Which of the following best describes a function? A function is any mathematical formula or graph. A function is any mathematical rule. A function is a formula that involves variables. A function is a rule that for each input has at most one output.

The Equidistant Theorem states that the distance between two points on a line is equal to the sum of the distances from each point to a third point. This theorem is often used to prove the existence of certain geometric shapes, such as triangles and circles.

The Equidistant Theorem is a useful tool for proving the existence of certain geometric shapes. By measuring the distance between two points and then measuring the distance from each point to a third point, the distance between the two points will be equal to the sum of the distances of the two points to the third point.

This theorem is helpful for constructing triangles and circles, as it allows us to quickly and accurately identify the necessary distances between the points. This theorem is also useful for finding the center of a circle, as the center of the circle is always equidistant from its circumference. As a result, the Equidistant Theorem is a fundamental theorem in geometry that is used to prove the existence of certain geometric shapes.

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The complete diagram map is given as,
1 - 3
2 - 5,
3 - 7,
8 - 17,
10 - 21
100 - 201

Given that,
To complete the map diagram,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
The given map diagram follows the general term as nth term = 2n + 1
So for n = 3
= 2 [3] + 1
= 7
Similarly,

10th = 21
100th = 2001

For the value 17

17 = 2n + 1
n = 8
So the 8th term is 17 in the map diagram,

Thus, The complete diagram map has been shown.

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The expression  that could represent the cost of 7 t-shirts and a $6 tax is (a)  7n + 6

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

Number of shirts = 7

Tax = $6

Represent the cost of each shirt with n

So, we have the following equation

Total cost = Number of shirts * Cost of each shirt + Tax

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

Total cost = 7 * n + 6

Evaluate

Total cost = 7n + 6

Hence, the expression is (a) 7n + 6

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The rate at which the volume of the cube is changing is 1200 in³/seconds.

Volume is the space occupied by a solid object.

To calculate the rate at which the volume of the cube is changing, we use the formula below.

Formula:

Where:

From the question,

Given:

If, the volume of a cube is V = L³,

Then,

Substitute these values into equation 1

Hence, the rate at which the volume is changing is 1200 in³/seconds.
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SAS triangle congruence theorem can be used to prove the triangle are congruent.

A triangle is a simple polygon with three sides and three interior angles. It is one of the basic forms of geometry in which three vertices are connected, and is represented by the symbol △. There are different types of triangles, classified based on their sides and angles. Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other. The congruence symbol is "≅".

Angle is the space between two intersecting lines or surface at or close to the point where they meet.

The SAS Postulate says that is the  triangles are congruent if any pair of the  corresponding sides and I their included angles are be congruent.

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Answer:

[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4  

Step-by-step explanation:

cos(a + b) = cos (a) cos(b) – sin (a) sin (b)

cos(75) =

cos(45 + 30) =  ==> break it down into more solvable angles

cos (45) cos(30) – sin (45) sin (30) =

[tex]\sqrt{2}[/tex]/2 * [tex]\sqrt{3}[/tex]/2 – [tex]\sqrt{2}[/tex]/2 * 1/2 =  ==> simplify

([tex]\sqrt{2}[/tex]*[tex]\sqrt{3}[/tex])/(2*2) – ([tex]\sqrt{2}[/tex]*1)/(2*2) =[[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4]

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The equation that describes the line that passes through (2, 1) and (0, -5) is: B. y = 3x - 5.

To find the equation of a line, find the value of the slope (m) and the y-intercept (b), and plug in the values into y = mx + b.

Given the points:

(2, 1) and (0, -5)

Slope (m) of the line = change in y / change in x = (-5 - 1) / (0 - 2)

Slope (m) = -6/-2

Slope (m) = 3

The y-intercept (b) = -5 (this is because it is the value of y when x = 0).

To write the equation, substitute m = 3 and b = -5 into y = mx + b:

y = 3x - 5

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The set of points includes all of the solutions is (x, - 4/5 x + 2).

