Select all of the conditions that prove that a quadrilateral is a rectangle.

A) Both pairs of opposite sides are congruent.
B) One pair of opposite sides is longer than the other pair of sides.
C) The diagonals bisect each other.
D) The diagonals are congruent.
E) The diagonals are perpendicular.

The average rate of change of these function f(x), g(x), h(x) on interval [4, 7] from least to greatest is f(x)<g(x)<h(x) with values A1 = -7.5 < A2 = -6 < A3 = -3.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

Average rate of change of any function say S(x) on [a,b] is -

A = [S(b) - S(a)]/b-a....(1)

Now. for function f(x) on interval [4, 7].

Here, use values of f(4) and f(7) from graph and find value of f(x)=y for x=4 and value of f(x)=y for x=7.

f(4) = -10, f(7) = 5

Substitute the values in equation (1) -

A1 = [f(7) - f(4)]/(4 - 7)

A1 = [5 - (-10)]/-2

A1 = 15/-2

A1 = -7.5

Average rate of change for function g(x) on interval [4, 7].

Here, use the values of g(4) and g(7) from table.

g(4) = 7, g(7) = 19

Substitute the values in equation (1) -

A2 = [g(7) - g(4)]/(4 - 7)

A2 = [19 - 7]/-2

A2 = 12/-2

A2 = -6

Average rate of change for function h(x) = x² - 9x + 5 on interval [4, 7].

Here, use the values of h(4) and h(7) by putting x = 4 and x = 7 in function h(x).

h(4) = x² - 9x + 5

h(4) = (4)² - 9(4) + 5

h(4) = 16 - 36 + 5

h(4) = -15

h(7) = x² - 9x + 5

h(7) = (7)² - 9(7) + 5

h(7) = 49 - 63 + 5

h(7) = -9

Substitute the values in equation (1) -

A3 = [h(7) - h(4)]/(4 - 7)

A3 = [-9 - (-15)]/-2

A3 = [-9 + 15]/-2

A3 = 6/-2

A3 = -3

Now, average rate of change of these function f(x), g(x), h(x) from least to greatest is f(x)<g(x)<h(x).

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The authors argue that Cypher's decision to go back into the Matrix was a betrayal of his friends because it showed that he was willing to abandon his beliefs and betray those closest to him in order to return to a life of comfort and ease within the Matrix.

By doing so, he effectively gave up his freedom and became a tool of the machines once again, thereby betraying the ideals of the rebellion and those who had fought alongside him to achieve it. Hence, The authors argue that Cypher's decision to go back into the Matrix was a betrayal of his friends.

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The requied solution are (f+g)(x) = 10x² + 10 - 5x and (f-g)(x) = 10x² + 6 + 5x.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

f(x) = 10x² + 8 and g(x) = 2 - 5x

To find (f+g)(x) we add f(x) and g(x) term by term.

(f+g)(x) = f(x) + g(x)

Substitute the values of given functions, and we get

(f+g)(x) = 10x² + 8 + (2 - 5x)

(f+g)(x) = 10x² + 10 - 5x

To find (f-g)(x) we subtract g(x) from f(x) term by term.

(f-g)(x) = f(x) + g(x)

(f-g)(x) = 10x² + 8 - (2 - 5x)

(f-g)(x) = 10x² + 6 + 5x

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So 213 employees left in the company after 13 years.

Given

Number of employee in the company=630

Decreasing rate in the company per year =8%

Time= 13 years

Let the number left in the company be x

Since the decrease rate is 8% we use 0.08

So after 13 years the employee left are

630(1-0.08)¹³=x

630(0.92)¹³=x

630*.338= 212.94

We can take approx as 213

so x= 213

So 213 employees left in the company after 13 years.

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For the given condition number of laps "l" is the independent variable.

A symbol (often a letter) is used in mathematics to represent an unknowable numerical value in an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.

