Use the Exterior Angle Theorem to find the measure of each angle.

Note that the expression that is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is:  42x²∛3x (Option B). Even if x = 0, then none of the answers would apply because the expression would automatically = 0.

To prove the above lets us factor and rewrite the radicand in exponential form as follows:

8x² ∛(5³ * 3x) + 2∛(3x⁶ * x)

Rework the expression using

ⁿ√ab = ⁿ√a * ⁿ√b:8x² * ∛5³ * ∛3x + 2∛x⁶ * ∛3x

Simplify the expression 8x² * 5∛3x + 2x² ∛3x

Multiply the monomials to get:
40x² ∛3x+2x²∛3x; Taking the coefficients for the like terms we have:

(40 + 2)x² ∛3x

Calculate the sum to get 42x²∛3x

Thus the simplified version of  8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x

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Full Question:

Select the correct answer. Which expression is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0

A) 42x³

B) 42x²∛3x

C) 10x⁴∛125x

D) 10x²∛125x³

When there are two factors—a fixed element and a variable factor—the law of variable proportions is created. According to the law of variable proportions, the marginal product of a factor will gradually decrease when its quantity is raised while the other elements remain constant.

We are aware that the relationship between the number of units of a variable factor and the entire physical product is shown by the law of variable proportions.

Additionally, the TPP increases initially at a rising pace, then at a falling rate, and finally declines if we maintain other parameters constant and increase the units of the variable factor.

According to the law of variable proportions, if a producer raises the units of a variable factor while keeping other elements constant, the total product will initially increase at an increasing pace, then it will increase at a diminishing rate, and finally it will begin to decline.

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All the equations in which z = 5 are a solution are given as follows:

A. 8 = z + 3.

D. 12z = 60.

E. 12 + z = 17.

The first equation is defined as

8 = z + 3.

Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:

z = 8 - 3

z = 5.

The second equation is given as follows:

z - 1 = 6.

Applying the addition operation, which is the inverse of the subtraction, the solution is given as follows:

z = 7.

The third equation is given as follows:

20 = 40z

Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:

z = 20/40

z = 0.5.

The fourth equation is given as follows:

12z = 60.

Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:

z = 60/12

z = 5.

The fifth equation is defined as

12 + z = 17.

Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:

z = 17 - 12

z = 5.

The equations are given by the image presented at the end of the answer.

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the volume of the rectangular prism is 1/2 x³.

What is rectangular prism?

The normal's length from the prism's base to its top base serves as a gauge for the structure's height. At their base, certain prisms have an angle. Prism's top end is referred to as the "base" since the word "base" can refer to either end of a prism. The area (A) of the base of a prism's base times its height (H) equals the prism's volume (V). Since A is the base area and H is the prism's height, the volume of the prism is therefore A H cubic units.

The base area is A = x*x =x²

The height is 1/2 x

The volume of the rectangular prism is A*H = 1/2 x³.

Hence the volume of the rectangular prism is 1/2 x³.

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The main difference between the 2D and 3D coordinate systems is that the 3D coordinate system adds a third axis (Z) to the two axes of the 2D coordinate system.

A coordinate system is a two-dimensional or three-dimensional system which is used to identify the location of a point or object in the space. It is represented by a set of axes, which are perpendicular and equally spaced from each other to form a grid-like structure. The coordinates of a point or object are determined by the intersection of the two or three axes. Common coordinate systems used in mathematics and science include the Cartesian, polar, and spherical coordinate systems.

A 2D coordinate system is a system in which two axes (X and Y) are used to define a point in a two-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the two axes. The two axes form a coordinate plane, which provides a visual representation of the system.

A 3D coordinate system is a system in which three axes (X, Y, and Z) are used to define a point in a three-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the three axes. The three axes form a coordinate space, which provides a visual representation of the system.

This third axis allows points in the 3D coordinate system to be represented in the third dimension. Additionally, the 3D coordinate system provides a more detailed representation of points, as it can represent points in all three dimensions.

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Answer:

c. $350.00

Step-by-step explanation

im sorry if this didn't help i wrote everything down on paper

Answer: $1.4

Step-by-step explanation:

let the price before the increase be x

1.2*x = 1.68

x=1.68/1.2 = 1.4

Price before increase = $1.4

After using the triangle inequality theorem, the possible values of the unknown side of the triangle is 15 < n < 25.

In this case, we are given that:

The lengths of the sides of a triangle are 20, 5, and n centimeters.

