*see attachment for the complete diagram and what is required.
Answer:
✅ST = 7 m
✅SU = 8 m
✅m<R = 46°
✅m<Q = 75°
✅m<S = 59°
Step-by-step explanation:
Given that ∆PQR ≅ ∆STU, therefore, their corresponding sides and angles would be congruent to each other.
Thus:
<P ≅ <S, therefore, m<P = m<S = 59°
<Q ≅ <T, therefore, m<Q = m<T = 75°
<R ≅ <U, therefore, m<R = m<U.
PQ ≅ ST, therefore, PQ = ST
QR ≅ TU, therefore, QR = TU
PR ≅ SU, therefore, PR = SU
Let's find the measure of the following with the information we already know:
✅ST = PQ = 7 m
✅SU = PR = 8 m
✅m<R = 180 - (m<P + m<Q) (sum of ∆)
m<R = 180 - (59°+ 75°) (substitution)
m<R = 180 - 134
m<R = 46°
✅m<Q = m<T = 75°
✅m<S = m<P = 59°
Answer:exact form 1295/261
Mixed number form 4 251/261
Step-by-step explanation:
For the carpet:
Given:
Area = x^2 + x - 20 ft^2
Length = x+ 5 ft
As a carpet is rectangular, the area is defined as the product of the length and the width. To obtain an expression of the carpet's width, the area is to be divided by the length, which is shown below:
__x_-_4___x + 5|x^2 + x - 20 x^2 + 5x -------- -4x - 20 -4x - 20 -------- 0
Therefore, the expression of width = x - 4.
Applying the value of x = 20 to obtain the measurements of the carpet, we obtain the following:
Width = x - 4 = 20 - 4 = 16ft
Length = x+ 5 = 20 + 5 = 25ft.
Therefore, the carpet is 25ft x 16ft.
For the wall:
The same principles apply to the wall as it is also assumed to be rectangular.
Given:
Area = <span>x^2 + 17x + 30 ft^2
Width = x + 2
To obtain the expression for the wall's length, Area is to be divided by the Width, which is shown below:
__x_+_15______x + 2|x^2 + 17x + 30 x^2 + 2x -------- 15x + 30 15x + 30 --------- 0
Therefore, the expression for the wall's length is x + 15.
Applying the value of x = 20 to obtain the wall's dimensions:
Length = x + 15 = 20 + 15 = 35ft.
Width = x + 2 = 20 + 2 = 22ft.
Therefore the wall has measurements of 35ft x 22ft.</span>
Answer:
B
Step-by-step explanation:
If you calculate the side of a square using pythagorean theorem, you would get a side length of sqrt37. Simple multiply this by 4
-2 is the only domain I think. The rest are not. Hope I’ve helped.
