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The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.

Then the area of the rhombus is given as,

A = (Product of diagonal of rhombus) / 2

A = (8 x 6) / 2

A = 48 / 2

A = 24 square centimeters

The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

The diagram is shown below.

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Answer:

Step-by-step explanation:

its C

Answer:

(12m+10)(2m-2)

hope this helps

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{4} {x}^{2} - 4 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{4} {x}^{2} = 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} = 4 \times 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \sqrt{4 \times 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \pm4[/tex]

[ but since we have been asked for positive solution, it will be 4 ]

Hence, the correct choice is : A.) 4

Answer:

A correlation of -1.00 indicates a strong negative correlation. This means that as one variable increases, the other variable decreases at a constant rate. In other words, there is a perfect inverse relationship between the two variables, with one increasing as the other decreases and vice versa. This is the strongest possible negative correlation.

The correlation coefficient ranges from -1 to 1, with -1 indicating a strong negative correlation, 0 indicating no correlation, and 1 indicating a strong positive correlation. Positive correlations indicate that as one variable increases, the other variable also increases. Negative correlations indicate that as one variable increases, the other decreases.

In summary, a correlation of -1.00 indicates a strong negative correlation, meaning that there is a perfect inverse relationship between the two variables.

Answer:

A.7

Step-by-step explanation:

You first have to add 8 and -15

Then, find the absolute value

So, the answer is 7

Rounded to the nearest minute, the answer is 12 minutes.

The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.

The radius of the Ferris wheel is half its diameter, which is 20/2 = 10 meters. When the Ferris wheel makes a full revolution, a person riding it will pass the loading platform twice: once on the way up and once on the way down. The highest point reached by the Ferris wheel is at the top, which is 10 + 1 = 11 meters above the ground.

To find out how many minutes of the ride are spent higher than 19 meters above the ground, we need to figure out at which times the rider is at or above this height. Let's call h(t) the height of the rider at time t. We know that h(t) is a sinusoidal function with a period of 10 minutes, an amplitude of 10 meters, and a vertical shift of 11 meters. In other words, we can write:

h(t) = 10 sin(2πt/10) + 11

To find out when h(t) is greater than 19, we solve the inequality:

10 sin(2πt/10) + 11 > 19

Subtracting 11 from both sides, we get:

10 sin(2πt/10) > 8

Dividing by 10, we get:

sin(2πt/10) > 0.8

The sine function is greater than 0.8 at two times in each period: once when it is increasing from 0.8 to 1, and once when it is decreasing from 1 to 0.8. We can find these times by solving the equations:

sin(2πt/10) = 0.8

sin(2πt/10) = -0.8

Using a calculator, we find that these equations have solutions at:

t = 1.167, 8.833, 3.5, 6.5

These times represent the four moments during the 10-minute period when the rider is at or above 19 meters. The first and fourth of these moments occur in the first half of the period, and the second and third occur in the second half.

Therefore, the total time spent higher than 19 meters is:

(8.833 - 1.167) + (6.5 - 3.5) = 11.6667 minutes

Rounded to the nearest minute, the answer is 12 minutes.

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The transformations are matched accordingly is given below.

A function transformation takes whatever the underlying function f (x) is and "transforms" (or "equates") it, which is a fancy way of saying you alter the equation and shift the graph over.

Parent function is given as f(x) = 2x - 6

The transformations are shifts f(x) 4 units down

f(x) → f(x) - 4

⇒ g(x)= 2x - 6 - 4 = 2x - 10

Then stretches f(x) by a factor of 4 away from the x-axis

f(x) → 4*f(x)

⇒ g(x) = 4(2x - 6) = 8x - 24

Now shifts f(x) 4 units right

f(x) → f(x - 4)

⇒ g(x) = 2(x - 4) - 6 = 2x - 14

To compresses f(x) by a factor of toward the y-axis (must be 4)

f(x) → f(4x)

⇒ g(x) = 2*4x - 6 = 8x - 6.

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The factors of the cubic function f(x) = 64x³ + 27 are (4x + 3) and (16x² − 12x + 9). The correct answer would be options (A), and (D).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.

The cubic function is given in the question, as follows:

f(x) = 64x³ + 27

The above expression can be rewritten as:

f(x) = (4x)³ + (3)³

Compare the sum of cubic formula a³ + b³ = (a + b)(a² - ab + b²) and we get

f(x) = (4x + 3)(16x² − 12x + 9)

Thus, the factors of the cubic function are (4x + 3) and (16x² − 12x + 9).

