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3 years ago

What is the equation of the line that passes through (-2, 2) and (1,-4)?

Mathematics

1 answer:

Reil [10]3 years ago

7 0

Answer:

$Equation \ of \ the \ line => (y -y_{2}) =m(x -x_{2} )$

$slope, m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{-4-2}{1--2} = \frac{-6}{3} = -2$

Equation the line passing through (-2, 2) and ( 1, -4)

$(y -- 4) = -2(x -1)\\\\(y +4) = -2x + 2\\\\y = -2x +2 -4 \\\\y = -2x -2$

option D

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Simplify the rational expression. State any restrictions on the variable.

AveGali [126]

Answer:

The last choice.

Step-by-step explanation:

$\dfrac{k^2-k-2}{k^2-4k-5}=\dfrac{(k+1)(k-2)}{(k+1)(k-5)}=\dfrac{k-2}{k-5}$

The value of k must be restricted from being one that makes the original denominator zero. Hence k ≠ -1 or 5.

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2 years ago

One of the digits of a two digit number is three times the other digit. If you interchange the digits of this two digit number a

STatiana [176]

Answer:

Step-by-step explanation:

well, we start by expressing the number:

a b

we understand that using the above expression, the value of the number is 10a + b

using the information in the question,

a = 3b (1)

and,

11b + 11a = 88 (2) (derived using 10a + b form)

hence, when substituting (1) into (2):

11b + 33b = 88

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hence, the number is 62

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3 years ago

What is the volume of a rectangular prism with a length of 4 a width of 6 and a height of 2?

pentagon [3]

Answer: Volume = 48

Step-by-step explanation:

V = L * W * H

V = 4 * 6 * 2

V = 48

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3 years ago

Write the equation of the ellipse with foci at (-2,2) and (4,2) and major axis of length 10 *

Luda [366]

Answer:

The answer to your question is $\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$

Step-by-step explanation:

Data

Foci (-2, 2) (4, 2)

Major axis = 10

Process

1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.

From the graph we conclude that it is a horizontal ellipse.

2.- Determine the foci axis (distance between the foci)

2c = 6

c = 6/2

c = 3

3.- Determine a

2a = 10

a = 10/2

a = 5

4.- Determine b using the Pythagorean theorem

a² = b² + c²

-Solve for b

b² = a² - c²

b² = 5² - 3²

b² = 25 - 9

b² = 16

b = 4

5.- Find the center (1, 2) From the graph, it is in the middle of the foci

6.- Find the equation of the ellipse

$\frac{(x - 1)^{2}}{5^{2}} + \frac{(y - 2)^{2}}{4^{2}} = 1$

$\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$

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3 years ago

Just trying to finish this so I can get my stanceboy racecar back

Free_Kalibri [48]

Answer:

x ≥ 4 AND x + y ≤ 10

Step-by-step explanation:

If you need up to 10 volunteers, then you can take 10 or less. If we add y and x, we'll get the total amount of people, therefore making the inequality:

x + y ≤ 10.

Now, he needs no fewer than 4 females, so he can take 4 or greater. This means that x should be greater than or equal to 4.

x ≥ 4.

Nothing was mentioned about how many males he needed (y) so these two inequalities match the situation.

Hope this helped!

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3 years ago