What is the solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given equation is

y = - 4/5 x + 2

The value of x can be any real number.

The value of y is - 4/5 x + 2.

The solution of the equation is (x, - 4/5 x + 2).

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Answer: 48

Step-by-step explanation:

[tex]\displaystyle\\\frac{32(150\%)}{100\%} =\\\\\frac{4800}{100}= \\\\48[/tex]

Answer:

48

Step-by-step explanation:

150% = 150/100 = 1.5

Then:

32 * 1.5 = 48

The side lengths of the new phone are proportional to the old phone, then the width of the new phone is 5.125 inches.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The dimensions of the older phones are,

Length, L(1) = 1.4 inches

Width, W(1) = 4.1 inches

The dimensions of the new phone are,

Length, L(2) = 1.75 inches

Width, W(2) = ?

Then the width of the new phone is,

1.4 × W(2) = 4.1 × 1.75

W(2) = (4.1 × 1.75)/1.4

W(2) = 5.125 inches.

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Using graphical method to solve the system of inequality, the number of banana is 2 and mango is 10

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In this question, we can set the unknown variables as;

0.2x + 2y = 20 ...eq(i)

x + y ≥ 12 ..eq(i)

Solving x and y

This can be done graphically;

The number of banana and mango is approximately 2 and 10 respectively

Kindly find the attached graph below

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Answer:

t = b + n

Step-by-step explanation:

for the 2 lines to be parallel then their slopes must be equal

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (x₁, a + n ) and (x₂, y₂ ) = (x₂, t ) ← 2 points on line k

m = [tex]\frac{t-(a+n)}{x_{2}-x_{1} }[/tex] = [tex]\frac{t-a-n}{x_{2}-x_{1} }[/tex]

repeat with

(x₁, y₁ ) = (x₁, a ) and (x₂, y₂ ) = (x₂, b ) ← 2 points on line j

m = [tex]\frac{b-a}{x_{2}-x_{1} }[/tex]

equating the 2 slopes gives

[tex]\frac{t-a-n}{x_{2}-x_{1} }[/tex] = [tex]\frac{b-a}{x_{2}-x_{1} }[/tex]

since the denominators are the same on both sides, then equate the numerators

t - a - n = b - a ( add a to both sides )

t - n = b ( add n to both sides )

t = b + n

The composition of two isometries is an isometry.

Proof:

Let T1 and T2 be isometries. T1(A) = A' and T1(B) = B'. Therefore by isometry T1, AB = A'B'

T2(A) = A'' and T2(B) = B''. Therefore by isometry T2, AB = A''B''

T2 º T1 = T2(T1(A)) = T2(A') = A'''. T2 º T1 = T2(T1(A)) = T2(B') = B'''. Therefore under composition AB = A'''B''' and distance is preserved.

The inverse of an isometry is an isometry.

Proof:

Given T and isometry. This means T(A) = A' and T(B) = B' with AB = A'B'

The inverse of T, T⁻¹maps A' to A and B' to B, so A'B' maps to AB.

But A'B' = AB and so the inverse is an isometry

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Option c; The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money. This is the correct statement about the survey.

What is politics?

Politics is a category of activities that are related to group decision-making or other types of power dynamics between people, such as the allocation of resources or status. Political science is the name of the area of social science that focuses on politics and governance.

Given,

A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. at the end of the questionnaire is an (optional) invitation to donate money to the political action committee.

We have to find the correct statement about the survey from the given options;

Because respondents are less inclined to support a group that solicits donations, the survey results will understate public support for this political action committee.

The correct statement about the survey is option c;

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There is sufficient evidence to conclude that μ, the true mean tension of the rackets, is less than 58 PSI.

The customer determined the tension of each racket after receiving them and came up with the following summaries: 0.9 PSI of standard deviation, 58 as the sample mean.

