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Alex17521 [72]
3 years ago
13

If one endpoint of a line segment is (2, 8) and the midpoint is (-4, 7), what is the other endpoint? (8, -5)

Mathematics
1 answer:
Pepsi [2]3 years ago
7 0

( - 10, - 22 )

using the midpoint formula,

let the other endpoint have coordinates (x, y) then

\frac{1}{2} (2 + x ) = - 4 ( multiply through by 2 )

2 + x = - 8 ( subtract 2 from both sides ) then

x = -8 - 2 = - 10 ← value of x-coordinate

Similarly for y-coordinate

\frac{1}{2} (8 + y ) = - 7 ( multiply through by 2 )

8 + y = - 14 ( subtract 8 from both sides )

y = - 14 - 8 = - 22 ← y -coordinate

the other endpoint is ( - 10, - 22 )




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**50 points Once again and brainliest** Please hurry ;w;
Pachacha [2.7K]

Answer:

Part A:

Two types of translation are;

1) Horizontal translation left T(0, 8),

2) Vertical translation T(16, 0)

Part B:

For the horizontal translation transformation, k = 8

For the vertical translation transformation, k = 16

Part C:

For the horizontal translation transformation, the equation is f(x + 8) = g(x)

For the vertical translation transformation, the equation is f(x) + 16 = g(x)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
I need help please.
Ivan

1. It is given that f(x) is 16 times the square root of x.

Putting that in mathematical terms we have,

f(x) = 16 * \sqrt{x}

also, y = f(x)

So, we have the function

y= 16 \sqrt{x}

4. We need to solve the inequality equation : 4x + 2y ≤ 6

Let us take the equation,

4x+2y ≤ 6

2y ≤ 6-4x

y ≤ \frac{6-4x}{2}

y ≤ 3-2x

So, any point (x,y) lies on the given inequality region, where y≤ 3-2x

5. Solving system of equations using addition method

Given:

-5x-y =38          ------> a

-6x-3y =60       -------> b

Divide the equation b by no. 3

(-6x-3y)/3 = 60/3

-2x-y = 20      -------> c

Subtracting equation c from a we have,

-5x-y - (-2x-y) = 38 - 20

-5x-y+2x+y = 18

-3x = 18

x = -6

Now, substituting the value of x in equation a, we get

-5(-6) - y =38

30-y =38

y= 30-38 = -8

y=-8

∴ x = -6 and y = -8

6. Finding composition of functions

Given : f(x) =15x + 7 ; g(x) = x² - 5x

To find : (f+g)(x)

(f+g) (x) = f(g(x))

So, replace the value of x in f(x) by g(x), where g(x)= x² - 5x

(f+g)(x) = 15(x²-5x) +7 =15x²-75x+7

∴ (f + g)(x) = 15x²-75x+7

7. System of 3 equations must be solved to find the solution

-8x-8y-5z=-6

7x-8y-9z =17

9x+2y+6z =-1

Solving by substitution method.

Isolate x from first equation :

x= (-6+8y+5z)/(-8)

Substitute this value of x in 2nd and 3rd equations.

7 (- \frac{-6+8y+5z}{8})-8y -9z = 17

9(- \frac{-6+8y+5z}{8}) + 2y + 6z = -1

Now, isolating y from the 2nd equation rewritten above, we have

y= - \frac{107 z + 94}{120}

Now substituting this value of y in the 3rd equation rewritten above, we have

9(- \frac{-6+8(-\frac{107 z + 94}{120})+5z}{8}) + 2(-\frac{107 z + 94}{120}) + 6z = -1

Isolating z from above equation, we have

z = -2

Substitute z= -2 in the equation of y, we have

y= - \frac{107 (-2) + 94}{120} = 1

y = 1

Substituting the value of y and z, in the equation of x, we have

x= (-6+8(1)+5(-2))/(-8) = 1

x = 1

∴ x=1 ; y = 1 ; z = -2

8. 5x ≤ 7

Solving the above equation, we have

x ≤ 7/5

Please see attachment for the graph.

9. The given function is : g(y) = \sqrt{y} -6

The domain is the set of values of y for which there can be a value of g(y).

Here g(y) can be real only if y is greater than or equal to 0.

∴ The domain of the given function is [0,∞) .

10. Given : y is a function of x.

Definition of function : A function is a relation that associates each element in the domain to one element of another set, the co-domain of the function.

∴ For each element x, in the domain, there is only one value of y in the range.


4 0
3 years ago
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally dis
aliya0001 [1]

(A)

P(<em>X</em> < 61.25) = P((<em>X</em> - 55.4)/4.1 < (61.25 - 55.4)/4.1)

… ≈ P(<em>Z</em> ≤ 0.1427)

… ≈ 0.5567

(B)

P(<em>X</em> > 46.5) = P((<em>X</em> - 55.4)/4.1 > (46.5 - 55.4)/4.1)

… ≈ P(<em>Z</em> > -2.1707)

… ≈ 1 - P(<em>Z</em> ≤ -2.1707)

… ≈ 0.9850

5 0
3 years ago
Please Help!!
Mrrafil [7]
Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. 
<span>If they join to work together they can complete the job in 3 hours. </span>
<span>1/x + 1/(x - 8) = 1/3 </span>
<span>3(x - 8) + 3x = x(x - 8) </span>
<span>x^2 - 14x + 24 = 0 </span>
<span>(x - 12)(x - 2) = 0 </span>
<span>Solutions: </span>
<span>x = 2 </span>
<span>x = 12 </span>
<span>Jimmy can complete the job on his own in 12 hours.</span>
6 0
3 years ago
What is the distance between the points (−7, 7) and (−7, 8) ?
Vesnalui [34]

Answer:1

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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