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Naily [24]
3 years ago
6

Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

Mathematics
1 answer:
Stella [2.4K]3 years ago
7 0

Answer:

B. See explanation

Step-by-step explanation:

Use the distance formula between two points (x_1,y_1) and (x_2,y_2):

d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

Find the lengths of all sides of quadrilateral DEFG:

DE=\sqrt{(-a-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\EF=\sqrt{(a+-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\FG=\sqrt{(a+b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\GD=\sqrt{(-a-b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\

All sides are of the same length. Now fond the slopes of all sides:

DE=\dfrac{2c-c}{0-(-a-b)}=\dfrac{c}{a+b}\\ \\EF=\dfrac{c-2c}{a+b-0}=-\dfrac{c}{a+b}\\ \\FG=\dfrac{c-0}{a+b-0}=\dfrac{c}{a+b}\\ \\GD=\dfrac{c-c}{-a-b-0}=-\dfrac{c}{a+b}\\ \\

The slopes of the sides DE and FG are the same, so these sides are parallel. The slopes of the sides EF and GD are the same, so these sides are parallel.

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Multiply -1/2 c(4c -2) Please ASAP
nalin [4]

Answer:

-2c^2 + c

Step-by-step explanation:

5 0
3 years ago
carlos and Jacob each improve their yards by planting daylilies and ivy. They bought their supplies from the same stores. Carlos
34kurt

Answer:

Cost of each daylilies = $3

Cost of each ivy pot = $3

Step-by-step explanation:

Given:

Cost of 4 daylilies and 4 ivy = $24

Cost of 4 daylilies and 8 ivy = $36

Find:

Cost of each daylilies

Cost of each ivy pot

Computation:

Assume;

Cost of each daylilies = a

Cost of each ivy pot = b

So,

4a + 4b = 24....... eq 1

4a + 8b = 36 ....... eq 2

Eq2 - Eq1

8b - 4b = 36 - 24

4b = 12

b = 3

So,

Cost of each ivy pot = $3

4a + 4b = 24

4a + 4(3) = 24

4a + 12

a = 3

Cost of each daylilies = $3

6 0
3 years ago
I need help <br> 1.<br> 2.<br> 3.
Reptile [31]

1. North America, Africa, Asia, Europe

2. South America, Antarctica, and Australia

3. North America, South America and Antarctica.

4 0
3 years ago
A large school district in southern California asked all of its eighth-graders to measure the length of their right foot at the
Ber [7]

Answer:

The probability of the sample mean foot length less than 23 cm is 0.120

Step-by-step explanation:

* Lets explain the information in the problem

- The eighth-graders asked to measure the length of their right foot at

  the beginning of the school year, as part of a science project

- The foot length is approximately Normally distributed, with a mean of

 23.4 cm

∴ μ = 23.4 cm

- The standard deviation of 1.7

∴ σ = 1.7 cm

- 25 eighth-graders from this population are randomly selected

∴ n  = 25

- To find the probability of the sample mean foot length less than 23

∴ The sample mean x = 23, find the standard deviation σx

- The rule to find σx is σx = σ/√n

∵ σ = 1.7 and n = 25

∴ σx = 1.7/√25 = 1.7/5 = 0.34

- Now lets find the z-score using the rule z-score = (x - μ)/σx

∵ x = 23 , μ = 23.4 , σx = 0.34

∴ z-score = (23 - 23.4)/0.34 = -1.17647 ≅ -1.18

- Use the table of the normal distribution to find P(x < 23)

- We will search in the raw of -1.1 and look to the column of 0.08

∴ P(X < 23) = 0.119 ≅ 0.120

* The probability of the sample mean foot length less than 23 cm is 0.120

4 0
3 years ago
If EF = 4x-15, FG=3x-7, and EG =20, find the value of x, EF and FG. The drawing is not to scale.
Andrej [43]

Step-by-step explanation:

EF = 4x - 15

FG = 3x - 7

EG = EF + FG = 20

so,

4x - 15 + 3x - 7 = 20

7x - 22 = 20

7x = 42

x = 6

EF = 4×6 - 15 = 9

FG = 3×6 - 7 = 11

4 0
2 years ago
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