1. Calculate the area of the
figure below. Round to the
hundredths place when
necessary.

By Euclidean geometry, the measure of the missing angle, the other acute angle, of the right triangle is equal to 47°.

Right triangles are triangles of which one of its angles is a right angle and the other two angles are acute angles. According to the statement, the measure of an acute angle of the right triangle is equal to 43°.

By Euclidean geometry, the sum of the internal angles in any triangle equals a measure of 180°. Then, the measure of the missing angle is:

90° + α + β = 180°

If we know that α = 43°, then the value of β is:

α + β = 90°

43° + β = 90°

β = 47°

The measure of the missing angle is equal to 47°.

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Answer:

The answer to your problem is, A. 5

Step-by-step explanation:

What is an outlier?

What just like it says an outlier it something “ away “ or “ out of civilization of its fellow numbers “

You can see that the hours of 8 - 10 they are all bunched up together

But you can see hour 5 seems a bit lonely

Which then we call he outlier

Thus the answer to your problem is, A. 5

The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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In the proportional relationship, the value of y when x = 7 is 28.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

Therefore, the value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.

Hence,

y ∝ x

y = kx

where

when y = 14 , x = 3.5

14 = 3.5k

k = 14 / 3.5

k = 4

Therefore,  let's find the value of y when x = 7.

y = 4 × 7

y = 28

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The vertexes of the original triangle are the points (-2,4), (-4,-2) and (-5,3). After the transformation the new vertexes will be:

Then, the new triangle is:

The members voted 2 more for mars than earth.

The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.

Given here, Mars has 8 votes while earth has 6 votes

Thus difference in votes is =8-6

                                              = 2

Hence, Mars got two more members than earth

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Answer:

Step-by-step explanation:

from the figure and the values ​​we understand that it is an isosceles right triangle, therefore with the two sides and the 2 angles are congruent,

so x = 25

Answer:

Yes

Step-by-step explanation:

Yes because the distance between each of its terms is equal

Answer: 48.76 square inches.

Step-by-step explanation: A regular pentagonal prism has 7 faces: 2 pentagonal bases and 5 rectangular faces.

To find the surface area, we need to find the area of each face and add them up.

The area of one pentagonal base can be found using the formula:

A = (5/4) * (edge length)^2 * cot(π/5)

Substituting the given values, we get:

A = (5/4) * (2)^2 * cot(π/5)

≈ 6.8819 square inches (rounded to the nearest hundredth)

Since there are two pentagonal bases, their total area is:

2A ≈ 13.7638 square inches

The area of one rectangular face can be found using the formula:

A = (edge length) * (height)

Substituting the given values, we get:

A = 2 * 3.5

= 7 square inches

Since there are five rectangular faces, their total area is:

5A = 5 * 7 = 35 square inches

Therefore, the total surface area of the regular pentagonal prism is approximately:

13.7638 + 35 = 48.7638 square inches

Rounding to the nearest hundredth, we get:

Surface area ≈ 48.76 square inches.

The surface area of a regular pentagonal prism is 193.82 square inches.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The formula for the surface area of a regular pentagonal prism is:

SA = 5 × base area + 5 × lateral face area

where the base area is the area of one of the pentagonal bases, and the lateral face area is the area of one of the rectangular faces.

Since the base is a regular pentagon, we can use the formula for the area of a regular pentagon:

Area of pentagon = (1/4) × n × s² × tan(180°/n)

where n is the number of sides of the pentagon (which is 5 since it's a regular pentagon), and s is the length of one of its sides.

In this case,

s = 2 inches

Area of pentagon = (1/4) × 5 × 2² × tan(180°/5)

Area of the pentagon = 6.8819 square inches

This is the area of one of the pentagonal bases.

Since there are two bases,

The total base area is:

Base area = 2 × 6.8819

                 = 13.7638 square inches

Now,

Each lateral face is a rectangle with a width equal to the base edge length (2 inches) and a height equal to the height of the prism (3.5 inches).

Lateral face area.

= base edge length × height

= 2 inches × 3.5 inches

= 7 square inches

Since there are five lateral faces, the total lateral face area is:

Lateral face area

= 5 × 7

= 35 square inches

Now we can add up the base area and lateral face area to get the total surface area:

SA = 5 × base area + 5 × lateral face area

     = 5(13.7638) + 5(35)

     = 193.819 square inches

Rounding this to the nearest hundredth.

SA = 193.82 square inches

Thus,

The surface area of a regular pentagonal prism is 193.82 square inches.

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Answer:

54+4.4 is greater

Step-by-step explanation:

if u need explanation than please ask

The statement (d) is true.

