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Ber [7]
3 years ago
15

If a line segment contains one endpoint at (2,3) and has a midpoint of (-2,6) what is the second endpoint of the line segment

Mathematics
1 answer:
olchik [2.2K]3 years ago
4 0

Answer:

Step-by-step explanation:

The coordinates of the midpoint M are the average of the coordinates of the two endpoints:

M_x = \dfrac{2+x}{2},\quad M_y = \dfrac{3+y}{2}

Plug the known coordinates of the midpoint:

-2 = \dfrac{2+x}{2},\quad 6 = \dfrac{3+y}{2}

Solve for x and y:

-4 = 2+x,\quad 12 = 3+y

x=-6,\quad y = 9

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Kimi and Jordan are each working during the summer to earn money in addition to
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Their earnings would be the same after 4 hours

Let the number of hours be x, and the weekly earning be y

So, the given parameters are:

<u>Kimi</u>

  • Earnings = $9 per hour
  • Weekly allowance = $8

So, the equation for Kimi's weekly earning is:

y =9x + 8

<u />

<u>Jordan</u>

  • Earnings = $7 per hour
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So, the equation for Jordan's weekly earning is:

y = 7x + 16

Equate both equations

7x + 16 = 9x + 8

Collect like terms

9x - 7x = 16 - 8

2x =8

Divide both sides by 2

x =4

Hence, their earnings would be the same after 4 hours

Read more about linear equations at:

brainly.com/question/13729904

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3 years ago
Find the distance between the points of intersection of the graphs of the functions.
Viefleur [7K]

Answer:

Find the value of x and y in coordinate form, that'll be the point of intersection.

Question 1

{ \rm{y =  {x}^{2} - 3x + 4 }} \\ { \boxed{ \tt{but \: y = x + 1 \: }}} \\  \\ { \rm{(x + 1) =  {x}^{2} - 3x + 4 }} \\  \\ { \rm{ {x}^{2} - 4x + 3 = 0 }} \\  \\ { \rm{(x - 3)(x - 1) = 0}} \\  \\ { \boxed{ \rm{x_{1} = 3 \:  \: and \:  \: x _{2}  = 1}}} \\  \\ { \boxed{ \tt{remember \: y = x + 1}}} \\  \\ { \rm{y _{1} = 4 \:  \: and \:  \: y _{2}  = 2 }}

Therefore, points of intersection are two

Answer: <u> </u><u>(</u><u>3</u><u>,</u><u> </u><u>4</u><u>)</u><u> </u><u>and</u><u> </u><u>(</u><u>1</u><u>,</u><u> </u><u>2</u><u>)</u>

Question 2:

Following the steps as in question 1

{ \rm{y =  {x}^{2}  - 4}} \\  \\{ \rm{2x - 4 =  {x}^{2}  - 4}} \\  \\ { \rm{ {x}^{2} = 2x }} \\  \\ { \boxed{ \rm{x = 2}}} \\ { \tt{remember : \: y = 2x - 4 }} \\ { \boxed{ \rm{y = 0}}}

Answer: <u>(2, 0)</u>

7 0
2 years ago
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4 0
3 years ago
The back of jake's property is a creek. Jake would like to enclose a rectangular area, using the creek as one side and fencing f
kow [346]

Answer:

The maximum possible area of the pasture  is 26,450 feet square.

Step-by-step explanation:

Let us assume the width of the rectangular area  = m  ft

and the length of the area = k ft

Also assume:  ( one side with k units IS NOT FENCED)

So, the total  perimeter of the fencing is:

2 m + k = 460

or, k = 460 - 2m  ........ (1)

Now, AREA OF THE RECTANGULAR PORTION = Length x  Width  = k x m

Put  k =  460 - 2m

We get:   A = m (460 - 2m)

or, A =  460 m  - 2m²

We need to find the maximum for the parabolic function A = 460 m  - 2m²

The function has a maximum value as the quotient in front of x^2 is negative: -2 < 0

A (max)  = c-\frac{b^2}{4a}   where a = -2, b = 460, c = 0

= -\frac{(460)^2}{4(-2)}  = 26,450

A max = 26,450 sq ft.

The maximum possible area of the pasture  is 26,450 feet square.

7 0
3 years ago
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