Answer:
v = 25
Step-by-step explanation:
The crucial information you need to know to solve this is to realize that HI and GH are the same length. However, why they are equal is not immediately obvious.
Both sides of the middle line (HF) are symmetrical, since G and I are the same distance away from the line, and they both lie on a line perpendicular to the middle line.
Note: we know they're the same distance away due to the small red marks in the lines, indicating that they're the same length.
The angles at G and I in the triangles are also the same, as the lines from G and I both meet at H. If they were different angles, they would each hit a different point on the middle line.
Thus, we can conclude that GH and HI are the same length.
Since we know the following:
GH = 4v - 75
HI = v
We can set GH and HI equal to each other and solve the equation.
4v - 75 = v
Subtract v from both sides:
3v - 75 = 0
Add 75 to both sides:
3v = 75
Divide both sides by 3:
v = 25
Answer: v = 25
Hope you could understand.
If you have any query, feel free to ask.
If this can be modelled by exponential decay, therefore
the function must be in the form of:
A = Ao (1 + r)^t
where A is the final value, Ao is the initial = 15000, r
is the rate of decay = -0.0015, t is time = 2010 – 1990 = 20
A = 15,000 (1 – 0.0015)^20
A = $14,556.36
Your picture shows the first step: use the distributive property to eliminate parentheses.
5*7 -5*x = 2*x -3
Now, you have an equation with a constant and an x-term on each side. I like to pick the x-term with the smallest (most-negative) coefficient and add its opposite to the equation.
Adding 5x, we have
35 = 7x -3
Adding 3 will get the x-term on one side and the constant on the other
38 = 7x
Now, we divide by the coefficient of x
38/7 = x = 5 3/7
This is the correct answer, even though it is not an integer.
_____
Check
5(7 -(5 3/7)) = 2(5 3/7) -3 . . . . substitute for x in the original equation
5(1 4/7) = 10 6/7 -3 . . . . . . . . . evaluate the parentheses on the left, do the multiplication on the right
5 20/7 = 7 6/7 . . . . . . . . . . . . do the multiplicaton on the left, the subtraction on the right
5 +2 6/7 = 7 6/7 . . . . . . . . . . . rewrite 20/7, realize 5+2=7. true
