Answer:
y = 2x + 2
Step-by-step explanation:
<em>(a) Slope </em>
The point-slope formula for a straight line is
y₂ - y₁ = m(x₂ - x₁)
The line goes through the points (-1, 0) and (0, 2).
2 – 0 = m[0 – (-1)]
2 = m
(b) y-intercept
y = mx + b
Use the point (0, 2)
2 = 2× 0+ b
2 = 0 + b
b = 2
∴ y = 2x + 2
The equation 4(x − 7) − 128 = 9x − 5(x + 6) has no solution
<h3><u>Solution:</u></h3>Given that 4(x − 7) − 128 = 9x − 5(x + 6)
We have to find the solution for this equation
4(x − 7) − 128 = 9x − 5(x + 6)
Let us use BODMAS rule to perform the sequence of operations
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.
So let us solve for brackets first
4x - 28 - 128 = 9x - 5x - 30
Now let us perform subtraction
4x - 156 = 4x - 30
Now move the terms from R.H.S to L.H.S
4x - 4x = -30 + 156
Since there is no value of x that will ever make this a true statement, the solution to the equation above is “no solution”
So this equation has no solution
Answer:
3.189 seconds
Step-by-step explanation:
You want f(t) = 0, so ...
0 = -16t^2 +13.4t +120
0 = t^2 -0.8375t -7.5 . . . . divide by -16
0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*
0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square
√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root
t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875
It will take the rock about 3.189 seconds to hit the ground.
_____
* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...
(t^2 -2at +a^2) = (t -a)^2
Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.
_____
<em>Comment on the question</em>
We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...
