What’s the full question?
Answer:
The width is 50 yards and the length is 141 yards.
Step-by-step explanation:
Let's call: L the length of the field and W the width of the field.
From the sentence, the perimeter of the rectangular playing field is 382 yards we can formulate the following equation:
2L + 2W = 382
Because the perimeter of a rectangle is the sum of two times the length with two times the width.
Then, from the sentence, the length of the field is 9 yards less than triple the width, we can formulate the following equation:
L = 3W - 9
So, replacing this last equation on the first one and solving for W, we get:
2L + 2W = 382
2(3W - 9) + 2W = 382
6W -18 +2W = 382
8W - 18 = 382
8W = 382 + 18
8W = 400
W = 400/8
W = 50
Replacing W by 50 on the following equation, we get:
L = 3W - 9
L = 3(50) - 9
L = 141
So, the width of the rectangular field is 50 yards and the length is 141 yards.
Answer:
x = 39
Step-by-step explanation:
there is a theorem that states that the midsegment in a trapezoid is equal to the sum of the bases divided by two
so, (36 + 42)/2 = x
36 + 42 = 78
78/2 = 39
Answer: Phillip is correct. The triangles are <u>not </u>congruent.
How do we know this? Because triangle ABC has the 15 inch side between the two angles 50 and 60 degrees. The other triangle must have the same set up (just with different letters XYZ). This isn't the case. The 15 inch side for triangle XYZ is between the 50 and 70 degree angle.
This mismatch means we cannot use the "S" in the ASA or AAS simply because we don't have a proper corresponding pair of sides. If we knew AB, BC, XZ or YZ, then we might be able to use ASA or AAS.
At this point, there isn't enough information. So that means John and Mary are incorrect, leaving Phillip to be correct by default.
Note: Phillip may be wrong and the triangles could be congruent, but again, we don't have enough info. If there was an answer choice simply saying "there isn't enough info to say either if the triangles are congruent or not", then this would be the best answer. Unfortunately, it looks like this answer is missing. So what I bolded above is the next best thing.
Answer:
The measure of angle B is 68° and the measure of angle C is 22°
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
m∠B+m∠C=90° -----> equation A
m∠B=3(m∠C)+2 ----> equation B
Substitute equation B in equation A and solve for m∠C
3(m∠C)+2+m∠C=90
4(m∠C)=90-2
4(m∠C)=88
m∠C=88/4
m∠C=22°
Find the value of m∠B
m∠B=3(22)+2=68°
therefore
The measure of angle B is 68° and the measure of angle C is 22°
