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2 years ago

The points (-4,2) and (4,r) lie on a line with slope -1. Find the missing cooridnate r

Mathematics

1 answer:

Oksanka [162]2 years ago

4 0

r = -6

Step-by-step explanation:

The slope of a line is defined as

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

Let $P_1(-4, 2)$ and $P_2(4, r)$ . Since m = -1, we can write

$-1 = \dfrac{r - 2}{4 - (-4)} \Rightarrow -1 = \dfrac{r - 2}{8}$

$r - 2 = -8 \Rightarrow r = -6$

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Subtract 2x^2-3xy+4y^2 from 3x^2-5xy-6y^2

Diano4ka-milaya [45]

Answer:

$-x^{2} +2xy+10y^{2}$

Step-by-step explanation:

$2x^2-3xy+4y^2-(3x^2-5xy-6y^2)\\2x^2-3xy+4y^2-3x^2+5xy+6y^2\\-x^{2} +2xy+10y^{2}$

8 0

3 years ago

2. BT bisects ZABC. MZABT = 4x-16 and m CBT = 2x + 6 Find MZABT.

Paladinen [302]

Answer:

The measure of angle ABT is 28°

Step-by-step explanation:

* Lets revise the bisector of a angle

- If a ray bisects and angle that mean the ray divide the angle into

two equal parts in measure

- Ex: if the ray BD bisects angle ABC, then the measure of angle ABD is

equal to the measure of angle CBD

* Lets solve the problem

∵ BT bisects ∠ABC

∴ m∠ABT = m∠CBT

∵ m∠ABT = 4x - 16

∵ m∠CBT = 2x + 6

- Equate the two values

∴ 4x - 16 = 2x + 6

- Lets solve the equation by subtracting 2x from both sides and

adding 16 to both sides

∴ 4x - 2x = 6 + 16

∴ 2x = 22 ⇒ divide both sides by 2

∴ x = 11

- Lets find the measure of angle ABT

∵ m∠ABT = 4x - 16

- Substitute x by 11

∴ m∠ABT = 4(11) - 16 = 44 - 16 = 28°

* The measure of angle ABT is 28°

6 0

3 years ago

A rocket is launched into the air. The height h(t), in yards, of the rocket is a function of time, t, in seconds, as shown in th

Vesna [10]

Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope. Because this is parabolic, we cannot find the exact rate of change as we could if this were a linear function. But we can use the same idea. When t = 3, h(t) = 33, so the coordinate point is (3, 33). When t = 6, h(t) = 0, so the coordinate is (6, 0). Plug those values into the slope formula:

$m=\frac{0-33}{6-3}$ and