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Ede4ka
1 month ago
11

If EF bisects CD, CG = 5x-1, GD = 7x-13, EF=6x-4, and GF = 13, find EG (MUST SHOW WORK)

Mathematics
1 answer:
AnnZ [12.3K]1 month ago
3 0

Answer:

EG = 19

Explanation:

We have a line segment CD that is bisected at point G by EF.

The length CG is expressed as 5x - 1,

while GD measures 7x - 13.

Since G bisects CD, these lengths are equal, so:

5x - 1 = 7x - 13

Solving for x,

2x = 12

x = 6

Further, EF equals 6x - 4, and GF is 13.

Because EF = EG + GF,

we write 6x - 4 = EG + 13

Rearranged, EG = 6x - 17

Substituting x = 6,

EG = 6*6 - 17

EG = 19

This is the final value.

I hope this helps you understand the solution.

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40 tens converts to how many hundreds? The calculation is 40 multiplied by 10, resulting in 400.
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What is the product of 2x2 – 3xy + y2 and 2x – 4y?
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Answer:

C. 4x^3 - 14x^2y + 14xy^2 - 4y^3

Step-by-step explanation:

Given:

Multiplication of 2x^2 – 3xy + y^2 and 2x – 4y

Multiplication refers to the product

(2x^2 – 3xy + y^2) (2x – 4y)

Expand the brackets

= 4x^3 - 8x^2y - 6x^2y + 12xy^2 + 2xy^2 - 4y^3

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= 4x^3 - 14x^2y + 14xy^2 - 4y^3

The result is

C. 4x^3 - 14x^2y + 14xy^2 - 4y^3

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1 month ago
A quadratic function has a line of symmetry at x = –3.5 and a zero at –9. What is the distance from the given zero to the line o
Svet_ta [12734]

Given:

A quadratic function has a line of symmetry positioned at x = –3.5 with one root located at –9.

To find:

The second root.

Solution:

It is understood that the line of symmetry splits the quadratic function's graph into two identical halves. Hence, both roots are equidistant from this line.

This implies that the line of symmetry passes through the midpoint of the two roots.

Let the other root be denoted as x.

-3.5=\dfrac{(-9)+x}{2}

Multiply both sides by 2.

-7=-9+x

Add 9 to both sides.

-7+9=-9+x+9

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1 month ago
Marlena solved the equation 2x + 5 = –10 – x. Her steps are shown below.
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Answer: step 1. property of equality through addition

step 2. property of equality through subtraction

step 3. property of equality through division

Detailed explanation:

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Response:

The width of the arch measures 105 meters

Detailed explanation:

The function that describes the width of the arch is

f(x) = -0.016(x - 52.5)² + 45

where x denotes the horizontal distance from the left end of the arch or the width at its base

f(x) indicates the vertical height of the arch

According to the given quadratic equation, the vertex coordinates of the parabola are (52.5, 45).

The vertex coordinates indicate that

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