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OleMash [197]
3 years ago
7

A ∠A and ∠ B ∠B are complementary angles. If m ∠ A = ( 2 x − 23 ) ∘ ∠A=(2x−23) ∘ and m ∠ B = ( x + 20 ) ∘ ∠B=(x+20) ∘ , then fin

d the measure of ∠ A ∠A.
Mathematics
1 answer:
son4ous [18]3 years ago
7 0

Answer:

∠A = 99°

Step-by-step explanation:

Complementary angles sum to 180°, thus

∠A + ∠B = 180 ← substitute values

2x - 23 + x + 20 = 180

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61

Hence

∠A = 2x - 23 = (2 × 61) - 23 = 122 - 23 = 99°

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Find the surface are of this figure
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Answer:

If I am correct, I think the surface area is 448.

Step-by-step explanation:

First start by finding the area of all the sides

Front side. 12 x 10 = 120

2 triangle sides: 8 x 10 = 80, 80 x 2 = 160

Bottom side: 6 x 12 = 72

Back side: 8 x 12 = 96

Then add up the surface area

120 + 160 + 72 + 96 = 448

Btw I don't know if I am correct, but I think this is the way you find surface area.

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c

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An instructor gives her class the choice to do 7 questions out of the 10 on an exam.
Maksim231197 [3]

Answer:

(a) 120 choices

(b) 110 choices

Step-by-step explanation:

The number of ways in which we can select k element from a group n elements is given by:

nCk=\frac{n!}{k!(n-k)!}

So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:

10C7=\frac{10!}{7!(10-7)!}=120

Then each student have 120 possible choices.

On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:

1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:

(5C3)(5C4)=\frac{5!}{3!(5-3)!}*\frac{5!}{4!(5-4)!}=50

2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:

(5C4)(5C3)=\frac{5!}{4!(5-4)!}*\frac{5!}{3!(5-3)!}=50

3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:

(5C5)(5C2)=\frac{5!}{5!(5-5)!}*\frac{5!}{2!(5-2)!}=10

So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:

50 + 50 + 10 = 110

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