When we choose alpha as 5% = 0.05, it means that we reject the null hypothesis whenever the p value from the hypothesis test is less than this. If not, we will accept the null hypothesis.

You can use a p value as low as 0.05 and still reject the null hypothesis H0.

On calculating the p value we get it as less than 0.05.

Therefore, we will accept the null hypothesis.

Hence , the true mean tension of the racket is 28 psi .

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C. The Roth IRA reduces the tax burden because its taxes are calculated in a lower bracket.

In a traditional IRA, contributions may be tax-deductible in the year they are made, but withdrawals in retirement are taxed as ordinary income. This means that the $1000.00 investment in a traditional IRA would be taxed at the investor's ordinary income tax rate when it is withdrawn in retirement. If the investor's ordinary income tax rate is 12%, then the tax burden on the $1000.00 investment in a traditional IRA would be $120.00.

In a Roth IRA, contributions are not tax-deductible, but withdrawals in retirement are tax-free. This means that the $1000.00 investment in a Roth IRA would be taxed at the investor's ordinary income tax rate when it is made, but it would not be taxed when it is withdrawn in retirement. If the investor's ordinary income tax rate is 10%, then the tax burden on the $1000.00 investment in a Roth IRA would be $100.00.

Overall, the tax burden on the $1000.00 investment in a Roth IRA is lower than the tax burden on the same investment in a traditional IRA because the taxes on the Roth IRA are calculated in a lower bracket (10% vs 12%).

77532 is the total cost to Russell

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Russell Slater bought 700 shares of Disney stock at $106.50 per share

The amount for 700 shares is 700×106.5

74550

commission of 4% of the purchase price.

We have to convert 4% to decimal value by dividing 4 by 100

0.04

Now multiply 0.04 with 74550 to get the commission

0.04×74550

2982

Now add this commission amount with 74550 to find total cost,

2982+74550

77532

Hence, 77532 is the total cost to Russell

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In the transformation of triangle abc, the pre-image of b' is b.

It's a triangle denoted as abc. abc is changed so that the resulting image is a'b'c''. It should be noted that there are many other forms of transformations, including dilation, vertical shift, horizontal shift, rotation about a point, reflection on a line, etc.

Corresponding vertices will be matched in all transformations. In other words, a will change to a'', b to b', and c to c''. Preimage of b' would just be b itself due to the transformation's ability to maintain image similarity and convert vertices appropriately.

Note that the correct question is:

In the transformation ABC A'B'C', the preimage of B' is ____.

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The expensive a car that you can afford is $42666.42.

What is interest rates?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

Given that you can deposit $325 each month. The interest rates is 4.25%.

Future Value of an Ordinary Annuity

[tex]S = R[\frac{(1+i)^n-1}{i}][/tex]

where

S is the future value;

R is the periodic payment;

i is the interest rate per period;

n is the number of periods.

The value of R is $325, i = 0.0425/12 = 0.00354

n = (12 × 9) =108

The future value is

[tex]S = 325[\frac{(1+0.00354)^{108}-1}{0.00354}][/tex]

S = 42666.42

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Answer:

all values greater than or equal to -11

Step-by-step explanation:

For a square root to be a real number, the value under the square root must be positive. Therefore, all values of x must ensure that the value under the square root remains positive.

Answer:

-------------------------------------------

The square root is  defined when the expression under the root is not negative.

It is shown as:

It is false that the range of the sine function is 0 ≤ ∅ ≤ π

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

Function: sine function

Also from the question, we have

Range: 0 ≤ ∅ ≤ π

As a general rule, we have:

This means that the range of the sine function is from [-1, 1].

This can also be represented as -1 ≤ ∅ ≤ 1

Hence. the given statement about the sine function is false

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Answer:

The answer is false.

Step-by-step explanation:

The range of the sine function is NOT 0 ≤ ∅ ≤ π

It takes about 13.33 hours for the friend to paint a room by himself.

