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denis23 [38]
3 years ago
9

Determain the equation, in slope intercept form, of the line of the line that has a slope of -6 and passes through the point P(-

3, 2)
Mathematics
1 answer:
Vinil7 [7]3 years ago
5 0

Answer:

<h2>         y = -6x - 16</h2>

Step-by-step explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

m = -6

(-3, 2)    ⇒   x₀ = -3,  y₀ = 2

The point-slope form of the equation:

y - 2 = -6(x + 3)

So:

y - 2 = -6x - 18         {add 2 to both sides}

y = -6x - 16             ←  the slope-intercept form of the equation

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What property does the number sentence show 8+0=8
givi [52]

For this case we have the following expression:

8 + 0 = 8

The sum has several properties.

One of them is the following one:

Neutral element: the sum has a neutral element that is 0. If you add 0 to any number the result is the same number.

Answer:

The property shown in the given expression is:

Neutral element.

7 0
3 years ago
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An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne
lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

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3 years ago
What is the simplified form of x+6/x+4 +x-3/3​
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Answer:

3x+2

Step-by-step explanation:

x+6/x+4+x-3/3

3x+6/4-3/3

3x+6/1/3

3x+6/3

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3 0
3 years ago
A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The
Yuliya22 [10]
Here is the answer: 3/4 (pi r^2 h)
5 0
3 years ago
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(x^(2)-11x+30)/(x^(2)-25)*(x^(2)+6x+5)/(x-5x-6) simplify the rational expression
DanielleElmas [232]
Simplify the following:
((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6))

The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6))

The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6):
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6))

x - 5 x = -4 x:
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Factor -2 out of -4 x - 6:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25))

x^2 - 25 = x^2 - 5^2:
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Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
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Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))
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