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3 years ago

Write an equation of the line that passes through the point (-6,-5) with slope 6

Mathematics

2 answers:

fenix001 [56]3 years ago

6 0

Answer:

y + 5 = 6(x + 6)

Step-by-step explanation:

Apply the point-slope formula y - k = m(x - h):

y + 5 = 6(x + 6)

lisabon 2012 [21]3 years ago

5 0

Answer:

y=6x-31

Step-by-step explanation:

We know that the line passes through the point (-6,-5) so we can substitute the x and y coordinates into the equation of a line y=mx+b, where y and x are the respective coordinates, m is slope, and b is the y-intercept. We can also plug in 6 to the equation for slope.

y=mx+b

-5=(6)(-6)+b

Solve for b, the y-intercept

b=-36+5=-31

Therefore, the equation of the line is: y=6x-31

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Anni [7]

Answer:

t-6=7 .................

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3 years ago

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Simplify the following expression: (5x2 + 3x + 4) − (2x2 + 5x − 1). If the final answer is written in the form Ax2 + Bx + C, wha

algol13

Answer:

A = 3

Step-by-step explanation:

Given

(5x² + 3x + 4) - (2x² + 5x - 1)

Remove the parenthesis from the first and distribute the second by - 1

= 5x² + 3x + 4 - 2x² - 5x + 1 ← collect like terms

= 3x² - 2x + 5

In the form Ax² + Bx + C

with A = 3

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3 years ago

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Which statements are true about these lines? Check all that apply. Line RS has a slope of 6. Line SW has an undefined slope. Lin

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Line SW is perpendicular to line RS, but not to line TV

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3 years ago

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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the

Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0

3 years ago

Distributions and Comparing Data Project

LenKa [72]

Answer:

1. The shape of the histogram created with MS Excel is approximately bell shaped and approximately evenly spread about the central (largest counts) values

The shape of the box plot created with MS Excel is approximately evenly distributed

2. The appropriate measure of central tendency for a bell shaped histogram is the mean and median, due to the approximately equal distribution about the highest frequency class

3. Part A

The 15 numbers between 1 and 20 generated by a random generator are;

1, 8, 8, 15, 4, 18, 11, 6, 17, 1, 18, 15, 10, 12, 11

The measure of center is the mean = (1+8+8+15+4+18+11+6+17+1+18+15+10+12+11)/15 = 155/15 = 31/3

The measure of spread used is the variance, s² = 32.38

$Where, \,s^2 =\dfrac{\sum \left (x_i-\bar x \right )^{2} }{n - 1}$

${\sum \left (x_i-\bar x \right )^{2} }$ = 453.333

n = 15

s² = 453. $\overline 3$ /(15 - 1) = 32.38

Part B

The measure of central tendency are the mean and the median because the size of the data (n = 15), is 75% of the population (N = 20) nd therefore the data is approximately normal and can be represented by the mean and the standard deviation

Step-by-step explanation:

4 0

3 years ago