Solve the equation. Find all real solutions. 9r3

The diameter of circles A,C and E are 32 cm, 24cm and 14 cm respectively

Karolina [17]

Answer:

AG = 4

AH = 21

EC = 12

CH = 5

HE = 7

Step-by-step explanation:

The complete question is

The diameters of circles A, C and E are 32 cm, 24 cm and 14 cm respectively.

Which of the following statements are true? Select all that apply.

•AG = 4

•GC = 10

•AH = 21

•EC = 12

•EH = 5

•CH = 5

•HE = 7

The picture of the question in the attached figure

Verify each statement

1) AG = 4

we know that

$AG=AC-GC$

$AC=32\2=16\ cm$ ----> radius of circle A

$GC=24/2=12\ cm$ ----> radius of circle C

substitute

$AG=16-12=4\ cm$

therefore

The statement is true

2) GC = 10

we know that

$GC=24/2=12\ cm$ ----> radius of circle C

therefore

The statement is false

3) AH = 21

we know that

$AH=AC+CH$

we have

$AC=16\ cm$ ----> radius of circle A

$CH=CE-HE$

$CE=12\ cm$ ----> radius of circle C

$HE=14/2=7\ cm$ ----> radius of circle E

so

$CH=12-7=5\ cm$

$AH=16+5=21\ cm$

therefore

The statement is true

4) EC = 12

we know that

$EC=24/2=12\ cm$ ----> radius of circle C

therefore

The statement is true

5) EH = 5

we know that

$EH=14/2=7\ cm$ ----> radius of circle E

therefore

The statement is false

6) CH = 5

we know that

$CH=CE-HE$

$CE=12\ cm$ ----> radius of circle C

$HE=14/2=7\ cm$ ----> radius of circle E

so

$CH=12-7=5\ cm$

therefore

The statement is true

7) HE = 7

we know that

$HE=14/2=7\ cm$ ----> radius of circle E

therefore

The statement is true

3 0

3 years ago

John worked "x" hours this week and Shanique worked eight hours less than John. Write an algebraic expression for the number of

sergij07 [2.7K]

Answer:

X>8

Step-by-step explanation:

X>8

6 0

3 years ago

How to find the central angle of a regular polygon

Annette [7]

Answer:

I hope this helps

Step-by-step explanation:

Central angle of a regular polygon:

The central angle of a polygon is the angle made at the center of a polygon by any two adjacent vertices as shown in the figure below.

In the above figure, the angles a, b, c, d, e and f are the central angles of the hexagon. There are 6 central angles in a hexagon. The number of central angles in a polygon is always equal to the number of sides of the polygon.

As you can see in the figure above, all the central angles of the polygon together will always form a complete circle. Hence the central angles add up to 360° in all polygons. Since a regular polygon has all equal sides, the central angles in a regular polygon are also equal.

So to find the measure of the central angles of a regular polygon follow the steps below:

First identify the number of sides ‘n’.

Then divide 360° by n.

For example: say you need to find the central angle of a regular pentagon.

First identify the number of sides ‘n’: here n = 5

Then divide 360° by n: 360° ÷ 5 = 72°.

Conversely, you can also find the number of sides of a regular polygon, when the central angle is given, by dividing 360 by the central angle.

Note: In the case of an irregular polygon, since there is no clear center for an irregular polygon, it has no central angle.

3 0

3 years ago

The greater of two consecutive integers is seven less than one-third the smaller integer. Find the integers

ikadub [295]

Answer:

Step-by-step explanation:consecutive integers are represented by x, x+1 , so for this problem the greater one is represented by x + 1.

Now you need to translate the problem. the greater is seven less than 1/3 the smaller

---> x + 1 = (1/3)*x - 7 ---> now solve for x (the smaller) and x+1 (the greater)

***hint: to get rid of fractions in an equation you can always multiply EVERYTHING by the denominator , 3 in this case

8 0

2 years ago

Question 9 (10 points)

Slav-nsk [51]

The length is 5cm long

5 0

3 years ago

Solve the equation. Find all real solutions. 9r3 - 144r = 0