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lara31 [8.8K]
3 years ago
5

????(−2, 10) is the midpoint of . If ???????? has coordinates (4, −5), what are the coordinates of ?????

Mathematics
1 answer:
Sonbull [250]3 years ago
8 0

Answer:

The coordinates of B are (-8,25).

Step-by-step explanation:

Consider the completer question is " M(−2, 10) is the midpoint of AB. If A has coordinates (4, −5), what are the coordinates of B".

Let coordinates of B are (a,b).

Formula for midpoint:

Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})

Midpoint of A and B is

Midpoint=(\dfrac{4+a}{2},\dfrac{-5+b}{2})

It is given that M(−2, 10) is the midpoint of AB.

(-2,10)=(\dfrac{4+a}{2},\dfrac{-5+b}{2})

On comparing both sides we get

-2=\dfrac{4+a}{2}

Multiply both sides by 2.

-4=4+a

Subtract 4 from both sides.

-8=a

The value of a is 8.

Similarly,

10=\dfrac{-5+b}{2}

Multiply both sides by 2.

20=-5+b

Add 5 on both sides.

25=b

Therefore, the coordinates of B are (-8,25).

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Satellite dishes are shaped like parabolas to optimally revive signals. The cross section of a satellite dish can be modeled by
Anna11 [10]

The cross section of the satellite dish is an illustration of a quadratic function

The quadratic function that models the cross-section is y = 1/6(x^2 - 9)

<h3>How to determie the equation of the cross-section?</h3>

The given parameters are:

Width = 6 feet

Depth = 1.5 feet

Express the width the sum of two equal numbers

Width = 3 + 3

The above means that, the equation of the cross section passes through the x-axis at:

x = -3 and 3

So, we have:

y = a(x - 3) * (x + 3)

Express as the difference of two squares

y = a(x^2 - 9)

The depth is 1.5.

This is represented as: (x,y) =(0,-1.5)

So, we have:

-1.5 = a(0^2 - 9)

Evaluate the exponent

-1.5 = -9a

Divide both sides by -9

a = 1/6

Substitute 1/6 for a in y = a(x^2 - 9)

y = 1/6(x^2 - 9)

Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)

Read more about quadratic functions at:

brainly.com/question/1497716

7 0
2 years ago
Stuck on this question. Help appreciated!!
marta [7]

Answer:

the missing is 4.98

Step-by-step explanation:

4 0
3 years ago
Help me solve this I wil give brainliest and 40 points
Verizon [17]

Answer:

Slope: -\dfrac{1}{2}

Equation: y=-\dfrac{1}{2}x+8

Step-by-step explanation:

The line of the best fit passes through the points (0,8) and (4,6).

If the line passes through the points (x_1,y_1) and (x_2,y_2) then the slope of the line is

\dfrac{y_2-y_1}{x_2-x_1}

Hence, the slope of the line of the best fit is

\dfrac{6-8}{4-0}=\dfrac{-2}{4}=-\dfrac{1}{2}

The equation of the line is

y=mx+b,

where m is the slope and b is y-intercept, so the equation of the line of the best fit is

y=-\dfrac{1}{2}x+8

4 0
3 years ago
The perimeter of a rectangle garden is 364 feet. If the width of the garden is 85 feet, what is it length?
kherson [118]

P=2(L+W)

P=364

L=99

sub and find W

364=2(99+W)

divide both sides by 2

182=99+w

subtract 99 from both sides

83=W

w=83ft

6 0
2 years ago
Seven less than twice a number is 5
marin [14]
Yes, i believe so because u can count back twice and u will get 5. You could al so do: 7-2=5. Hope this helps
8 0
3 years ago
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