The theorem of triangle inequality stated that the lengths of any two of a triangle's sides added together must be bigger than the length of the third side. Given two sides, x and y, we can use the triangle inequality theorem to predict that the length of the third side will be between x + y and x - y.

Therefore,

x - y < n < x + y

20 - 5 < n < 20 + 5

15 < n < 25

As the result, the possible value of the unknow side of the triangle would be 15 < n < 25.

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Answer:

[tex]\Huge \boxed{\boxed{\textbf{False}}}[/tex]

Step-by-step explanation:

A quadrilateral must have four right angles in order to be a rectangle, not simply one. A quadrilateral with a single right angle, however, can take on a wide range of shapes, like a right angled triangle or an irregular quadrilateral. A shape having multiple sides and one right angle, for example, could be an irregular quadrilateral.

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________________________________________________________

Answer:

x = 149 degree

Step-by-step explanation:

First, we have to find the missing angle of the triangle

1 triangle = 180 degree

We know 2 angles, one is 63 degrees and one is 86 degrees.

63 + 86 = 149 degree

180 - 149 = 31 degree

So, the angle of the triangle is 31 degrees. Now we know that angle add with the x to get 180 degrees, so

180 - 31 = 149 degree

So, x = 149 degree

The amount of shovels that can be produced in h hours is 960 shovels

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

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

In the given equation,

The number of shovels produced are

C(x)=26*20+400

=520+400

=920 shovels

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The area of the triangle having sides 3 cm 4 cm and 5 cm is calculated to be 6 cm².

Given that,

The sides of the triangle are said to be 3 cm, 4 cm and 5 cm.

By looking at the lengths of the sides of the triangle, it is clear that they are the sides of a right angled triangle. The Pythagorean theorem can be used to verify this.

5² = 3² + 4²

25 = 25

So, 5 is said to be the hypotenuse side of the right triangle and 3, 4 are said to be the base and height of the right triangle.

The formula to find out the area of the triangle is given by,

Area A = 1/2 × Base b × Height h

A = 1/2 × b × h

From the above conclusion, b and h are found to be 3, 4.

So, A = 1/2 × b × h = 1/2 × 3 × 4 = 6 cm²

Thus, the area of the required triangle is calculated to be 6 cm².

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Answer:

B. 2x² + 11

Step-by-step explanation:

(f - g)(x) means:

f(x) - g(x)

We've been given what each of these is equal to, so substitute that in:

3x² + 2 - (x² - 9)

Simplify. Don't forget to distribute that minus in the middle to both terms in x² - 9

3x² + 2 - x² + 9

Next, combine like terms.

2x² + 11

Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2. Either conditional solutions or identities are categories for equations.

Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional solutions or identities are categories for equations. An identity holds true for whatever value of the variables.

given

5x + y = 3

5x + y = 2

x = y-3/ 5

y - 3 +y = 2

2y = 5

y = 5/2

x = 3

Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2.

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Answer:

x=8

Step-by-step explanation:

11x+2=90

11x=88

x=8

Answer:

19. X=8

20. x=7

The possible algebraic equations, obtained based on the algebraic expressions in the question are;

1. [tex]\frac{x}{8} = y[/tex]

2. 15 - n = m

3. 25 + x = y

An algebraic expression is a collection of numbers and variables that are combined together, but without indicating the value indicated by the collection.

What is an algebraic equation?

An algebraic equation is a mathematical statement that expresses the equivalence of two expressions.

The algebraic expressions can be presented as follows;

1. Some number divided by 8

Let x represent the number divided by 8, and let y represent the result when x is divided by 8. The variables x and y can be defined based on the details in the question

The equation with x as the number and y as the result can be presented as follows;

2. n less than 15

The expression n less than 15 is; 15 - n

Let m represent the value of the expression; 15 - n, an algebraic equation based on the details is therefore;

3. 25 more than a number

Let x represent the number, we get

25 more than a number = 25 + x

The y represent the result or value of the expression 25 + x, we get the following algebraic equation;

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Answer:

$1223.75

Step-by-step explanation:

40 times $22.25 = $890

$22.25 times 1.5 to get overtime pay = $33.375

$33.375 times 10 hours overtime = $333.75

$890 + $333.75 = $1223.75

Using formula of midpoint of a line, the endpoint have coordinates of (-29, 10)

The midpoint of a line is a point that divides the line into two equal parts. The coordinates of the midpoint can be found by taking the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.

