Given, IJ = 3x + 3, HI = 3x - 1, and HJ = 3x + 8.
Since I is a point on line segment HJ, we can write


Put x=2 in HJ=3x+8.

Therefore, the numerical length of HJ is 14.
Answer:
Step-by-step explanation:
From the given right-angle triangle
The angle = ∠60°
-
The adjacent to the angle ∠60° is 1/2.
- The opposite to the angle ∠60° is y.
The hypotenuse = x
<u>Determining the value of x:</u>
Using the trigonometric ratio
cos 60° = adjacent / hypotenuse
substituting adjacent = 1/2 and hypotenuse = x


∵ cos (60°) = 1/2

Dividing both sides by 2

Simplify

Thus, the value of hypotenuse x is:
x = 1
<u>Determining the value of y:</u>
Using the trigonometric ratio
sin 60° = opposite / hypotenuse
As we have already determined the value of hypotenuse x = 1
substituting opposite = y and hypotenuse = 1
sin 60° = y/1
y = 1 × sin 60°
∵ 
Therefore, the value of y is:
Summary:
Answer:
34
Step-by-step explanation:
-5y=-45
y=-45/-5
=9
y=9
then
5y-11=5×9-11
=45-11
=34