Question 7: Option 1: x = 33.5°
Question 8: Option 3: x = 14.0°
Step-by-step explanation:
<u>Question 7:</u>
In the given figure, the value of perpendicular and hypotenuse is given, so we have to use any trigonometric ratio to find the value of angle as the given triangle is a right-angled triangle
So,
Perpendicular = P = 32
Hypotenuse = H = 58
So,

Rounding off to nearest tenth
x = 33.5°
<u>Question 8:</u>
In the given figure, the value of Base and Perpendicular is given, we will use tangent trigonometric ratio to find the value of x
So,
Perpendicular = P = 5
Base = B = 20
So,

Rounding off to nearest tenth
x = 14.0°
Keywords: Right-angled triangle, trigonometric ratios
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The solution to given system of equations are 
<em><u>Solution:</u></em>
Given that we have to find solution to the system of equations
<em><u>Given equations are:</u></em>
x + 2y = 10 ------ eqn 1
y = 12x + 3 ------ eqn 2
We can solve the above equations by substitution method
<em><u>Substitute eqn 2 in eqn 1</u></em>
x + 2(12x + 3) = 10
x + 24x + 6 = 10
25x = 10 - 6
25x = 4

<em><u>Substitute the above value of x in eqn 2</u></em>

Thus the solution to given system of equations are 
Answer: ½ x + 6 < 34 ; x < 56
Step-by-step explanation:
- Subtract 6 on both sides. ½ x < 28.
- Divide ½ on both sides. x < 56.