Given that (an) -1 is a sequence of real numbers and f: [1,00) +R is a function that is integrable on [1,6] for every b > 1. We have to prove or disprove the following statements:a) If a f(x) dx is convergent, then § f(n) is convergent.b) We have: Ž ith53 1+2 n=0c) If È an is convergent, then Î . is convergent.d) If an converges absolutely, then am is convergent.(a) If f(x)dx is convergent, then §f(n) is convergent.Statement a is true.Proof:If f(x)dx is convergent, then limm→∞ ∫1mf(x)dx exists.Using the summation by parts formula, we get:∫1mf(x)dx = (m − 1)∫1mf(x)·1m−1dx + ∫1mf′(x)·1−1mdxRearranging the above equation, we get:f(m) = 1m−1∫1mf(x)dx − 1m−1 ∫1mf′(x)·1−1mdxSince limm→∞ f′(x)·1−1m = 0 for every x ∈ [1, 6], it follows that limm→∞∫1mf′(x)·1−1mdx = 0Therefore, limm→∞f(m) = limm→∞1m−1∫1mf(x)dx exists. Therefore, the statement (a) is true.(b) We have: Ž ith53 1+2 n=0Statement b is false since the series diverges.(c) If Èan is convergent, then Î.an is convergent.Statement c is false.Proof:Since f(x) is integrable on [1, 6] for every b > 1, it follows that f(x) is bounded on [1, 6].Let M be such that f(x) ≤ M for every x ∈ [1, 6].Given that ∑n=1∞ an converges, it follows that limn→∞an = 0Since f(x) is integrable on [1, 6] for every b > 1, it follows that limx→∞f(x) = 0Therefore, we have:limn→∞∣∣∣∣∫n+1n(f(x)−an)dx∣∣∣∣≤Mlimn→∞∣∣∣∣∫n+1n(f(x)−an)dx∣∣∣∣=Mlimn→∞an=0Since the limit of the integral is zero, it follows that limn→∞∫∞1(f(x)−an)dx exists. But this limit is not equal to zero since it is equal to limn→∞f(n) which does not exist. Therefore, the statement (c) is false.(d) If ∑n=1∞ |an| converges, then ∑n=1∞ an converges. Statement d is true. Proof: Since ∑n=1∞ |an| converges, it follows that limn→∞|an| = 0 Therefore, there exists a number M such that |an| ≤ M for every n. By the comparison test, it follows that ∑n=1∞ an converges.

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The simplified expression is 10 + 4000 + 7 + 17 + 121121 + 20 + 100 + 49.

In mathematics, an expression is a combination of numbers, variables, operators, and/or constants which evaluates to a single value. It can also be thought of as a combination of symbols that represent a value. Expressions are used to make calculations and solve equations. Examples of expressions include 3 + 5 = 8, x2 + 5x + 6 = 0, and 5/3. Expressions are fundamental to mathematics as they are used to represent mathematical concepts and operations.

Simplifying an expression means to reduce it to its most basic form. In this case, the expression contains a mix of numbers, which can all be reduced to their lowest form. 10 can be reduced to 10, 4000 can be reduced to 4000, 7 can be reduced to 7, 017 can be reduced to 17, 121121 can be reduced to 121121, 20 can be reduced to 20, 100 can be reduced to 100 and 49 can be reduced to 49.

Therefore, the simplified expression is 10 + 4000 + 7 + 17 + 121121 + 20 + 100 + 49.

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Answer:

nico

Step-by-step explanation:

Answer:

The answer is x<2

-2x^5 + 14x^4 - 36x^3 + 52x^2 - 64x + 48=0

Step-by-step explanation:

The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Answer:

It will be 29.39

Step-by-step explanation:

Hope this Helped

\( \sin ^{ - 1} ( \frac{4}{9}) = 26.39\)

Answer:

$8645.73

Step-by-step explanation:

Using the compound interest formula :

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

A = final amount = 18000

r = rate = 6.5% = 0.065

n = number of compounding tines per period, biannually, once in 2 years = 0.5

18000 = P(1 + 0.065/0.5)^(0.5*12)

18000 = P(1 + 0.13)^6

18000 = P(2.081951752609)

18000 / 2.081951752609 = P

= 8645.7334

= $8645.73

The graph of the function f(x) = x³ – 2x² – 19x + 20 passes through the  x-axis at  –4, 1, and 5.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The function is given as

f(x) = x³ – 2x² – 19x + 20

By hit and trial. Let x = 1, we have

f(x) = 1³ – 2(1)² – 19(1) + 20 = 0

Then the equation will be

f(x) = (x – 1)(x² – x – 20)

f(x) = (x – 1)(x – 5)(x + 4)

Then the graph of the function passes through x-axis at  –4, 1, and 5.

The graph is shown below.

