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3 years ago

Write the equation of the line to n slope intercept from (3,5) and (-3,-1)

Mathematics

1 answer:

miv72 [106K]3 years ago

7 0

Answer:

The equation of your line is y=1x+2

Step-by-step explanation:

first you take y2-y1/x2-x1

y2=-1 y1=5

x2= -3 x1= 3

that gives you your slope so (-1-5)/ (-3-3) = 1

y=mx+b

mx is your slope

y=1x+b

to solve for b you input your slope and one of your points (I used (3,5)

5=1(3) +b

solve for b and you get 2

then put your mx and b into the equation of a line

y=1x+2

and thats your answer

You can also check your work by using a graphing calculator and checking that the line goes through those two points.

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According to u.s. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 108 inches, where by "gi

Pepsi [2]

Let x represent the side length of the square end, and let d represent the dimension that is the sum of length and girth. Then the volume V is given by
V = x²(d -4x)
Volume will be maximized when the derivative of V is zero.
dV/dx = 0 = -12x² +2dx
0 = -2x(6x -d)
This has solutions
x = 0, x = d/6

a) The largest possible volume is
(d/6)²(d -4d/6) = 2(d/6)³
= 2(108 in/6)³ = 11,664 in³

b) The dimensions of the package with largest volume are
d/6 = 18 inches square by
d -4d/6 = d/3 = 36 inches long

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3 years ago

6 feet<br> 12 feet<br> What is the area of the given composite shape?

Reika [66]

Answer:

choice A; 128.52 square feet

Step-by-step explanation:

This shape is made up of a semi-circle and a rectangle. The area of the rectangle will be 12*6 = 72 sq ft.

The formula for area of a circle is $\pi$ * $r^{2}$ . also r=radius. We are given the diameter, 12 feet. The radius is diameter/2, so the radius of the circle will be 6 feet.

Since pi is infinite we round it to 3.14.

Plug in the values and our expression will be (3.14* $6^{2}$ )/2 because it is a semi-circle. Simplify that to (3.14*36)/2 = 113.04/2 = 56.52 sq ft.

Remember to add the area of the rectangle and semi-circle. 72 + 56.52 = 128.52 sq ft.

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3 years ago

If two cylinders are similar and the ratio between the altitude lengths is 2:3, what is the ratio of their volumes

hram777 [196]

Given:

ratio of altitude height = 2/3

Required:

ratio of volume

Solution:

Assuming that the only difference that the cylinders has is the height, we can solve for the ratio of the volume.

The volume of a cylinder is equal to πr²×height.

ratio of volume = πr²×2/πr²×3

We cancel the pi and the r² since we assume that the cylinders have the same radius.By cancelling, we are left with:

ratio of volume = 2/3

8 0

3 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

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3 years ago

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krek1111 [17]

Answer: 5 9 18. The youngest child would be 5, the middle child would be 9, and the eldest would be 18 years old.

Step-by-step explanation: 5 + 4 = 9, 9(2) = 18 Hope this helps :D

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3 years ago