The formula of midpoint of a line is given as

M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2

-21, 8 = (x₂ + x₁) / 2, (y₂ + y₁) / 2

For x - coordinate;

-21 =  (x₂ + x₁) / 2

-21 = -13 + x₁ / 2

-21 * 2 = -13 + x₁

-42 = -13 + x₁

x₁ = -42 + 13

x₁ = -29

For y - coordinate

8 = (y₂ + y₁) / 2

8 = (6 + y₁) / 2

16 = 6 + y₁

y₁ = 16 - 6

y₁ = 10

The endpoint is (-29, 10)

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A unbiased estimator is a statistic that accurately reflects the population mean, μ. A statistic is unbiased when the mean of its sampling distribution is equal to μ.

Mathematically, this can be expressed as:

E(x) = μ

Where E(x) is the expected value of x and μ is the population mean.

This means that if we take a sample from a population and calculate the mean from that sample, the expected value of that mean should be equal to the population mean. This can be seen in the following example:

Let's say we have a population with a mean of 30. We take a sample of size 5 from this population and calculate the sample mean, x. The expected value of x should be equal to 30. We can calculate this using the formula:

E(x) = ∑xi/n

Where xi are the values in the sample and n is the sample size.

For our example, E(x) = (30 + 30 + 30 + 30 + 30) / 5 = 30

This shows that x is an unbiased estimator of μ.

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The margin of error of the intervals 11.13 < μ < 15.03 is 1.95

In order to get the margin of error, we would first have to find the samole mean.

The sample mean x = the upper limit + lower limit / 2

the upper limit = 15.03

The lower limit = 11.13

Then we would have: 15.03 + 11.13 / 2

= 26.16 / 2

= 13.08

Then the margin of error would be

upper limit - sample mean

= 15.03 - 13.08

= 1.95

The margin of error is given as 1.95

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The option that illustrates the truth value of the given conditional statement is; T T → T

A conditional statement is considered to be true when the antecedent and consequent statements are both true or if the antecedent is false. When the antecedent is false, it means that the truth value of the consequent does not matter; the conditional will always be true.

We are given the conditional statements at;

If 5 = 3 + 2, then 3 + 2 = 5

Now, a conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 5 = 3 + 2 which is true and 3 + 2 = 5 which is also true.

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A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line. The slope of the line y = 2/7x - 8 is 2/7. To find the slope of the line that is perpendicular to it, we take the negative reciprocal of 2/7 which is -7/2.

We know that the line we're trying to find passes through the point (-4, 2), so we can use this point and the slope to write the equation of the line in point-slope form:

y - y1 = m (x - x1)

where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.

So the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is:

y - 2 = -7/2 (x + 4)

Simplifying this, we get

y = -7/2 x - 8

Therefore the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is y = -7/2 x - 8

Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4

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Answer:below

Step-by-step explanation:

y=1/3x

Answer:

The power is 15 watts.

Step-by-step explanation:

It is equivalent to:

0.02012 mechanical horsepowers

0.02039 metric horsepowers

0.02011 electrical horsepowers

0.001529 boiler horsepowers

Answer:

It would take her 22 minutes to text 143 words.

Step-by-step explanation:

First, you take 91 and divide that by 14.

You then get 6.5

Then you divide. 143/6.5

You then get 22.

Guadalupe can text 143 words in 22 minutes.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Guadalupe can text 91 words in 14 minutes.

Since,

Guadalupe can text 91 words in =  14 minutes.

Thus, Guadalupe can text 1 word in  =  14/91 minutes.

So, Guadalupe can text 143 words in =  14*143/91 minutes.

Guadalupe can text 143 words in = 22 minutes.

Therefore, in 22 minutes, Guadalupe can text 143 words.

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a. The equation that represents the number of inches y you have knitted after x days will be y = 4x.

b. The inches you have knitted after 7 days will be 28 inches.

c. After 30 days, you'll have knitted 100 inches.

From the information, you're You are knitting a blanket at a rate of 4 inches per day and after 4 days, you have knitted 16 inches.

The equation that represents the number of inches y you have knitted after x days will be:

y = 4 × x

y = 4x

The inches you have knitted after 7 days will be:

= 7 × 4

= 28 inches.

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The wideness of the actual balcony would be = 5.2 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

The actual size = scale factor × blueprint

where actual length = 9 inches

blueprint = 11.7 = 140.4 inches

scale factor = actual size/blue print

= 140.4/9 = 15.6

If the blue print width size = 4

the actual size = 4× 15.6 = 62.4 inches = 5.2 feet

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Answer:

She's thinking of 19 and -7.

Step-by-step explanation:

x+y=12

x-y=26

-----------

2x=38

x=38/2

x=19

19+y=12

y=12-19=-7