All categories

3 years ago

Given: E is the midpoint of DF Prove: 2DE = DF

2 answers:

6 0

E is the midpoint so it's HALF of DF

Since it's half that means DE and EF have the same length.

Therefore DE multiplied by 2 is DF.

Considering DF is the full length.

Svetlanka [38]3 years ago

3 0

Answer:

2DE = DF.

Hence Proved.

Step-by-step explanation:

Given : E is the midpoint of DF.

To Prove : 2DE = DF

Proof :

We have given a line DF .

D____________F.

Mid point = E

Mid point : It is that point that divide the line in to two equal parts .

D______E______F.

So, DE = EF.

We can say DE= $\frac{1}{2}DF$ .

On multiplying both sides by 2.

2DE = DF.

Hence Proved.

Therefore, 2DE = DF.

Hence Proved.

You might be interested in

What is the perimeter of triangle DEF?

Vikki [24]

Given:

Triangle DEF

To find:

The perimeter of triangle DEF.

Solution:

Coordinate of D = (-1, 1)

Coordinate of E = (2, 1)

Coordinate of F = (-1, 4)

Distance formula:

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

Distance of DE:

Here, $x_1=-1, y_1=1, x_2=2, y_2=1$

$d=\sqrt{(1-1)^2+(2-(-1))^2}$

$d=\sqrt{0+9}$

d = 3 units

Distance of EF:

Here, $x_1=2, y_1=1, x_2=-1, y_2=4$

$d=\sqrt{(4-1)^2+(-1-2)^2}$

$d=\sqrt{9+9}$

$d=\sqrt{18}$

d = 4.2 units

Distance of FD:

Here, $x_1=-1, y_1=4, x_2=-1, y_2=1$

$d=\sqrt{(1-4)^2+(-1-(-1))^2}$

$d=\sqrt{9+0}$

d = 3 units

Perimeter of ΔDEF = DE + FE + FD

= 3 + 4.2 + 3

= 10.2 units

The perimeter of triangle DEF is 10.2 units.

5 0

3 years ago

Mr.Johnson purchased 20 concert tickets for a total of $225. The concert tickets cost $15 for adults and $10 for children under

taurus [48]

Answer:

Step-by-step explanation:

Let the number of adult tickets be x while children ticket be y. Since the total tickets were 20 then we can form the equation

x+y=20

Making x the subject then x=20-y

Considering the cost of each ticket

15x+10y=225

Substituting x with 20-y then

15(20-y)+10y=225

300-15y+10y=225

Collecting like terms

300-225=15y-10y

75=5y

Y=75/5=15

To find x, we already know that x=20-y hence x=20-15=5

Therefore, children tickets are 15 while adult tickets are 5.

The question only needs us to know the children tickets, y which is 15

3 0

3 years ago

Read 2 more answers

A What is the median number for the numbers 4, 8, 10, 5, 9?*

natka813 [3]

First we need to sort from the smallest number to the largest number.

4, 5, 8, 9, 10

Median is the middle number.

Your answer is 8.

4 0

3 years ago

Values for the area A of the rectangle shown are 12 ≤ A ≤ 36.

Step2247 [10]

A compound inequality is used to combined multiple inequalities.

The compound inequality is: $12 \le 6x \le 36$ .
The solution to the compound inequality is: $2 \le x \le 6$

We have:

$12 \le A \le 36$

$Length = 2x$

$Width = 3$

The area of the rectangle is:

$A = Length \times Width$

So, we have:

$A =2x \times 3$

$A = 6x$

Substitute 6x for A in $12 \le A \le 36$

$12 \le 6x \le 36$

Divide through by 6

$2 \le x \le 6$

Hence,

The compound inequality is: $12 \le 6x \le 36$ .
The solution to the compound inequality is: $2 \le x \le 6$

Read more about compound inequalities at:

brainly.com/question/17957246

4 0

2 years ago

Someone please, HELP!!!!

Brrunno [24]

Range: maximum - minimum
IQR: third quartile - first quartile
median: middle number once all numbers are put in numerical order

8 0

3 years ago