The expected value of y when x is equals to 45 in the equation is 35.06
<h3>How to find variable from an equation?</h3>
The equation is given as follows;
y = -2.61x + 152.51
where
- x = variable 1
- y = variable 2
Therefore,
when
x = 45
y = -2.61x + 152.51
y = -2.61(45) + 152.51
y = - 117.45 + 152.51
y = 35.06
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Answer:
i)D:
ii)R: 
iii) Y-int:(0,-1)
Step-by-step explanation:
i) The given absolute value function is;
.
The absolute value function is defined for all real values of x.
The domain is all real numbers.
ii) The range is all y-values that will make x defined.
The given function,
.
has vertex at, (-2,-3) and opens upwards.
This implies that, the minimum y-value is -3.
The range is 
iii) To find the y-intercept substitute x=0 in to the function.
.
.
.
.
The y-intercept is (0,-1)
See attachment for graph.
Answer:
16m tall
Step-by-step explanation:
Distance casted by the shadow = 32m = hypotenuse
Angle of elevation = 30 degrees
Required
Height of the building = opposite
Using the SOH CAH TOA identity
sin theta = opp/hyp
sin 30 = x/32
0.5 = x/32
x = 0.5 * 32
x = 16m
Hence the building is 16m tall
4 x -5 = -20 then 12 + -20 = -8