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Answer:

C

Step-by-step explanation:

Set it up like a formula

feet = inches/feet = cm/inches

Answer:

the school block me

Step-by-step explanation:

from seinge this image

The correct translation for each function is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

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Answer:

See Below.

Step-by-step explanation:

We are given that:

\(\displaystyle \cos(A - B) = \cos A\cos B + \sin A \sin B\)

Part 5.2.1

Note that:

\(\displaystyle \cos ( A + B) = \cos (A - (-B))\)

Then from the given identity:

\(\displaystyle \cos(A - (-B)) = \cos A \cos( -B) + \sin A \sin (-B)\)

Cosine is an even function and sine is an odd function. That is:

\(\displaystyle \cos(- \theta) = \cos \theta \text{ and } \sin (-\theta) = -\sin\theta\)

Hence:

\(\displaystyle \cos(A + B) = \cos A \cos B - \sin A \sin B\)

Part 5.2.2

We want to verify that:

\(\displaystyle \cos^2 (A - B) = 4\cos^2 B \sin^2 B\)

From the identity:

\(\displaystyle \cos (A - B) = \cos A \cos B + \sin A \sin B\)

Since A + B = 90°, A = 90° - B. Hence:

\(\displaystyle \cos (A - B) = \cos (90^\circ - B) \cos B + \sin (90^\circ - B) \sin B\)

Sine and cosine are co-functions. That is:

\(\displaystyle \sin \theta = \cos (90^\circ - \theta) \text{ and } \cos\theta = \sin(90^\circ - \theta)\)

Hence:

\(\displaystyle \cos (A - B) = \sin B\cos B + \sin B \cos B = 2\sin B \cos B\)

And by squaring both sides:

\(\displaystyle \cos ^2 (A - B) = 4\sin^2 B\cos^2 B\)

To determine the side lengths of the real object using a scale factor of 3:1, we need the corresponding side lengths from the scale drawing.

To find the side lengths of the real object, we can multiply the corresponding side lengths of the scale drawing by the scale factor.

For example, if the scale drawing has a side length of 4 units, the corresponding side length of the real object would be 4 * 3 = 12 units.

Similarly, for any other side length in the scale drawing, we can multiply it by 3 to find the corresponding side length in the real object.

It's important to note that the scale factor must be applied consistently to all sides of the object. If one side length is multiplied by the scale factor, all other side lengths should also be multiplied by the same factor to maintain proportionality between the scale drawing and the real object.

By applying the scale factor of 3:1, we can determine the side lengths of the real object based on the given side lengths of the scale drawing.

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The approximate value of x in the equation 5 to the power of 2x=20 is 0.93

From the question, we have the following parameters that can be used in our computation:

5 to the power of 2x=20

As an expression, we have

5^(2x) = 20

Take the natural logarithm of both sides

so, we have the following representation

2x = ln(20)/ln(5)

Evaluate the quotients

This gives

2x = 1.86

So, we have

x = 0.93

Hence, the value of x is 0.93

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Parallel lines have the same slope.

The slope of y = 9x + 9 is 9, because of the 9 in 9x.

The slope of a parallel line would also be 9.

Answer:c

Step-by-step explanation:

Answer:

The Answer is m(d) = 3.2(0.999)^d

Step-by-step explanation:

There are five possibilities for whole numbers such that radical expression 4 ≤ √3 + √x ≤ 5: {6, 7, 8, 9, 10}

In this problem we have the case of a radical expression, from which we need to determine at least a whole number such that following inequality is fulfilled:

4 ≤ √3 + √x ≤ 5

This can be done by algebra properties. First, determine the limits of the inequality:

4 ≤ √3 + √x

4 - √3 ≤ √x

(4 - √3)² ≤ x

x ≥ (4 - √3)²

x ≥ 16 - 8√3 + 3

x ≥ 19 - 8√3

√3 + √x ≤ 5

√x ≤ 5 - √3

x ≤ (5 - √3)²

x ≤ 25 - 10√3 + 3

x ≤ 28 - 10√3

There are five possibilities for five whole numbers: 6, 7, 8, 9, 10

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The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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The time the mechanic is away from the shop is 2 hours.

To find the time the mechanic is away from the shop, we need to know either the distance of the round trip or the speed of the mechanic on one of the legs of the trip.

For example, if we know that the distance of the round trip is 30 miles, we can use the formula:

time = distance / speed

where speed is the average speed for the round trip, which is given as 15 miles per hour.

So, the time the mechanic is away from the shop would be:

time = 30 miles / 15 miles per hour = 2 hours

But without knowing the distance of the round trip or the speed of the mechanic on one of the legs of the trip, we cannot calculate the time the mechanic is away from the shop.

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