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shusha [124]
3 years ago
14

The line segment, AB has a point C as its midpoint. If A is at (2,2) and C is at (5,4) what are the coordinates of the endpoint

B
A:(-1,0)
B:(3.5,3)
C:(5,4)
D:(8,6)
Mathematics
2 answers:
Alecsey [184]3 years ago
5 0

Answer:

( 8 , 6 )

Step-by-step explanation:

A = ( 2 , 2 ) and C = ( 5 , 4 )

→ Form an equation

\frac{2+x}{2} =5   and   \frac{2+y}{2}=4

→ Now solve them

2 + x = 10 and 2 + y = 6

→ Simply find the values

x = 8 and y = 6

nikdorinn [45]3 years ago
3 0
  • Let the coordinates of B be ( x , y ). Now , Let A ( 2 , 2 ) be ( x₁ , y₁ ) & B ( x , y ) be ( x₂ , y₂ )

SOLUTION :

  • All you need to apply is the formula of Midpoint i.e \sf{ \bold{( \frac{x_{1} + x_{2}}{2}  \: , \frac{y_{1} + y_{2}}{2} )}}

  • Plug the known values :

\large{ \rightarrow{ \tt{ \: (5 \: ,4 \: ) = ( \frac{2 + x}{2}  \: , \frac{2 + y}{2} )}}}

  • Equating corresponding values :

\large{ \tt{5 =  \frac{2 + x}{2} }}

\large{ \rightarrow{ \tt{10 = 2 + x}}}

\large{  \rightarrow{\tt{10 - 2 = x}}}

\boxed{ \large{ \rightarrow \tt{x = 8}}}

  • Value of x = 8

\large{ { \tt{4 =  \frac{2 + y}{2} }}}

\large{ \rightarrow{ \tt{8 = 2 + y}}}

\large{ \rightarrow{ \tt{8 - 2 = y}}}

\boxed{ \large{ \rightarrow{ \tt{y = 6}}}}

  • Value of y = 6

\large{ \boxed{ \tt{OUR \: FINAL \: ANSWER  :  \: D. \: (8 \:, 6 \: ) }}}

:) Hope I helped! Let me know if you have any questions regarding my answer! ~

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A line that includes the point (1, 3) has a slope of -7. What is its equation in slope-intercept
Alex787 [66]

Answer:

y = -7x + 10

Step-by-step explanation:

Using a point slope form equation

y - y1 = m( x - x1)

Given

Point = ( 1 , 3)

Slope = -7

Insert the values into

y - y1 = m(x - x1)

x1 = 1

y1 = 3

y - 3 = m( x - 1)

m = -7

y - 3 = -7(x - 1)

Using a slope intercept form equation

y = mx + c

Open the bracket

y - 3 = -7x + 7

y = -7x + 7 + 3

y = -7x + 10

The equation of the line is

y = -7x + 10

6 0
3 years ago
The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.
seraphim [82]

Keywords:

<em>Quadratic equation, vertex shape, parabola </em>

For this case we have to rewrite the given quadratic equation, in the form of vertex, for this, we must take into account that a quadratic equation of the form ax ^ 2 + bx + c = 0, can be rewritten in the form of vertex as: y = a (x-h) ^ 2 + k. Vertice is the lowest or highest point of the parabola. The vertex is given by: (h, k). So, let: f (x) = 4x ^ 2 + 48x + 10, to find the equation in the form of vertex, we follow the steps below:

Step 1:

We take the common factor to the first two terms of the equation:

f (x) = 4 (x^2 + 12x) + 10

Step 2:

We work square:

We divide the coefficient of the term "12x" by 2 and its result is squared, that is:

(\frac {12} {2}) ^ 2 = 36

So, we have:

f (x) = 4 (x^2 + 12x + 36-36) + 10

Step 3:

We simplify:

f (x) = 4 (x^2 + 12x + 36) + 10- (4 * 36)

Step 4:

We factor:

f (x) = 4 (x + 6) ^ 2-134

Thus, h = -6\ and\ k = -134

Answer:

The equation in the form of vertex is: f (x) = 4 (x + 6) ^ 2-134, and the vertex is (h, k) = (- 6, -134)

4 0
3 years ago
Read 2 more answers
What is the answer to this question
laila [671]
The area to this question is 1963.4
4 0
3 years ago
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A guy wire 1393 feet long is attached to the top of a tower. When pulled taut, it touches level ground 741 feet from the base of
andrew-mc [135]

Answer:

  57.9°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between trig functions and sides of a right triangle. Here, you're given the side adjacent to the angle of interest, and the hypotenuse of the triangle. This suggests the CAH relationship is the one of interest:

  Cos = Adjacent/Hypotenuse

  cos(angle) = (741 ft)/(1393 ft)

  angle = arccos(741/1393) ≈ 57.863° . . . . . use the inverse cosine function

  angle ≈ 57.9°

The wire makes an angle of approximately 57.9° with the ground.

5 0
3 years ago
I’m having a hard time working on my assignment can someone please help me <br> ASAP
icang [17]

Answer:

1. y=4

2.x=1

3. Y intercept (0.5)

4.x intercept (-2.5,0)

5.slope is 2

6. y=2x+5

Step-by-step explanation:

1&2use the graph to see that when x is -1 it touches y at 4.

3.Y intercept is where the line touches the Y Axis in this case at (0.5)

4.x intercept is where the line touches at the X axis

5.slope you can do rise over run, it goes up 4

from one point to another and 2 across, 4/2=2.

6. y=mx+b

mx is slope, so its 2 and b is the y intercept is 5 so its 2x+5.

3 0
3 years ago
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