Answer:
The coordinates of point S are (5, 9) will make line PQ // line RS ⇒ A
Step-by-step explanation:
<em>Parallel lines have the same slopes</em>
The slope of a line = Δy/Δx, where
Let us first find the slope of the line PQ.
∵ P = (-2, -2) and Q = (0, 7)
∴ Δx = 0 - (-2) = 0 + 2 = 2
∴ Δy = 7 - (-2) = 7 + 2 = 9
∴ The slope of PQ = 9/2
∵ Line PQ // line RS
∴ The slope of line PQ = the slope of line RS
∴ The slope of line RS =9/2
∵ Point R = (3, 0) and point S = (x, y)
∵ The slope of line RS = 9/2
∵ The slope = Δy/Δx
∴ Δy/Δx = 9/2
→ That means Δy = 9 and Δx = 2
∵ Δy = y - 0
∵ Δy = 9
∴ 9 = y
∵ Δx = x - 3
∵ Δx = 2
∴ 2 = x - 3
→ Add 3 to both sides
∴ 2 + 3 = x - 3 + 3
∴ 5 = x
∴ The coordinates of point S are (5, 9) will make line PQ // line RS
Answer:
2069.
Step-by-step explanation:
Let Devyani's age in 2073= x years and y be her fathers age Then:
y = 7x
- and in 8 years time ( 2081) we have:
y + 8 = 3(x + 8)
y = 3x + 24 - 8
y = 3x + 16. Eliminating y from the 2 equations:
7x = 3x + 16
4x = 16
x = 4.
So in 2073 she was 4 years old
Therefore she was born in 2069.
Answer:
Mr Rowdy 9/7
Miss Rivera 16/15
No, the ratios are not equivalent
Step-by-step explanation:
Answer:
How is genetic information passed from parents to offspring in humans?
But when people talk about genes being passed on, they generally don't mean genes being passed on from cell to cell during cell division. Instead, they usually mean genes being passed on from parents to children. This is known as "heredity" or "inherited genes."
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 22x + 3
Factor out the negative
f(x) = -( 16x^2 -22x -3)
= -(8x+1)(2x-3)
Find the x intercepts
Set y = 0
0 = -(8x+1)(2x-3)
Using the zero product property
8x+1 =0 2x-3 = 0
8x = -1 2x = 3
x = -1/8 x =3/2
The x intercepts are ( -1/8, 0) and ( 3/2, 0)
The end behavior
-16 x^2 is the dominate term
Let x →-∞
f(-∞) = -16 (-∞)^2 = -16 (∞) = -∞
As x goes to negative infinity y goes to - infinity
Let x →∞
f(∞) = -16 (∞)^2 = -16 (∞) = -∞
As x goes to infinity y goes to - infinity
We know this is a downward facing parabola a < 0 and this is a quadratic
We have the x intercepts
We can find the axis of symmetry from the zeros
(-1/8+ 3/2) /2 = (-1/8 + 12/8)/2 = (11/8)/2 = 11/6
The axis of symmetry is x = 11/16
Using the axis of symmetry and the equation, we can find the maximum point
y = -(8*11/16+1)(2*11/16-3) = 169/16
The vertex is at (11/16, 169/16(