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In 30 years, the amount that Jenna will have is $411, 235

This account balance is as a result of Jenna's annuity payments.

The amount that Jenna's account will be worth in 30 years can be found by the future value of annuity formula which is :

= Annuity deposited periodically x Future value of annuity factor, 10 % , 30 years

Annuity deposited periodically = $ 2, 500

Future value of annuity factor = 164.49402268886

The value of the account balance will be:

= 2, 500 x 164.49402268886

= $411, 235

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Answer: $411,235, Annuity Payments

Step-by-step explanation:

I have took the test and know the answer is correct

The percentage multiplier to find the 53% of a price is 0.53

The given percentage value = 53%

Percentage of a quantity is defined as the number or the ratio, that can be expressed as the fraction of 100. To find the percentage of a number, divide the number by the whole quantity and multiply by 100. Percentage of a number is usually expressed as by using percentage sign "%"

Here we have to find the percentage multiplier

To find the percentage multiplier divide the given percentage by 100

The percentage value = 53%

The percentage multipler = 53 / 100

Divide the numbers

53 / 100 = 0.53

Therefore, the percentage multiplier is 0.53

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The probability of both events is the sum minus the intersection. The answer should be rounded to two decimal places.

To calculate the probability of someone using a cell phone while driving or had no speeding violation, first calculate the individual probabilities of each event. The probability of someone using a cell phone while driving is P(cell phone) and the probability of someone having no speeding violation is P(no speeding violation). Then, add these two probabilities together, P(cell phone) + P(no speeding violation). This will give you the total probability of both events occurring. Finally, subtract the probability of the intersection, which is the probability of someone using a cell phone while driving and having no speeding violation. This will give you the total probability of someone using a cell phone while driving or having no speeding violation. Round the answer to the hundredths place.

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The value of x is given as follows:

x = 131º.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Hence the measure of the top angle of the bottom triangle is given as follows:

a = 180 - 98

a = 82.

The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence, considering that the sum of the measures of the internal angles of a triangle is of 180º, their measures are given as follows:

2b + 82 = 180

2b = 98

b = 49.

Considering the vertical angles, the base angles of the top triangle are given as follows:

b = 49.

Hence the value of x is given as follows:

x = 180 - 49

x = 131º.

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Answer:

-1/3

Step-by-step explanation:

Yhe equation 6x^2 + x - 2 has two roots, alpha and beta, that can be found by using the quadratic formula or by factoring.

The sum of the roots (alpha and beta) can be found by using the formula:

-b/a

where a = 6, b = 1 and c = -2

-1/6

The product of the roots (alpha and beta) can be found by using the formula:

c/a

where a = 6, b = 1 and c = -2

-2/6 = -1/3

So, the sum of the roots is -1/6 and the product of the roots is -1/3.

The value of x and y in the geometric sequence are 1/r and 1

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

If the first term of the sequence is a ,second term is ar , third term = ar²

r = ar²/ar

In the sequence 2y, 2xy, 2, xy/2, ...

r = 2y/2xy

therefore r = 1/x

r = 2/2xy

r = 1/xy

therefore 1/x = 1/xy

therefore y = 1

x = 1/r

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Answer:

(4,3)

Step-by-step explanation:

The expression that represents the value of the stock after two years in terms of x is 1.6144x

After the first year, the value of the stock increased by 39%, which means that the stock's new value will be -

x + 0.39x = 1.39x

After the second year, the value of the stock decreased by 16%, which means that the stock's new value will be -

1.39x - 0.16(1.39x) = 1.16(1.39x)

Simplifying this expression, we get,

1.16(1.39x) = 1.6144x

Therefore, the expression that represents the value of the stock after two years in terms of x is 1.6144x.

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The complete question is -

Aubrey bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 39%. During the second year the value of the stock decreased by 16%. Write an expression in terms of x that represents the value of the stock after the two years have passed.

The statements that are true about rectangles are mentioned in options  

A,B,C,E.

Rectangles -A shape with four sides and internal angles is a rectangle. The lengths of the other two sides are offset by two. The rectangle's diagonal sides are of identical length.

The opposite sides of a rectangle are equal and parallel to one another.

The diagonals cut each other in half, but not exactly.

All diagonals are the same length.

The rectangle's diagonals line up.

The total internal angles add up to the same value

Every internal angle has the same value.

A rectangle has congruent angles on all sides.

A rectangle's opposing angles are congruent.

We may thus infer that the statements about rectangles in the options are accurate based on the aforementioned features.

