1) gradient of line = Δ y ÷ Δ x
= (5 -2) ÷ (3 - (-6))
= ¹/₃
using the point-slope form (y-y₁) = m(x-x₁)
using (3,5)
(y - 5) = ¹/₃ (x -3)
y - 5 = ¹/₃x - 1
⇒ <span> y = ¹/₃ x + 4 [OPTION D]
</span>2) y = 2x + 5 .... (1)
<span> </span>y = ¹/₂ x + 6 .... (2)
by substituting y in (1) for y in (2)
2x + 5 = ¹/₂ x + 6
³/₂ x = 1
x = ²/₃
by substituting found x (2)
y = ¹/₂ (²/₃) + 6
y = ¹⁹/₃
∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]
3) Yes [OPTION A]
This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.
4) No [OPTION B]
Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.
An ellipse is divided into two axes, the longer axis is the
major axis and the shorter axis is the minor axis. The length of the major axis
of an ellipse is equal to the sum of two distance: the distance between any
point on the ellipse and one on focus and the distance between the same point
and the other focus. The focus is the point that helps define an ellipse and
every ellipse has two foci. These two distance are also called the red line
segment and blue line segment. Given 6 for red line segment and 4 for blue line
segment therefore, the length of the major axis of the ellipse is 10.
Answer:
32.0 cm
Step-by-step explanation:
volume of a hemisphere = (2/3)πr3
r = cube root (Volume * 3/2 * 1/π )
r = cube root ( 8514 * 3/2 * 1/π)
r = 15.96
in the nearest tenth r = 16.0 cm
D= 2r
D= 2(16)
D= 32cm
Answer:
StartFraction 16 over 81 EndFraction
Step-by-step explanation:
There are 4 prime numbers from 2 to 10 (2, 3, 5, 7) and 9 numbers from 2 - 10. Total possibilities: 9 * 9 = 81
Prime possibilities: 4 * 4 = 16
Therefore the answer is 16/81 or StartFraction 16 over 81 EndFraction
A quadratic equation is an equation that includes a squared term. For example, 3x + 7 = 28 is not a quadratic equation as it only has x, whereas x^2 + 5x + 6 = 0 is a quadratic equation as it includes x^2. Quadratic equations also usually have two solutions, whereas linear equations (like my first example) only have one.
I hope this helps! Let me know if you would like me to explain anything more :)
