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TiliK225 [7]
3 years ago
6

Write an equation in standard form of the line that contains the point (-2,4) and is parallel to (has the same slope as) the lin

e y = 8x-3.
Mathematics
1 answer:
CaHeK987 [17]3 years ago
8 0

Answer:

The equation of the line in standard form is -8x + y = 20

Step-by-step explanation:

The standard form of the linear equation is Ax + By = C, where

  • A, B, and C are integers

The slope-intercept form of the linear equation is y = m x + b, where

  • m is the slope
  • b is the y-intercept

Parallel lines have equal slopes

∵ The line is parallel to the line y = 8x - 2

→ Compare it with the slope-intercept form above

∴ m = 8

∵ The parallel lines have the same slopes

∴ The slope of the line = 8

→ Substitute it in the slope-intercept form above

∴ y = 8x + b

∵ The line passes through the point (-2, 4)

∴ x = -2 and y = 4

→ Substitute x by -2 and y by 4 in the equation to find b

∵ 4 = 8(-2) + b

∴ 4 = -16 + b

→ Add 16 to both sides

∴ 4 + 16 = -16 + 16 + b

∴ 20 = b

→ Substitute the value of b in the equation above

∴ y = 8x + 20

→ Subtract both sides by 8x

∵ y - 8x = 8x - 8x + 20

∴ y - 8x = 20

→ Switch x and y

∴ -8x + y = 20

∴ The equation of the line in standard form is -8x + y = 20

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Answer:

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Step-by-step explanation:

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Disjoint Events are the events that have zero probability of occurring together. If all the three above items are disjoint, it means that it can never happen that two of them happen together.

The total (summed) probability of a valid probability distribution, with disjoint sets = 1 . In given case, total probability = 0.2 + 0.7 + 0.3 = 1.2 ; i.e > 1.

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Based on the given diagram we see that all the exterior angle is in a straight line with the interior angle.

Using the known angle measure, we know that the shape has angles of measure, 123 degrees, 94 degrees,  79 degrees, and '180 - x' degrees

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Now using the knowledge gained lets set up the equation

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Therefore x is 116 degrees.

Hope that helps!

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2 years ago
The length of the box is 2 1/2 m, it is 1 9/16 times its width. What is the height of the box if its volume is 12 3/4 m3?
skelet666 [1.2K]

Answer:

3\frac{3}{16} meter

Step-by-step explanation:

We have to write first what is known from the information.

Let's say, length is L, width is W, and height is H

1. The length of the box is 2 1/2 m = 2,5 m = 5/2 m, it is 1 9/16 = 25/16 times it's width (L). So we have the equation :

L ≡ \frac{5}{2} = \frac{25}{16} W

Then we find the W. From the fraction above, we found W equals to \frac{8}{5} = 1,6 meter

2. What is the height of the box, if its volume is 12 3/4 m^3 = 51/4 m^3

Formula of a volume is :

The area wide times the height

In this problem, the equation is :

L × W × H = Volume

Insert the numbers,

\frac{5}{2} × \frac{8}{5} × H = \frac{51}{4}

From the fraction above, we can find that H equals to

3\frac{3}{16} meter

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