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2 years ago

The diagram shows a regular pentagon, ABCDE, a regular octagon, ABFGHIJK, and an isosceles triangle, BCF. Work out the angle x

Mathematics

1 answer:

AVprozaik [17]2 years ago

5 0

Answer:

x is 31.5°

Step-by-step explanation:

Here, we have each interior angle of a regular octagon = 135°

Each interior angle of a regular pentagon = 108°

Therefore, 135° + 108° + ∡B = 360°

Hence, ∡B = 360° - (135° + 108°) = 117°

Since, AB = BC = BF ( sides of a regular polygons (octagon and pentagon))

Hence, ΔCBF is an isosceles triangle and ∡x = ∡CFB from which we have;

∡x + ∡CFB + 117° = 180°

∴ ∡x + ∡CFB = 180° - 117° = 63°

Hence, ∡x = 63° - ∡CFB = 63° - ∡x which gives

2·∡x = 63°

Hence, ∡x = 63°/2 = 31.5°

∡x = 31.5°.

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vector u is represented by the directed line segment RS and vector v is represented by the directed line segment OP. if R=(8,-2)

melamori03 [73]

The given points are

R=(8,-2) , S=(11,-6), O=(-3,-9), and P=(0,-13)

To find the value of u and v, we have to perform subtraction of the points . That is

$u= RS = =$

$v = OP = =$

Since we get the same values of u and v , therefore the two vectors are equal .

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2 years ago

The combined ages of a dog and his owner are 96 years in total. The owner is 3 times older than his dog. How old is the owner?

nikitadnepr [17]

Answer:

72 yrs old.

Step-by-step explanation:

The combined age

D+O=96

The owner is 3 times older than dog

O=3D

D+3D=96

4D = 96

D= 24

Now substitute the value of D in O=3D

O=3.24= 72

The owner is 72 years old.

5 0

2 years ago

The New Mexico Division of Fish and Wildlife keeps track of the silvery minnow population in the Rio Grande River. They tagged 5

sattari [20]

Answer:

279 silvery minnow

Step-by-step explanation:

Number of Silvery Minnows initially tagged = 54

Number of minnows captured = 62

Number of tagged minnows in captured ones = 12

Remember that in the very beginning there were no tagged minnows. 54 minnows were captured, tagged and released. This means, there are total 54 tagged minnows in the entire population. Lets say there are x number of minnows in total.

So, in x minnows, 54 are tagged ones.

When 62 minnows are captured, only 12 are tagged ones and remaining are un-tagged. Since, the minnows were randomly captured, we can develop a proportion from this case to estimate the total population of minnows in the Rio Grande River.

Ratio of tagged minnows to total population must be equal to the ratio of captured tagged minnows in total captured minnows.

i.e.

$54 : x = 12 : 62\\\\ \frac{54}{x} = \frac{12}{62}\\\\ 62(54)=12x\\ \\ x = 279$

This means, there were 279 silvery minnows in the Rio Grande River.

3 0

2 years ago

Jacob spends 60 minutes in the gym every day doing freehand exercises and running on the treadmill. He runs on the treadmill 30

elixir [45]

Answer:

x + y = 60

x = y + 30

substitution:

(y + 30) = y = 60

2y + 30 = 60

2y = 30

y = 15

15 minutes for freehand

No, because if he spends 40 minutes on the treadmill, he would have spent 10 minutes for freehand exercises. His total time in the gym would be 50 minutes, not 60.

8 0

2 years ago

A bicycle wheel has an inside radius of 12 inches. Which expression could be used to find the inside circumference of this wheel

il63 [147K]

Step-by-step explanation:

We have given that,

The inner radius of a bicycle wheel is 12 inches.

It is required to find the expression to find the inside circumference of this wheel.

The outer surface of the wheel is equal to its circumference. It is given by :

$C=2\pi r$

r is radius of wheel

$C=2\times 3.14\times 12\\\\C=75.36\ \text{inches}$

This is the required explanation.

5 0

2 years ago