Q. Select all the statements that are true about rectangles.

A Diagonals are congruent.

B Diagonals bisect angles.

C Opposite angles are congruent.

D Diagonals are perpendicular.

E Diagonals bisect each other.​

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Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Given are three tables in x and y and we have to find which table shows a linear relation.

We know in  a linear relation between x and y the graph would be a straight line and also the slope would be constant

i.e. change of y/change of x for any pair in the table would be a constant.

Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.

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Using trigonometric ratio, the height of the pole is approximately 60 feet

The angle of elevation is the angle between the horizontal and a line from the observer to a point above the horizontal. In other words, it is the angle between the ground and the line of sight to an object above the ground.

Using trigonometric ratio to solve the angle of elevation problem, the height of the pole can be calculated using the tangent of the triangle.

tanθ = opposite / adjacent

tan 55 = x / 42

x = 42 * tan 55

x = 59.98 ft≅ 60 feet

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It will take 20 pounds for both charges to be the same.

An equation containing variables with its highest power as one is called linear equation.

To ship a package,

UPS charges $4 for the first pound and $0.50 for each additional pound.

FedEx charges $6 for the first pound and $0.40 for each additional pound.

These can be written in the linear equation form as,

Let p be the pound charges by both UPS and FedEx,

then, 4+0.50p-------(1)

6+0.40p-----(2)

When the charges are same, (1)=(2)

4+0.50p = 6+0.40p

⇒0.10p=2

⇒p=20

Hence, this means that, it will take 20 pounds for both charges to be the same.

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Answer: 27

Step-by-step explanation:

8^x+1 = 64

8^x+1 = 8²

x+1 =2

x = 2 - 1

x = 1

To Find :

3^2x +1

Substitute the value of x :

3^2(1)+ 1

3^2+1

3^3

27

Answer: The distance between Star B and Star C can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side). In this case, the lengths of the two shorter sides are the distances from Star A to Star B (50 lightyears) and from Star A to Star C (120 lightyears).

So, we have:

(Star B to Star C)^2 = (Star A to Star B)^2 + (Star A to Star C)^2

(Star B to Star C)^2 = 50^2 + 120^2

(Star B to Star C)^2 = 2500 + 14400

(Star B to Star C)^2 = 16900

Taking the square root of both sides:

Star B to Star C = √16900

Star B to Star C = 129 lightyears

So, Star B and Star C are 129 lightyears apart.

Step-by-step explanation:

The two values of y such that the barn is 50 yards from the well are given as follows:

y = -47 and y = 53.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following equation:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For this problem, we have that D = 50, hence the equation is given as follows:

sqrt[(-2 - (-2))² + (y - 3)²] = 50

y - 3 = ±50.

Hence the values of y are given as follows:

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The correct answer is C. (1, 5) is the ordered pair which is the solution to the system of equations.

A group of two or more equations with the same variables is referred to as a system of equations. The set of values for the variables that make all of the equations in a system of equations true is known as the solution.

The solution to the systems of equations is x = 1 and y = 5.

To solve this system of equations, we can begin by subtracting the two equations to get y - y = -x + 6 - (x + 4).

Simplifying, we get -2x = 2.

Then, dividing both sides of the equation by -2, we get x = -1.

We can now substitute the value of x into either one of the original equations to find the value of y.

If we substitute x = -1 into the first equation, we get y = -1 + 4, which simplifies to y = 3.

Therefore, the solution for this system of equations is x = -1 and y = 3.

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Answer:

I have graphed it and attached it in the explanation part.

Step-by-step explanation:

Answer:

  A.  Bimodal

Step-by-step explanation:

You want a description of the shape of the histogram shown.

The mode of a dataset is the value that appears most often. When two values have that distinction, the data is said to be "bimodal."

Here, the most a data item appears is 6 times. Two data items have that distinction: 2 and 7. Hence, the shape of the distribution is ...

  A.  Bimodal

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The slope of the line that models this situation is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (0, 8).

Points on y-axis = (4, 20).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (20 - 4)/(8 - 0)

Slope, m = 16/8

Slope, m = 2.

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The piecewise function's domain and range are all real numbers, excluding x = 6, and all real numbers, respectively.

The broad range of values within which we are permitted to enter into our function is known as the area of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The piecewise function is a function.

In the image that is attached, a function is shown.

The function's defined values are its domain, and its attainable values are its range.

With the exception of the x = 6 range, all real numbers fall inside the domain.

As a result, choice c is the right one.

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