Answer:
m = 10 , n = 5
Step-by-step explanation:
using the cosine and tangent ratio in the right triangle and the exact values
cos45° =
and tan45° = 1 , then
cos45° =
=
=
( cross- multiply )
m = 5
×
= 5 × 2 = 10
-----------------------------------------
tan45° =
=
= 1 , then
n = 5
11(x+10) = 132
Distributive property
11x + 110 = 132
Now isolate the variable.
11x + 110 = 132
-110 -110
132 - 110 = 22
11x = 22
11x/11 = 22/11
x= 2
Answer: x = 2
Hey there!
1. The graph was flipped vertically and now opens downward.
We know this because there is a negative sign in front of the equation:
2. The graph was moved 3 units to the left.
We know this because there is 3 added to x inside of the parenthesis. Remember, inside (parenthesis) is opposite and acts on x, outside (parenthesis) is same and acts on y.
3. The graph was moved 5 units up.
We know this because there is 5 added at the end of the equation. It acts on y because it is outside of the parenthesis.

Hope this helps!
Let
x-------> the width of the rectangular area
y------> the length of the rectangular area
we know that
y=x+15------> equation 1
perimeter of a rectangle=2*[x+y]
2x+2y <= 150-------> equation 2
substitute 1 in 2
2x+2*[x+15] <=150--------> 2x+2x+30 <=150----> 4x <=150-30
4x <= 120---------> x <= 30
the width of the rectangular area is at most 30 ft
y=x+15
for x=30
y=30+15------> y=45
the length of the rectangular area is at most 45 ft
see the attached figure
the solution is<span> the shaded area</span>
Answer:
m∠A = 48.81°
Step-by-step explanation:
Given triangle is a right triangle and we have to measure ∠A.
Since, opposite side and adjacent sides of angle A has been given
So we will apply tangent rule to get the measure of angle A.
tan(∠A) =
tan(∠A) = 
∠A = 
∠A = 48.814
≈ 48.81°