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3 years ago

(5, 3) and (8, -2) Write the standard form of the equation of the line that passes through the given points.

Mathematics

2 answers:

Firlakuza [10]3 years ago

8 0

Answer is given above

Lerok [7]3 years ago

3 0

Slope = (y2 - y1) / (x2 - x1)
(5,3)...x1 = 5 and y1 = 3
(8,-2)..x2 = 8 and y2 = -2
now we sub
slope = (-2 - 3) / (8 - 5) = -5 / 3

y = mx + b
slope(m) = -5/3
use either of ur points..(5,3)...x = 5 and y = 3
now we sub and find b, the y int
3 = -5/3(5) + b
3 = -25/3 + b
3 + 25/3 = b
9/3 + 25/3 = b
34/3 = b

ur equation is y = -5/3x + 34/3...but we need it in standard form

y = -5/3x + 34/3
5/3x + y = 34/3
5x + 3y = 34 <=== standard form

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Graph g is a translation of the graph of y= sin x (dashed line).a) write down the equation of g b) write down the coordinates of

labwork [276]

Answer:

a) $G(x)= \sin x + 2$

b) The coordinates of P are

$\displaystyle \left( \frac{3\pi}{2},1\right)$

Step-by-step explanation:

Translation

The dashed line shows the graph of the function

$y = \sin x$

This function has a maximum value of 1, a minimum value of -1, and a center value of 0.

Graph G shows the same function but translated by 2 units up, thus the equation of G is:

$\boxed{G(x)= \sin x + 2}$

b) The coordinates of P correspond to the value of

$x = \frac{3\pi}{2}$

The value of G is

$\displaystyle G(\frac{3\pi}{2})= \sin \frac{3\pi}{2} + 2$

Since

$\sin \frac{3\pi}{2}=-1$

$\displaystyle G(\frac{3\pi}{2})= -1+ 2=1$

The coordinates of P are

$\displaystyle \left( \frac{3\pi}{2},1\right)$

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2 years ago

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Ksju [112]

Answer:

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Step-by-step explanation:

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3 years ago

A parabola can be drawn given a focus of (6,-1) and a directrix of y = 9. What can be said about the parabola?

zavuch27 [327]

Answer:

Since the focus is at (-6,-11) and the directrix is at y=9:

The vertex is halfway between the focus and the directrix, so the vertex is at (-6,-1). (Draw this on graph paper if that doesn't make sense.)

The general form (conics form) of a parabola: 4p(y-k)=(x-h)^2 (vertex is (h,k) and "p" is the distance between the focus and vertex (or between vertex and directrix)).

(h,k) = (-6,-1)

p = 10 (distance between focus and vertex), so 4p = 40.

Therefore:

40(y+1)=(x+6)^2

Or if you need to rearrange to "vertex form": y=(1/40)(x+6)^2 - 1

Step-by-step explanation:

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2 years ago

What are all the prime and composite factors of 45

Helen [10]

I may not know many but here it goes...
1,3,5,9,45

Hope this helped you!

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3 years ago

The quotient of a number and -7 decreased by 2, is 10.

klasskru [66]

Hello!

This expression can be broken down into 3 separate parts:

1. "the quotient of a number and (-7)"
2. "decreased by 2"
3. "is 10"

We'll begin with the first part. The word "quotient" implies the result of a division problem. Therefore, this part can be represented by the following expression (let "x" represent the unknown number):

$\frac{x}{(-7)}$

Now we'll move on to the second part. If something is decreased by a value of 2, we know that 2 is being subtracted. Therefore, this part can be represented by the following expression:

– 2

Now we'll move on to the third and final part. The phrase "is 10" implies that the operations preceding this part are equal to 10. Therefore, this part can be represented by the following expression:

= 10

Finally, put the three parts together to create the following equation:

$\frac{x}{(-7)}$ – 2 = 10

The equation has now been fully translated. If, however, you are required to find the unknown value (x), begin by adding 2 to both sides of the equation:

$\frac{x}{(-7)}$ = 12

Now multiply both sides by (-7):

x = (-84)

We have now proven that the unknown number is equal to (-84).

I hope this helps!

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2 years ago