<u>Answer(s):</u>
- Part-1: B and C
- Part-2: C and E
<u>Verification:</u>
<u>Part-1:</u>
Let's simplify the expression.
- => 4(w + 3) - 2
- => 4w + 12 - 2
- => 4w + 10
<u>We got the result, which is 4w + 10. Now, let's see which expressions are equal to 4w + 10.</u>
<u>Option A</u>
- 4w + 3 - 2 = 4w + 10
- => 3 - 2 = 10
- => 1 ≠ 10 (Incorrect)
<u>Option B</u>
- 4w + 12 - 2 = 4w + 10
- => 12 - 2 = 10
- => 10 = 10 (Correct)
<u>Option C</u>
- 4w + 10 = 4w + 10
- => 0 = 0 (Correct)
<u>Option D</u>
- 14w = 4w + 10
- => 10w ≠ 10 (Incorrect)
<u>Option E</u>
- 4w + 12 - 8 = 4w + 10
- => 12 - 8 = 10
- => 4 ≠ 10 (Incorrect)
<u>Option F</u>
- 4w + 4 = 4w + 10
- => 4 ≠ 10 (Incorrect)
Hence, <u>Option B and C are correct.</u>
<h3>__________________________________________________</h3>
<u>Part-2:</u>
Let's simplify the expression.
- 3(2n + 3) + 9
- => 6n + 9 + 9
- => 6n + 18
Now, let's verify all options to see which are correct.
<u>Option A</u>
- 15n + 9 = 6n + 18
- => 9n ≠ 9 (Incorrect)
<u>Option B</u>
- 6n + 3 + 9 = 6n + 18
- => 6n + 12 = 6n + 18
- => 12 ≠ 18 (Incorrect)
<u>Option C</u>
- 6n + 18 = 6n + 18
- => 0 = 0 (Correct)
<u>Option D</u>
- 6n + 6 + 9 = 6n + 18
- => 6n + 15 = 6n + 18
- => 15 ≠ 18 (Incorrect)
<u>Option E</u>
- 6n + 27 - 9 = 6n + 18
- => 6n + 18 = 6n + 18
- => 0 = 0 (Correct)
<u>Option F</u>
- 3(5n) + 9 = 6n + 18
- => 15n + 9 = 6n + 18
- => 9n ≠ 9 (Incorrect)
Hence, <u>the answers are Option C and E.</u>
<h3>__________________________________________________</h3>
Hoped this helped.
Answer:
20
Step-by-step explanation:
24/6=4 so that 4 times that 5 give u the answer 20
Answer:
θ = 36.9°, 90°, 216.9°, or 270°
Step-by-step explanation:
4 sin 2θ − 3 cos 2θ = 3
Use double angle formulas:
4 (2 sin θ cos θ) − 3 (cos²θ − sin²θ) = 3
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3
Use Pythagorean identity:
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 (sin²θ + cos²θ)
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 sin²θ + 3 cos²θ
8 sin θ cos θ − 6 cos²θ = 0
2 cos θ (4 sin θ − 3 cos θ) = 0
2 cos θ = 0
θ = 90° or 270°
4 sin θ − 3 cos θ = 0
4 sin θ = 3 cos θ
tan θ = 3/4
θ = 36.9° or 216.9°
Answer:
1. 110°
2. 139°
Step-by-step explanation:
1. 180° in a triangle
180 - 40 - 30 = 110°
2. 180° in a triangle
angles on a straight line add up to 180°
180 - 64 - 75 = 41°
180 - 41 = 139°
<span>Provided that no one can receive more than one prize, there are 50*49*48= 117600 ways to distribute the prizes. The first prize can be given to any of the 50 people, the second to any of the remaining 49, and the third to the remaining of the 48, multiplying these possibilities together leads to the answer.</span>