Triangle DEF has vertices D(1,1), E(2,0), and F(0,4). It is transformed by a rotation 180 degrees about the origin followed by a dilation with a scale factor of 3. Find the coordinates of the vertices of triangle D”E”F”.

The volume of the display case is 60 + 120 = 180. The correct answer is B. 36.

Volume is a measure of the three-dimensional space something occupies or contains. It is often expressed as a calculation of length x width x height. It can also refer to the amount of something, such as the volume of a liquid, or the amount of space a container holds. Volume is an important concept in mathematics, science, engineering, and many other fields. It is used to measure the size of a solid, liquid, or gas, and to quantify the amount of material in an object or a space.

The volume of a rectangular prism is determined by multiplying its length, width, and height. The volume of a display case made of one rectangular prism stacked on top of a second rectangular prism is equal to the sum of the volumes of each rectangular prism.

The volume of the first rectangular prism is 3 x 4 x 5 = 60.
The volume of the second rectangular prism is 4 x 5 x 6 = 120.

Therefore, the volume of the display case is 60 + 120 = 180. The correct answer is B. 36.

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The values of Sin A, Cos B and Tan A are: 41.8, 2.8 and 6.9 respectively

The ratios of the sides of a right triangle are called trigonometric ratios.", if in trigonometry the ratios of the sides of a triangle are called 'trigonometric ratios' then what if the triangle is not a right triangleA =

In triangle 1

SinA = Opposite/Hypothenuse

Son A = 6/9

Sin A = 0.6669

A = Sin ⁻¹0.6667

A = 41.8⁰

For triangle 2

Cos B = Adjacent /Hypothenuse

Cos 45 = x/4

AB = 4*0.7071

AB = 2.8

For triangle 3

Tan a = Opp/Adjacent

Tan60 = AB/4

AB = 4*Tan60

AB = 4* 1.7321

AB = 6.9

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To find the greatest common factor of these three terms, we need to factor each one and identify the highest power of each factor that is common to all three. Then, we can multiply those factors together to find the GCF.

Let's begin by factoring each term:

1/4n^2m^3 = (1/4) * n^2 * m^3

5/20n^7m^8 = (1/4) * n^7 * m^8

3/12n^2m^8 = (1/4) * n^2 * m^8

Now, we can see that each term has a common factor of 1/4, so we can factor that out:

1/4 * (n^2 * m^3)

1/4 * (n^7 * m^8)

1/4 * (n^2 * m^8)

To find the highest power of each factor that is common to all three terms, we need to look at the exponents. The highest power of "n" that is common to all three terms is 2, and the highest power of "m" that is common to all three terms is 3. Therefore, the GCF is:

1/4 * n^2 * m^3

This simplifies to:

n^2m^3/4

So, the correct option is (c) n^2m^3/4.

the correct length of the frame is 17 inches.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Area of rectangle is A = a*b

Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.

This will be:

d² = 15² + 8²

d² = 225 + 64

d² = 289

d = ✓289

d = 17

Therefore, the correct option is 17 inches.

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Answer:

Step-by-step explanation:

The Conjugate Roots Theorem states that imaginary roots come in pairs. If -8i is a root of the polynomial, then so is +8i.

If both -8i and +8i are factors, we rewrite them as (x + 8i) and (x - 8i) in factored form. Since imaginary terms aren't accepted, you can FOIL these to get a quadratic with no imaginary terms.

x2 - 8ix + 8ix - 64i2

Simplify. Replace i2 with -1 because √-1 = i

x2 - 64(-1)

x2 + 64

The quadratic x2 + 64 has roots -8i and 8i. You can use the quadratic formula to verify this.

Now, let's tackle the rest of the polynomial. If x2 + 64 is a factor of the polynomial

x4 + 10x3 + 85x2 + 640x + 1344, divide it out to see what is left. I will use long division of polynomials. Note, I am using the square root symbol as a division symbol.

x2 + 10x + 21

x2 + 64 √ (x4 + 10x3 + 85x2 + 640x + 1344)

x4 + 64x2

_____________

10x3 + 21x2

10x3 + 640x

__________

21x2 +1344

21x2 + 1344

___________

0

There is no remainder, meaning x2 + 64 went in evenly. The quotient left when we divide out x2 + 64 from

x4 + 10x3 + 85x2 + 640x + 1344 is x2 + 10x + 21. Factor the quotient to get (x + 7)(x + 3).

x4 + 10x3 + 85x2 + 640x + 1344 = (x2 + 64)(x + 7)(x + 3)

You can check this factored form by FOILing out, and you should get the original polynomial.