Given The amount of time, t, to finish a race and the number of laps, I,

there are two types of variables,

dependent and independent variables,

In an algebraic equation, an independent variable is one whose values are not impacted by changes. When there are two variables in an algebraic equation, x and y, and each value of x depends on every other value of y, x is an independent variable, and y is a dependent variable.

for the given condition,

the time taken to finish the race directly varies with the number of laps,

so time is dependent on the number of laps and a number of laps "l" is the independent variable.

Hence the independent variable is the number of laps, "l".

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The complete question is,

The amount of time, t, to finish a race and the number of laps, l, around a track. What is the independent variable?

Answer: 7

Step-by-step explanation:

yarn = 4 1/5 = 21/5

measure of one piece = 3/5

no. of pieces of yarn = 21/5÷3/5

= 21/5×5/3

= 105/15 = 7

So the number of pieces of yarn cut will be 7

Answer:

7

Step-by-step explanation:

4.2' yarn

cut into 0.6' pieces

4.2/0.6 =7

Answer:

Step-by-step explanation:

The required length of a side of the rhombus is 10 cm.

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.

Let diagonals intersect each other at o,

In ΔROQ

RQ = [tex]\sqrt{OR^{2}+OQ^{2}}[/tex]

RQ =[tex]\sqrt{36+64} =\sqrt{100}[/tex]

RQ = 10 cm

Thus, required length of the side of rhombus is 10 cm.

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Complete question:

PQRS is a rhombus. The shorter diagonal PR measures 12 units and QS = 16 units. The measure of angle PQR = 60°. Find the length of a side of the rhombus.​

The coordinates of the rotated image are:

A' = (1, 1)

B' = (1, 3)

C' = (-2, 1)

Option A is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

Triangle ABC.

A = (1, 1)

B = (3, 1)

C = (1, 4)

When rotated 90 degrees counterclockwise around (1, 1).

A = (1, 1) will stay the same.

B = (3, 1) will change into B' = (1, 3)

C = (1, 4) will change into C' = (-2, 1)

Now,

The coordinates of the image after reflection are:

A' = (1, 1)

B' = (1, 3)

C' = (-2, 1)

This image is found in option A.

Thus,

The rotated image of the triangle is in option A.

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The length of Mid segment QT is 57.56 units.

The incenter of a triangle can be discovered by drawing the triangle's angle bisectors and then locating the location of their intersection. This is possible with the aid of a compass.

The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.

the single point where the three internal angle bisectors of a triangle meet and which also serves as the circumference of the circle around which it is inscribed.

The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.  

ΔQUT is right triangle

QU = 55

UT= 17

Using Pythagoras Theorem

QT² = QU² + UT²

QT² = 55² + 17²

QT = √3314

QT = 57.56

Thus, The length of Mid segment QT is 57.56 units.

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Christian is making a circular pizza. The diameter of the pizza is 12 inches. The pizza crust on the outside will be about 12 inches thick.

The formula for determining a pizza's circumference is C = 2πr, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the pizza's radius.

We must determine the pizza's circumference in order to locate the crust on the pizza's outer edge. C = 2πr is the formula for a circle's circumference, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the circle's radius.

The pizza has a diameter of 12 inches, so the radius, or 6 inches, is half of that. Thus, the pizza's circumference is:

                 C= 2π6 = 12π

The pizza's circumference represents the crust's outer edge. C = 26 inches = 12 inches As a result, the pizza's crust on the outside measures about 12 inches.

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The statement does not makes a sense because i is an imaginary unit and has fixed value √-1.

What is meant by value ?

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The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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The area of the square is given by:

A = x^2 - 16x + 64

Remember that the area of a square of side length S is given by the formula:

A = S^2

Here we know that the side length is x - 8, then we can just replace that on the formula above to get:

A = (x - 8)^2

Now we can expand that:

A = (x - 8)^2 = (x - 8)*(x - 8)

A = x^2 - 16x + 64

That is the area.

