Question text

Prove that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures

pychu [463]

The attached figure reprsents a prove that a rectangle has congruent diagonals.

Given: rectangle ABCD

Prove: BD ≅ AC

4 0

3 years ago

Complete the page for 15 points.

sergey [27]

Answer:

1. 15, 16, 17

2. 21, 23, 25

3. 44, 46, 48

4. -4, -3, -2

Step-by-step explanation:

1)

Step 1. Writing an equation

Let's set x as the second number in the equation.

This means that the first number is x-1, and the third number is x+1.

We know that the sum of the three numbers is 48, so:

(x-1)+x+(x+1)=48

Step 2. Solving the equation

x-1+x+x+1=48

x+x+x-1+1=48

3x=48

x=16

So the answer is 15, 16, 17

2)

Again, let's set x as the middle number.

Odd numbers are 2 numbers apart, so the first number is x-2, and the third is x+2.

This means that the equation must be:

(x-2)+x+(x+2)=69

x+x+x=69

3x=69

x=23

The numbers are 21, 23, and 25

3)

x will be the middle number

Even numbers are 2 numbers apart, so the first number is x-2, and the third is x+2.

This means that:

x-2+x+x+2=138

x+x+x=138

3x=138

x=46

The numbers are 44, 46, and 48.

4)

x will be the middle number.

x-1=first number, x+1=third number

x-1+x+x+1=-9

3x=-9

x=-3

The numbers are -4, -3, and -2.

3 0

4 years ago

At the start of the year a summer holiday to Spain cost £650. It increased by 11% in

olga nikolaevna [1]

Answer:

Final cost = £779

Step-by-step explanation:

It is given that:

Cost of summer holiday = £650

Amount increased by 11%

Increased cost = 11% of 650

Increased cost = $\frac{11}{100}*650$

Increased cost = 0.11 * 650 = £71.50

Amount after increment = 650 + 71.50 = £721.50

Further increase = 8%

Amount = 0.08 * 721.50 = £57.72

Final cost = 721.50 + 57.72 = £779.22

Thus,

Final cost = £779

5 0

3 years ago

I need all of these awnser a please !

valentinak56 [21]

8.180-65-90=25
180-80-60=40
So, 180-40-25=115.

9.(180-40)divide by 2=70
X=180-70
X=110

10.180-118=62
So, 180-62-90
=28

11.not confident yet

12.180-60=120

13. (180-66)divide by 2 =57
180-57=123
(180-123)divide by 2
=28.5

14.180-68-44=68
180-58-73=49
So,180-68-49=63
(Its the same)

3 0

3 years ago

Kenji is decorating papers with a total of 15 heart stickers and 12 star stickers for the child he is babysitting. If he wants t

Marina CMI [18]

Answer: The greatest number of pages Kenji can decorate = 3

Step-by-step explanation:

Given: Total heart stickers = 15

Total star stickers =12

If all the papers identical, with the same combination of heart and star stickers and no stickers left over.

Then the greatest number of pages Kenji can decorate = GCD(15,12) [GCD=greatest common divisor]

Since 15 = 3 x 5

12=2 x 2 x 3

GCD(15,12) =3

Hence, the greatest number of pages Kenji can decorate = 3

7 0

3 years ago