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“Complete the proof (geometry)”

The length of the arc is 15.70 km

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

The formula is given by

s = ϴ × r,

where

s is the arc length

r is the radius of the circle

θ is the central angle of the arc in radians

Given :- Radius = 10km

             Angle = 90 ° = [tex]\pi[/tex]/2 radians          (1 radian = 180°/[tex]\pi[/tex])

By using formula we get

Length of arc = 10 x[tex]\pi[/tex]/2 = 5[tex]\pi[/tex] km           ([tex]\pi[/tex] = 3.14)

                     = 15.70 km

Thus the length of the arc is 15.70 km

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The value of OB based on the information given about the triangle is 3 units.

It should be noted that dilation is the process of enlarging or shrinking of an object.

In this case, the triangle is dilated. Therefore, the length of OB will be:

= 3/4 × 4 = 3 units.

Therefore, the correct option is B.

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Answer:

D

please mark brainiest

Simplifying equation is done by either reducing the complexity or the components parts of an equation for better understanding.

This means to make simpler, either by reducing in complexity, reducing to component parts, or making easier to understand.

Simplification is an act of simplifying an equation or expression.

For instance,

Simplify 4(3x + 2) - 4(2x)

= 12x + 8 - 8x

= 12x - 8x + 8

= 4x + 8

Simplify 1/2 + 2/3

= (3+4) / 6

= 7/6

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The total amount of Chandra's investments after 8 years is $110.03

The formula for calculating the compound interest is expressed as;

A = P(1+r/n)^nt

where

P is the amount invested = $75

r is the rate. = 0.048

t is the time =8years

n = 12 (monthly)

Substitute

A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03

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Answer:

20 because Brendan is 30

The surface area of the cone is: A. 184π units².

Surface area of a cone = πr(l + r), where r is the radius and l is the slant height.

Given the following:

Surface area of a cone = π8(15 + 8)

Surface area of a cone = 184π units²

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Answer: A

Step-by-step explanation:

Let c(y)=x.

[tex]\implies x=y^3 -5\\\\x+5=y^3\\\\y=\sqrt[3]{x+5}\\\\c^{-1}(x)=\sqrt[3]{x+5}[/tex]

The computation shows that the average monthly amount is 61.64.

The amount that's left will be:

= 3314.85 + (2 × 926.65) - (1800 × 2) - 1075

= 3314.85 + 1853.3 - 3600 - 1075

= 493.15

The average monthly amount will be:

= 493.15/8

= $61.64

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Answer: (5,5)

Step-by-step explanation:

The perpendicular to y=x has slope -1, and thus the equation of the perpendicular from (1,9) is [tex]y=-x+10[/tex].

Finding the point where they intersect, since both equations are set equal to y, we know that -x+10=x, and thus x=5.

If x=5, then y=5 as well.

So, F has coordinates (5,5).

Answer:

Second choice

Step-by-step explanation:

Analyse each sentences: The sum of x and y is 5 can be mathematically expressed as [tex]\displaystyle{x+y = 5}[/tex] since both are sum together and equal to 5.

Next, the value of y is one more than value of x can be mathematically expressed as [tex]\displaystyle{y=x+1}[/tex] because value of y is one more than value of x so y will be the value of x add with 1.

Therefore, form the simultaneous equation:

[tex]\displaystyle{\left \{ {{x+y=5} \atop {y=x+1}} \right}[/tex]

Hence, the answer is second choice.

Answer:

a = -22/13.

Step-by-step explanation:

By the Remainder Theorem

p(3) = remainder    when p(x) is divided by x-3.

q(3)  is equal to the same remainder.

So we have:

p(3) = q(3) , so

a(3)^3 + 4(3)^2 + 3(3) - 4 = 3^2 - 4(3) + a

27a + 36 + 9 - 4 = 9 - 12 + a

27a - a = 9 - 12 - 36 - 9 + 4

26a = -12 - 36 + 4

26a = -44

a = -44/26

a = -22/13.

Answer:

60

Step-by-step explanation:

The yellow and green angles form a right angle, so the measures of those combined will be 90 degrees.

90 - 30 = 60

The explicit function that defines the sequence is 15/2 - 9n/2

The sequence is given as:

3, -3/2, -6, -21/2

The above sequence is an arithmetic sequence, with the following parameters

The explicit formula is then calculated as:

T(n) = a + (n -1) * d

This gives

T(n) = 3 +(n -1) * -9/2

Expand

T(n) = 3 + 9/2 - 9n/2

Evaluate

T(n) = 15/2 - 9n/2

Hence, the explicit function that defines the sequence is 15/2 - 9n/2

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The word problem can be:

"let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?"

And the solution is N = 12.

We want a problem that can be described by 3 divided by 1/4.

So, let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?

The solution to that question is given by:

[tex]N = \frac{3}{1/4}[/tex]

2) To solve this, we can use a really simple model.

In one unit, we have 4 fourts.

Then in 3 units, we have 3*4 = 12 fourts.

Then the answer is 12.

3) How to use multiplication?

Remember that dividing by a fraction is equivalent to multiplying by the inverse of said fraction, then:

[tex]N = \frac{3}{1/4} = 3*(4/1) = 12[/tex]

We got the same thing as above.

