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2 years ago

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The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Select two options. The length of

segment YZ is 15.3 cm. The measure of the angle formed by the radius and the apothem is 30°. The length of segment XY can be found by solving for a in 202 – 7.652 = a2. The length of segment WZ is 20 cm. The measure of the central angle, ∠ZXW, is 45°.

2 answers:

KATRIN_1 [288]2 years ago

6 0

The correct answers on edge are C and E

disa [49]2 years ago

6 0

Answer:

C.The length of segment XY can be found by solving for a in 202 – 7.652 = a2.

E. The measure of the central angle, ∠ZXW, is 45°.

Step-by-step explanation:

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A bee flies at 9 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 13 minutes, and then

Usimov [2.4K]

Answer: 576 feet

Step-by-step explanation:

You have to do a little subtracting and a little interpreting to get the answer. First you must assume that the bee travels in a straight line. This is math so we can assume this is true, although thousands would disagree.

Second you must assume that because it is loaded with nectar that it travels at a slower rate (not an unreasonable assumption).

Third you have to assume that the distance there is the same distance as coming back. Again this is math. We can make this assumption.

Find the travelling time.

The bee spends 12 minutes hunting down the nectar in the flowerbed. Since it was away from the hive for a total of 16 minutes, the travelling time is

16min - 12min = 4 min

Convert the Minutes to seconds.

1 minute = 60 seconds

4 minutes = 4*60 = 240 seconds.

Find the time each way.

The total time is 240 seconds, but it is not divided evenly.

Let the time there = t

Let the time back = 240 - t

The distances are the same.

r = 6 m/s

r1 = 4 m/s

t1 = t

t2 = 240 - t

dthere = dback

d = rate * time

6 m/s *t = 4 m/s (240 - t) Remove the brackets on the right.

6 * t = 4*240 - 4t Combine the like terms on the right.

6t = 960 - 4t Add 4t to both sides

6t + 4t = 960 - 4t + 4t Combine

10t = 960 Divide both sides by 10

10t/10 = 960/10 Do the division

t = 96 Time going to the flower bed

Find the distance

d = ?

r = 6 m/s

t = 96 second

d = r*t

d = 6 * 96 = 576 feet Answer

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1 year ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

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Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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1 year ago

James and Dan are partners in a small company. From each year’s profit, James is paid a bonus of $15000 and the remainder is sha

jarptica [38.1K]

Answer:

total20000

bonus15000

remaining 20000-15000=5000

ratio 2+3=5x

Dan part =3x

Dan value=( 5000/5)*3=3000

Step-by-step explanation:

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1 year ago

To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. The

kupik [55]

Answer:

The height of the building is 153.664 meter.

Step-by-step explanation:

Consider the provided function.

$s(t) = 4.9t^2 + v_0 t + s_0$

Here t represents the time v₀ represents the initial velocity, s₀ represents the initial height and s(t) represents the height after t seconds.

It is given that the splash is seen 5.6 seconds after the stone is dropped.

That means after 5.6 seconds height s(t) = 0, Also the initial velocity of the stone is 0.

Substitute respective values in the above function.

$0 = 4.9(5.6)^2 +5.6(0)+ s_0$

$0 = 4.9(31.36)+ s_0$

$s_0=-153.664$

As height can't be a negative number so the value of s₀ is 153.664.

Hence, the height of the building is 153.664 meter.

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2 years ago

Max wrote the number 0.785. After multiplying his number by a power of 10, he arrived at the number 7,850.0. What power of 10 di

kondaur [170]

Answer:

10 to the 4th power

Step-by-step explanation:

the decimil point was moved four spaces to the right resutiong to the 4th power.

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1 year ago