The answer of the given question based on the plotting graph , the steps are given below .

An inequality is a statement that compares two values or expressions and indicates that one is greater than, less than, or equal to the other. Inequalities can be solved or simplified using various algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides by the same quantity, or factoring and finding the roots of the expressions

To plot the inequality 4x - 5y ≤ -15, you can follow these steps:

4x - 5y ≤ -15

-5y ≤ -4x - 15

y ≥ (4/5)x + 3

Let's choose x = 0 and x = 5.

When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).

When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).

Plot these two points and draw  straight line through them.

4x - 5y ≤ -15

4(0) - 5(0) ≤ -15

0 ≤ -15

Since this is not true, the point (0,0) is not in the region that satisfies the inequality. Shade the region above the boundary line to show the region that satisfies the inequality.

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This is untrue since the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.

An inequality is a comparison that shows that one value or expression is larger than, less than, or equal to another. Different algebraic methods, such as adding, subtracting, multiplying, or dividing both sides by the same amount, or factoring and determining the roots of the equations, can be used to resolve or simplify inequalities.

Plotting the inequality 4x - 5y ≤-15 can be done by doing the following:

To solve for y, rearrange the inequality first:

4x - 5y ≤ -15

-5y ≤ -4x - 15

y ≥ (4/5)x + 3

You are then provided with the boundary line's equation. Plot two points on a graph, then draw a straight line through them to represent this line. You can use the equation to determine the values of y that correspond to any two x values to plot the line.

Let's choose x = 0 and x = 5.

When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).

When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).

Plot these two spots and a line should be drawn directly between them.

Now select a point that is not on the border line to shade the area that satisfies the inequality. (0, 0) is the simplest position to select. In the inequality, replace the x and y values of this point.

4x - 5y ≤ -15

4(0) - 5(0) ≤ -15

0 ≤ -15

Since this is untrue, the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.

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Answer:

Step-by-step explanation:

D

It would take 211 months for the bank account to double in value at a 4.1% APR compounded monthly.

We are going to use the rule of 72 which states that the number of years it takes for an investment to double is approximately equal to 72 divided by the annual interest rate.

The annual interest rate is 4.1% compounded monthly.

Monthly interest rate = 4.1% / 12

Monthly interest rate = 0.0034166667

Now we can use the rule of 72:

Doubling time = 72 / (0.0034166667 x 100)

Doubling time = 210.731705261

Doubling time = 211 months.

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The time taken by Amy to travel to the place was t = 4 hours.

A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.

In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.

Let the time taken to get back = t + 1.

Now, it took one hour less time to get there thus time = t.

Now, average speed is given as:

average speed = total distance / total time

Substituting the values:

50 km/h = d / t

d = 50t  .........(1)

40 km/h = d / (t + 1)

d = 40(t + 1)......(2)

Setting the value of d as equal we have:

50t = 40(t + 1)

50t = 40t + 40

10t = 40

t = 4

Hence, the time taken by Amy to travel to the place was t = 4 hours.

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The correct answer is C.  320×pi

What occurs when something is rotated around a pole? What kind of shape is the point closest to the pole making?

Obviously, a circle.

that means rotating the rectangle around the x-axis creates a round object (with the bottom area being a circle).

so, all answers about a prism (rectangular bottom shape) are automatically wrong.

again, just imagine to rotate a small sheet of paper around a pole (the x-axis acts like one in this scenario).

the result is solid with a circular bottom area, and it maintains this shape all the way to the top.

it is a cylinder!

and what is its radius?

well, the outermost point of the rectangle is 8 points away from the x-axis. when we rotate this rectangle, that attribute remains, of course. and every point on the side surface of the resulting cylinder has the same distance from the central x-axis : 8.

so, the radius is 8.

and the volume of a cylinder is

ground area × height = pi×r² × height

in our case

pi×8² × 5 (the width or "height" of the rectangle) = pi×64 × 5 = 320×pi

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The surface area of the square base pyramid is 138 inches².

The pyramid above is a square base pyramid. The surface area of the pyramid can be calculated as follows:

Therefore,

surface area of the pyramid = base area + 2al

where

Therefore,

a = 6 inches

l = 8.5 inches

Hence,

base area = 6² = 36 inches²

a = 6 inches

l = 8.5 inches

Therefore,

surface area of the pyramid = 36 + 2 × 6 × 8.5

surface area of the pyramid = 36 + 102

surface area of the pyramid = 138 inches²

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The company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.

In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.

