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3 years ago

Write an equation in slope-intercept form for the line containing the giving points (10,2) (2,-2)

Mathematics

2 answers:

zysi [14]3 years ago

7 0

(y - yo) = m.(x - xo)

(-2 - 2) = m.(2 - 10)

-4 = m.(-8)

m = -4/-8

m = 1/2

(y - yo) = 1/2.(x - xo)

(y - 2) = 1/2.(x - 10)

y - 2 = 1/2x - 5

y = 1/2x - 5 + 2

y = 1/2x - 3

hichkok12 [17]3 years ago

5 0

Answer:

y = $\frac{1}{2}$ x - 3

Step-by-step explanation:

Slope formula: $\frac{y2-y1}{x2-x1}$

Plug in the 2 points:

$\frac{-2-2}{2-10}$

$\frac{-4}{-8}$

$\frac{1}{2}$

Plug either point and the slope into y = mx + b:

2 = $\frac{1}{2}$ (10) + b

solve for b:

2 = 5 + b

b = -3

Rewrite the equation:

y = $\frac{1}{2}$ x - 3

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A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108

Morgarella [4.7K]

Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

$4x+L=108$

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

$V=x^2L$

If we express L in function of x using the restriction equation, we get:

$4x+L=108\\\\L=108-4x$

We replace L in the volume formula and we get

$V=x^2L=x^2*(108-4x)=-4x^3+108x^2$

To maximize the volume we derive and equal to 0

$\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18$

We can replace x to calculate L:

$L=108-4x=108-4*18=108-72=36$

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

4 0

3 years ago

Read 2 more answers

Slope is 0 and (3,2) is on the line

USPshnik [31]

Answer:

y = 2

Step-by-step explanation:

if slope is 0 y stays the same and y is 2 on the point

7 0

3 years ago

Help please, not sure how to do this...

olga nikolaevna [1]

Answer:

8.38

Step-by-step explanation:

The underlined number is in the hundredths place, so that means that we're going to round there. That means that you look at the number to its right and if it's lower than 5, it stays the same. However, if it's 5 or higher, you round it up. For example, if the number was 8.386, we would round it to 8.39.

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3 years ago

There are 3 red and 8 green balls in a bag. If you randomly choose balls one at a time, with replacement, what is the probabilit

Kaylis [27]

So, the total number of balls is 11. We want to pick 2 red balls and 1 green ball. WLOG (since order doesnt matter here), we can say he picks red, green, red. That means on his first pick, he has a $\frac{3}{11}$ chance of picking the red ball, and he places it back in the bag. The probability of picking a green ball is $\frac{8}{11}$ , and then he places the ball back in the bag. The probability of picking the last red ball is the same as the last red ball example, and we simply multiply the probabilities together as per the multiplication rule to get:

$\frac{3}{11}\frac{3}{11}\frac{8}{11}=\frac{3*3*8}{11^3}=\frac{72}{1331}$

Now, without replacement the order does matter. He picks a red ball, a red ball then a green ball. The probability of picking the first red ball is $\frac{2}{11}$ , and the probability of picking the second red ball is $\frac{1}{10}$ and the probability of picking the green ball is $\frac{1}{9}$ . We want to multiply thm again, as per the multiplication rule like the last problem.