If two persons are working on the same project together, their work rates add up and they can finish the project faster. If x is the time taken by person 1 to complete a task, then the work rate is 1/x. If y is the time taken by person 2 to complete a task, then the work rate is 1/y.  Then, the formula to calculate the work-rate problem is [tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{t}[/tex].

Here, the rate of work done by person 1 is 1/8. Together, the rate is 1/5. Then,

[tex]\begin{aligned}\frac{1}{8}+\frac{1}{y}&=\frac{1}{5}\\\frac{y+8}{8y}&=\frac{1}{5}\\5y+40&=8y\\3y&=40\\y&=\frac{40}{3}\\&=13.33\end{aligned}[/tex]

Therefore, the answer is 13.33 hours.

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The shape of the sampling distribution of the mean for samples of size 45 will be normal.

This is because the sampling distribution of the mean approaches normality as the sample size increases. The center of the sampling distribution will be 67 inches, which is the mean height of the population. The spread of the sampling distribution will be determined by the standard deviation of the population and the sample size. Specifically, the standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution will be 3.8 inches / sqrt(45) = 0.55 inches.

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Work done by the vector is 11π/16.

We know that,

the given closed curve in the plane is,

F(x,y) = [tex](\frac{x^{2}y }{4} + \frac{y^{3} }{3} )[/tex] i+xj

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = [tex]\frac{x^{2}y }{4} +\frac{y^{3} }{3}[/tex] and Q = x

so the partial differentiation is,

[tex]\frac{dP}{dy} = \frac{x^{2} }{4} + y^{2}[/tex]  and  [tex]\frac{dQ}{dx}[/tex] = 1

By the Green's theorem work done by F is given as,

W = ∫ F dr

W = ∫∫ ( [tex]\frac{dQ}{dx} - \frac{dP}{dy}[/tex] )dxdy

W = ∫∫ [tex](1 - \frac{x^{2} }{y} -y^{2} )dxdy[/tex]

Let C = x² + y² = 1

and x = rcosθ, y = rsinθ ;

0 ≤ r ≤ 1; 0 ≤ θ ≤ 2π

Therefore

W = ∫∫ (1 - r²cos²θ/4 - r²sin²θ) [tex]|\frac{d(x,y)}{dr,0} |[/tex] dθdr

and d(x,y)/d(r,θ) = [cosθ  -rsinθ; sinθ  rcosθ] = r

Thus

W = ∫∫ (1 - r²cos²θ/4 - r²sin²θ)rdθdr

after solving we get,

W = 11π/16.

Hence the work done along with the vector is 11π/16.

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False Reason:...This is false if (x=5)  (y=3). and denotes the requirement that both be true.

This is true: (z=8) > (x=5) The entire statement is false because it relies on the and condition rather than the OR condition.

What is an example of a Boolean expression?

A Boolean expression(named for mathematician George Boole) is an articulation that assesses to one or the other valid or misleading. Let's take a look at some examples from common speech: Pink is my favorite color. valid • I'm anxious about PC programming. False This book is a laugh-out-loud good read.

Which three Boolean expressions are there?

There are three fundamental Boolean operators: What's more, OR, and NOT.

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To beat the school long jump record, John must jump an additional 5 1/4 inches

From the given question, we are to determine how farther John must jump in order to break the record

From the given information,

"A high school track team's long jump record is 23 ft 1 3/4 in"

and

"John's best long jump is 22 ft 8 1/2 in"

First, we will convert the distances to inches

NOTE: 1 ft = 12 inches

23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in

22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in

Now, to determine how farther John must jump, we will subtract the distances

277 3/4 in - 272 1/2 in = 5 1/4 in

Hence, he must jump 5 1/4 in farther

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POLYGON

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.

TYPES OF POLYGON

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Answer:

70

Step-by-step explanation:

1 million = 10 hundred thousands because 100,000 x 10 = 1,000,000

The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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Answer:

48

Step-by-step explanation:

0.8 * 60 = 48