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Answer unzipped,new bases, sealed

Step-by-step explanation:

The percentages budgeted for all categories is 14.06%

A total of $900 seems to be spent on various health-related expenses:

medication costs, health club dues, and health insurance

seeing a doctor

If we go back in time, we can observe that the rate of doctor visits is double that of prescriptions, which is half that of health insurance,

which is 1/4 times that of health club dues.

As a result, if we consider x to be health club dues, health insurance is included.

4x medical visits, medicines, and health club dues 2x \s

sums to $900 = 8

The amount set up for health insurance is thus $112.5.

112 .5 * 12.5% = 14.06%

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Answer:

Step-by-step explanation:

refreh it

For the gumballs in Julia's bag

Sample space = lemon-lime, watermelon, grape.

The correct option is B.

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

Given,

Number of lemon limes gumballs in the bag = 2 lemon-lime gumballs

Number of watermelon gumball in the bag = 1 watermelon gumball

Number of grape gumballs in the bag = 3 grape gumball

Sample space is the set of all the possible outcomes the experiment

Here, Julia has 1 watermelon, 2 lemon-lime, and 3 grape gumballs

Sample space = lemon-lime, watermelon, grape

Hence { lemon-lime, watermelon, grape} is the sample space for gumballs in Julia's bag.

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The middle term in the simplified product for (x + 3)(x – 4) will be B. -x.

A polynomial with only terms is a binomial. For instance, the binomial x + 2 is composed of the terms x and 2.

Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is also referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form.

The product of (x + 3)(x – 4) will be:

= x² - 4x + 3x - 12

= x² - x - 12

In this case, the middle term in the simplified product is -x.

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The given value of 157 pounds is a statistic.

This is because it is a numerical measurement describing a characteristic of a sample. A statistic is a value calculated from a sample, whereas a parameter is a value calculated from a population. In this case, the sample is the 40 randomly selected members of the health and fitness club, and the statistic is the average weight of those members. This statistic is used to make inferences about the larger population of all members of the health and fitness club, but it is not the same as the parameter, which would be the true average weight of all members of the club.

Therefore, The given value of 157 pounds is a statistic.

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The composite translation for this problem is represented as follows:

<3, -9>

The four translation rules are defined as follows:

Another notation is the <x,y> notation, in which:

For the composition of translations, we add the movements, hence:

Meaning that the first option is the correct option.

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The answer is A cause- and- effect relationship between two variables can best be determined When the two variables are identified.

Because the cause and effect relationship is chancing when the variables are identified or there exists a direct relationship between the variable. i.e. when the variables are identified or have a retrogression between the variables.The use of a controlled study is the most effective way of establishing reason between variables. In a controlled study, the sample or population is resolve in two, with both groups being similar in nearly every way.

There are three criteria that must be met to establish a cause- effect relationship. The cause must do before the effect. Whenever the cause occurs, the effect must also do. There mustn't be another factor that can explain the relationship between the cause and effect.

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The mean is 120 and the standard deviation is 20.

How to find the mean and standard deviation?

We must calculate the mean and standard deviation from the curve in the preceding graph.

As we can see from the normal distribution curve that the center is at 120.

As a result, 120 is the distribution's mean.

From the above curve:

Mean + Standard deviation = 140

We know that the Mean = 120.

120 + Standard Deviation = 140

Standard Deviation = 20

Therefore, 20 is the standard deviation.

Therefore, from the given data we can find that the Mean is 120 and the Standard deviation is 20.

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In 2009, Florida would have 558 hospitals if it had the same hospital beds per million residents as Texas. This is a little more than what Florida's real number of hospitals was in 2009. (343).

A mathematical technique called proportional reasoning is used to compare the ratios of two or more identical quantities.

The proportionate reasoning theory is being used in this query.

In this instance, we're contrasting Florida's hospital density per million residents with Texas' hospital density per million residents.

We may predict the number of hospitals in Florida given the same ratio as Texas by comparing these two ratios.

1. Determine Texas's hospital density per million residents: 428 hospitals divided by 26.4 million residents equals 16.2 hospitals per million residents.

