Find the value of x. A. 76 B. 98 C. 66 D. 122
2 answers:
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Answer:
<u>Given expression:</u>
<u>The first root is valid when:</u>
- 2x + 2 ≥ 0 ⇒ 2x ≥ - 2 ⇒ x ≥ - 1
<u>The second root is valid when:</u>
- 6 - 4x ≥ 0 ⇒ 4x ≤ 6 ⇒ x ≤ 1.5
<u>So the variable x can get values within interval:</u>
- -1 ≤ x ≤ 1.5 or
- x = [-1, 1.5]
Answer:
The measure of middles angle is 113.5° .
Step-by-step explanation:
Given as :
The measure of the largest angle is 10 less than 5 time the smallest angle.
The measure of the middle angle is 6 more than twice the measure of the largest angle
Let The largest angle = L
Let The middle angle = M
Let The smallest angle = S
As per statement
Largest angle = 5 times smallest angle - 10
i.e L = 5 × S - 10 .....1
Again
Middle angle = twice largest angle + 6
i.e M = 2 × L + 6 ......2
Since for any Triangle sum of three angles = 180°
i.e ∠L + ∠M + ∠S = 180°
Or, ( 5 × S - 10 ) + ( 2 × L + 6 ) + S = 180°
Or, ( 5 × S - 10 ) + [ 2 × (5 × S - 10 ) + 6 ] + S = 180°
Or, 5 S - 10 + (10 S - 20 + 6) + S = 180°
Or, 5 S - 10 + 10 S - 20 + 6 + S = 180°
Or, (5 + 10 + 1) S - 24 = 180°
Or, 16 S = 180° + 24
Or, 16 S = 204
∴ S =
i.e S = 12.75
So, The measure of smallest angle = S = 12.75°
And
L = 5 × 12.75 - 10
i.e L = 53.75
So, The measure of Largest angle = L = 53.75°
And
M = 2 × L + 6
Or, M = 2 × 53.75 + 6
i.e M = 107.5 + 6 = 113.5
So, The measure of middles angle = M = 113.5°
Hence, The measure of middles angle is 113.5° . Answer