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Stels [109]
3 years ago
12

Write the equation of the line that passes through (–1, 5) and has a slope of 3 in point-slope form.

Mathematics
1 answer:
LekaFEV [45]3 years ago
6 0

using the formula

y - y1 = m(x - x1)

where m is the slope or gradient

from the question, x1 = -1 and y1 =5

and gradient/slope m = 3

substituting them in the formula

y - 5 = 3(x - ( - 1))

y - 5 = 3(x + 1)

y - 5 = 3 x + 3

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What is the slope of the line that passes through the points (10, 3) and (2, 3) ?
Margarita [4]
Slope: (y2-y1)/(x2-x1)
(3-3)/(2-10) = 0/-8 = 0
The slope is 0
3 0
2 years ago
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Consider the function V=g(x), where g(x) =x(6-2x)(8-2x), with x being the length of a cutout in cm and V being the volume of an
Andrej [43]

Answer:

The maximum volume of the open box is 24.26 cm³

Step-by-step explanation:

The volume of the box is given as V=g(x), where g(x)=x(6-2x)(8-2x) and 0\le x\le3.

Expand the function to obtain:

g(x)=4x^3-28x^2+48x

Differentiate  wrt  x to obtain:

g'(x)=12x^2-56x+48

To find the point where the maximum value occurs, we solve

g'(x)=0

\implies 12x^2-56x+48=0

\implies x=1.13,x=3.54

Discard x=3.54 because it is not within the given domain.

Apply the second derivative test to confirm the maximum critical point.

g''(x)=24x-56, g''(1.13)=24(1.13)-56=-28.88\:

This means the maximum volume occurs at x=1.13.

Substitute x=1.13 into g(x)=x(6-2x)(8-2x) to get the maximum volume.

g(1.13)=1.13(6-2\times1.13)(8-2\times1.13)=24.26

The maximum volume of the open box is 24.26 cm³

See attachment for graph.

6 0
3 years ago
The answer for this math problem because I don’t really understand it
andreyandreev [35.5K]

Answer:

See below

Step-by-step explanation:

Start by subtracting 5.2 from both sides of the equation

  so  "subtraction property of equality "    I suppose ......

then the next step would be divide both sides by 2.5  

  which would be division property of equality  

3 0
2 years ago
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If angle 0 is in quadrant I, what is the value of
Brilliant_brown [7]

Answer:

the \: answer \: is \: c \:  =  -  \frac{ \sqrt{14} }{5}

Step-by-step explanation:

\sin^{2}0 + ( \frac{ \sqrt{11} }{5} ) ^{2}  = 1( \sin^{2}0 +  \cos^{2} 0 = 1)

{ \sin }^{2}0 +  \frac{11}{25} = 1   \\  { \sin }^{2}0 =  \frac{14}{25}

\sin0_{1} =  -  \frac{ \sqrt{14}}{5} while \sin0_{2} =  \frac{ \sqrt{14} }{5}

  • Therfore theta is QI
  • Therfore sin theta >0
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4 0
1 year ago
WORTH 25 POINTS PLEASE HELP!!!
GalinKa [24]
Just subtract the smaller volume from the larger:

10 × 10 ×15 - 7 × 9 × 12 

First you would multiply 10 × 10 × 15 = 1500 and then multiply 7 × 9 × 12 = 756.

After you would subtract 1500 - 756 which would give you 744

I hope that helped!
7 0
3 years ago
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