2. Determine Florida's hospital density per million residents: 343 hospitals / 19.5 million residents = 17.6 hospitals per million residents.

3. Multiply the population of Florida (19.5 million) by the number of hospitals per million of the population of Texas (16.2) to arrive at 315.3 hospitals: 19.5 million people x 16.2 hospitals per million of the population.

The result should be rounded to the next whole number: 315 hospitals are equal to 315.3 hospitals.

5. Contrast Florida's actual hospital count in 2009 with the expected number of hospitals there (315). (343).

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Answer: Based on the information provided, it appears that the graph represents a linear equation, which is a straight line. The equation of a straight line can be represented in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line, we need two points on the line. We can use the points (x1, y1) and (x2, y2) to calculate the slope of the line, m, using the formula:

m = (y2 - y1) / (x2 - x1)

Without knowing the coordinates of the points on the graph it is not possible to give the equation of the line.

To find the cost of ordering 6 pounds of mushrooms, we would substitute 6 for x in the equation of the line and solve for y.

y = mx + b

y = m(6) + b

Without the equation of the line, it's not possible to find the cost of ordering 6 pounds of mushrooms.

Step-by-step explanation:

D. 19 elements are in ALB.

| A | =6 and | B | = 13,

4 elements are common to sets A and B.

but | A ∪ B | ≠ 6 + 13.

Image search results for Set A has six components, set B has thirteen, and sets A and B share four elements.

A. 14 B. 15 C. 16 D. 19.The formula for A union B complement is (A U B)’ = A’ B’ or (A U B)c = Ac Bc, where or c represent the complement of a set. As one of De-Laws Morgan’s of Union of Sets, this formula of A union B complement is named after the mathematician De-Morgan. A U B (which denotes the union of two sets A and B) is a set that contains all of the components of A and B.

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here we are given a triangular prism and we are interested in finding its surface area .

The given prism comprises of 2 triangular faces and 3 rectangular faces . We can separately find the area and then add them up to find the resultant surface area.

Finding area of triangle:-

There are 2 triangles so the total area would be ,

Area = 2(ar. of one ∆)

Area = 2 ( 1/2 * base * height)

Area = 2 ( 1/2 * 16m * 5m )

Area = 80m²

Finding area of rectangle:-

Area = 3 ( length* breadth)

Area= 3 ( 17m * 10m)

Area = 3 * 170m²

Area = 510m²

Total area,

Net Surface area= area of rectangle+ area of triangle= (80+510)m² = 590m² [ required answer]

And we are done!

Answer: To determine which loan(s) meet Jeremy's criteria of no more than an effective rate of 7.000% annually, we need to calculate the effective rate for each loan.

The effective rate is the true annual interest rate that a borrower will pay on a loan, taking into account the frequency of compounding.

Loan A: 6.785% normal rate compounded semi-annually

To calculate the effective rate, we can use the formula:

(1+ (nominal rate/2))^2 - 1

Effective rate = (1+ (6.785/2))^2 - 1 = 6.897%

Loan B: 6.795% nominal rate compounded, manually

Since the loan is compounded manually, the effective rate is the same as the nominal rate.

Effective rate = 6.795%

Loan C: 6.659% nominal rate, compounded weekly

To calculate the effective rate, we can use the formula:

(1+ (nominal rate/number of compounding periods per year))^(number of compounding periods per year) - 1

Effective rate = (1+ (6.659/52))^52 - 1 = 6.759%

Since 6.897% > 7.000% and 6.795% > 7.000% and 6.759% < 7.000%. So Loan C with 6.659% nominal rate, compounded weekly meets Jeremy's criteria.

Step-by-step explanation:

Answer: a. The independent variable in the equation C(a) = 5a is a. It represents the number of art classes Amir attends.

b. The dependent variable in the equation C(a) = 5a is C(a). It represents the cost Amir incurs as he attends art classes. The dependent variable is dependent on the independent variable because the cost will change as the number of classes attended changes.