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Answer:

170.097 grams are in 6 ounces

Answer:

170.097 g to nearest thousandth

Step-by-step explanation:

1 ounce = 28.34952 g

6 = 170.09712 g

The height & speed are mathematically given as

t = 0.2 s

u = 4 m/s

Generally, the equation for height is  mathematically given as

h = 0.2gt^2

Therefore

0.2 = 0.5 * 9.8 *[tex]t^2[/tex]

0.2 = 4.9 *[tex]t^2[/tex]

t = 0.2 s

b)

In conclusion, the initial speed is

s = ut

Therefore

u = 0.8 / 0.2

u = 4 m/s

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 6x+-2y^{2}+4xy^{2}+3x^{2} +5xy^{2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Group\:like\:terms \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =3x^2+6x-2y^2+4xy^2+5xy^2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Sum\:similar\:elements:\:4xy^2+5xy^2=9xy^2 \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 3x^2+6x-2y^2+9xy^2 \end{gathered}$} }[/tex]

The stores that will be in the sample are - 00, 02, 05, 08, 11, 14, 17, 20, 23.

What comprises the sample?

An analytical subset of a larger population is referred to as a sample in statistics. A sample are used in research so that it can be done quickly and with more manageable data. However, obtaining such a sample may be costly and time-consuming. Randomly generated samples do not have significant bias if they are large enough.

Stores in the Sample

Since it is given that the sample is made up of every third store, starting from the first retail store. The stores have been numbered systematically from 00 to 23.  Since a systematic sampling is done, after picking the first store, the third store will be picked, that is, 02, and then 05, and so on till 23.

Thus, the following retail stores will be present in the sample,

00, 02, 05, 08, 11, 14, 17, 20, 23

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Answer:

18

Step-by-step explanation:

3*3*3 = 27, assuming all 3 digits can occupy each space

However, 0 cannot start a number, so it becomes:

3*3*2, which is 18.

Payment Every Month =  $2,514.58

Total of 1 Payments =  $2,514.58

Total Interest               =  $14.58

What is simple intertest ?

Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accumulated.

Solution:

Principal value = $2500

Interest rate = 7%

Time = One month

Formula for simple interest calculation:

                                                                [tex]=\frac{Principalamount*rate *time}{100} \\=\frac{2500*7*(\frac{1}{12}) }{100}\\ =14.588[/tex]

Total Simple interest on $2500 for month $14.588.

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The point estimate here is 0.

Calculating the Mean of Each Set

The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}

The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}

The mean of set S1 = (20+25+27+23+22+20+17)/7

= 154/7

= 22

The mean of set S2 = (22+23+37+20+25+19+18)/7

= 154/7

=22

Calculating the Point Estimate

The formula for point estimate is given as,

Point Estimate  = The mean of set S1 - The mean of set S2

Point Estimate = 22-22

Point Estimate = 0

Therefore, the point estimate for the difference between the means of the two populations or sets is 0

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the statement which defines a translation is option A that is  "A translation proportionally stretches or compresses an object based on a given scale factor".

What is Translation ?

"Translation" moves points the same distance along lines that are parallel to each other.

Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.

Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points.

There, the statement which defines a translation is option A that is  "A translation proportionally stretches or compresses an object based on a given scale factor".

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Answer:

The correct answer is:  A translation moves points a specified distance along a line parallel to a specified line

Step-by-step explanation: I got it right on plato.

The approximate length of side AB is 14.0. The correct option is B. 14.0 units

From the question, we are to determine the measure of side AB

First, we will determine the measure of angle A

A + B + C = 180° (Sum of angles in a triangle)

A + 65° + 35° = 180°

A = 180° - 65° - 35°

A = 80°

Now, using the law of sines

c/sinC = a/sinA

c = AB

a = BC =  24

Thus,

c/sin35° = 24/sin80°

c = (24×sin35°)/sin80°

c = 13.978

c ≈ 14.0

∴ AB = 14.0

Hence, the approximate length of side AB is 14.0. The correct option is B. 14.0 units

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The algebraic expression for the given statement is: 2x² - 3 = y.

To wrote an algebraic expression is translate a statement using numbers, variables, and mathematical sign into a mathematical statement.

Square of x is: x²

Product of x² and 2 is: 2x²

Thus, we would have:

2x² - 3 = y

The algebraic expression is: 2x² - 3 = y.

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The equation of the new function is f'(x) = -|x|

The function is given as:

f(x) = |x|

The rule of flipping the graph over the x-axis

(x, y) = (x, -y)

So, we have:

f'(x) = -f(x)

Substitute f(x) = |x|

f'(x) = -|x|

Hence, the equation of the new function is f'(x) = -|x|

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Answer:

109.36 yards  to nearest hundredth

Step-by-step explanation:

1 meter =  1.09361 yards

So 100 m = 109.361 yards

The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of sine and cosine will be always less than a unit.

In a unit circle, the radius of the circle represents the hypotenuse of the triangle. Since the hypotenuse is the largest side of the triangle, the ratio of the perpendicular to the hypotenuse and the base to the hypotenuse both will be less than the hypotenuse, therefore, 1. Hence, the value of sine and cosine will be always less than a unit.

In construction, we use trigonometry. For figuring areas of triangular shapes, similar to many concepts and phenomena in mathematics.

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Answer:

2^-6

Step-by-step explanation:

(1/8)^2 = (2^-3)^2 = 2^-6

Answer:

6b

You can just simply combine the variable, 6, and the coefficient, b.