more than y
x=20+y
sub 20+y for x
20+y+y=90
20+2y=90
minus 20 both sides
2y=70
divide by 2 both sideds
y=35
sub back
x=20+y
x=20+35
x=55
∠ABC=55°
∠ABD=35°