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3 years ago

The midpoint M of QR has coordinates (7, 8). Point R has coordinates (4, 6). Find the

Mathematics

1 answer:

djyliett [7]3 years ago

3 0

Answer:

q= (5.5, 7)

Step-by-step explanation:

add the x-axis together then divide by two and do the same with the y-axis

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I don't understand how to do this problem.

Delicious77 [7]

Answers:

x = 4
EF = 14
CF = 7
EC = 7

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Work Shown:

C is the midpoint of segment EF. This means that EC = CF. In other words, the two pieces are congruent.

Use substitution and solve for x
EC = CF
5x-13 = 3x-5
5x-13+13 = 3x-5+13
5x = 3x+8
5x-3x = 3x+8-3x
2x = 8
2x/2 = 8/2
x = 4

Now that we know that x = 4, we can use this to find EC and CF

Let's compute EC
EC = 5x - 13
EC = 5*x - 13
EC = 5*4 - 13 ... replace x with 4
EC = 20 - 13
EC = 7

Let's compute CF
CF = 3x - 5
CF = 3*x - 5
CF = 3*4 - 5 ... replace x with 4
CF = 12 - 5
CF = 7

As expected, EC = CF (both are 7 units long).

By the segment addition postulate, we can say EC+CF = EF

EC+CF = EF
EF = EC+CF
EF = 7+7
EF = 14

8 0

3 years ago

In the figure below, ∠DEC ≅ ∠DCE, ∠B ≅ ∠F, and segment DF is congruent to segment BD . Point C is the point of intersection betw

Rzqust [24]

Answer:

Step-by-step explanation:

Given:

∠DCE ≅ ∠DEC

∠B ≅ ∠F

DF ≅ BD

To prove:

ΔABC ≅ ΔGFE

Solution:

Statements Reasons

1). ∠DCE ≅ ∠DEC 1). Given

2). ∠ACB ≅ ∠GEF 2). Vertically opposite angles to the

congruent angles.

3). ∠B ≅ ∠F 3). Given

4). DB ≅ DF 4). Given

5). DC + CB ≅ DE + EF 5). Segment addition postulate

6). DC ≅ DE 6). Property of isosceles triangle

7). CB ≅ EF 7). Transitive property

8). ΔABC ≅ ΔGFE 8). ASA property of congruence

4 0

3 years ago

Need help ! Simplify the rational expression.state any excluded values.2x/-5x+x^2

mario62 [17]

I assume it is:

2x/(-5x+x^2), then you can simplify the x, but only if it is not zero:

2/(x-5), for x different to zero.

3 0

3 years ago

An 11-inch by 8-inch piece of cardboard has squares cut out of the corners and is folded up to make an open-top box. If the volu

12345 [234]

Volume=14in^3

$\\ \sf{:}\implies (side)^3=14$

$\\ \sf{:}\implies side=\sqrt[3]{14}$

$\\ \sf{:}\implies side=2.5in$

Now

L=11in
B=8in

$\\ \sf{:}\implies Area=11(8)=88in^2$

Cut it into 10 parts as per question(Open side means five sides hence it will be 5×2=10)

$\\ \sf{:}\implies 88/10=8.8in$

Now divide by previous side

$\\ \sf{:}\implies \dfrac{8.8}{2.5}=3.52=3.5$

Option D

6 0

2 years ago

Two circles are concentric if they have the same center.

vaieri [72.5K]

The equation of the circle is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

<h3>Equation of a circle </h3>

From the question, we are to determine the equation of the circle

The equation of circle is given by

(x - h)² + (y - k)² = r²

Where (h, k) is the center

and r is the radius

From the given information,

The two circles are concentric

∴ (h , k) = (4, 6)

But the other circle has a radius that is twice as large

∴ r = 2 × 2

r = 4

Thus,

The equation of the circle becomes

(x - 4)² + (y - 6)² = 4²

(x - 4)² + (y - 6)² = 16

Hence, the equation which represents a circle that is concentric with the circle shown but has a radius that is twice as large is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

Learn more on Equation of a circle here: brainly.com/question/1506955

#SPJ1

8 0

2 years ago