Assuming that the failure of the flagship product follows a binomial distribution with a probability of 1% of failure within 2 years of purchase, let's calculate the expected cost to the company without a warranty and with the warranty.

Without the warranty, the expected cost to the company is given by:

Expected cost without warranty = 0.01 x $1300 = $13

With the warranty, the expected cost to the company is given by:

Expected cost with warranty = $5 - (0.99 x $0) = $5

Therefore, the company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.

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Using functions, we can find that the given equation is a quadratic equation so, the graph will be a parabola.

Option B is correct.

Simple functions like linear and quadratic functions are simple to graph. The fundamental concept behind graphing functions is to locate the shape, if at all possible. A line would be the graph of a linear function of the type f(x) = axe + b, for instance; a parabola would be the graph of a quadratic function of the form f(x) = ax² + bx + c.

By replacing some random x values into the function, one can locate some spots on it by determining the corresponding y values for each value.

Here in the question,

Given equation will be:

-(x+3)(x + 1)

Solving it we get:

= -x² -x + 3x + 3

= -x² + 2x + 3

So, graph for this function will be a parabola as the function is a quadratic function.

Therefore, the graph of the function will be the 2nd graph. Option B is correct.

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Answer:

10x^2 - 4x - 32

Step-by-step explanation:

(2x - 4)(5x + 8)

10x^2 + 16x - 20x - 32

10x^2 - 4x - 32

The selection method that assures a fair chance of being selected to go first between Carla and Hattie is A) Flip a fair coin. If it lands on heads, Carla will go first. If it lands on tails, Hattie will go first.

A fair chance is based on an equal probability of being selected.

A fair coin of head and tail offers a fair chance to two contenders on who should play the game first.

In this situation, since Carla gets the heads, he has 50% chance of being selected to go first.

Equally, Hattie has a 50% chance to go first getting the tails.

Thus, the correct selection method is Option A.

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Answer:

[tex]x=\dfrac{\ln \left(\frac{21}{25}\right)}{\ln 6125}[/tex]

Step-by-step explanation:

Given equation:

[tex]2 \cdot 5^{3x+2} = 6 \cdot 7^{1-2x}[/tex]

Divide both sides of the equation by 2:

[tex]\implies 5^{3x+2} = 3 \cdot 7^{1-2x}[/tex]

Take natural logs of both sides:

[tex]\implies \ln \left(5^{3x+2}\right) = \ln \left(3 \cdot 7^{1-2x}\right)[/tex]

[tex]\textsf{Apply the product law:} \quad \ln xy=\ln x + \ln y[/tex]

[tex]\implies \ln 5^{3x+2} = \ln 3 + \ln 7^{1-2x}[/tex]

[tex]\textsf{Apply the power law:} \quad \ln x^n=n \ln x[/tex]

[tex]\implies (3x+2)\ln 5 = \ln 3 + (1-2x)\ln7[/tex]

Expand:

[tex]\implies 3x\ln 5+2\ln 5=\ln 3+\ln7-2x\ln7[/tex]

Collect the terms in x on the left side and the constants on the right side of the equation:

[tex]\implies 3x\ln 5+2x\ln7=\ln 3+\ln7-2\ln 5[/tex]

Factor out the common term x on the left side:

[tex]\implies x(3\ln 5+2\ln7)=\ln 3+\ln7-2\ln 5[/tex]

[tex]\textsf{Apply the power law:} \quad n \ln x=\ln x^n[/tex]

[tex]\implies x(\ln 5^3+\ln7^2)=\ln 3+\ln7-\ln 5^2[/tex]

Simplify:

[tex]\implies x(\ln 125+\ln 49)=\ln 3+\ln7-\ln 25[/tex]

[tex]\textsf{Apply the product law:} \quad \ln x + \ln y=\ln xy[/tex]

[tex]\implies x(\ln (125 \cdot 49))=\ln (3\cdot 7)-\ln 25[/tex]

[tex]\implies x(\ln 6125)=\ln 21-\ln 25[/tex]

[tex]\textsf{Apply the quotient law:} \quad \ln x - \ln y=\ln \left(\dfrac{x}{y}\right)[/tex]

[tex]\implies x(\ln 6125)=\ln \left(\dfrac{21}{25}\right)[/tex]

Divide both sides of the equation by ln 6125:

[tex]\implies x=\dfrac{\ln \left(\frac{21}{25}\right)}{\ln 6125}[/tex]

Answer:

Step-by-step explanation:

you have to match the numbers on the lines of the plane, they have to match up with each other it goes (x,y) the x line is the one going to the side, and the y is the one going up to down

Hence ,10 Hispanic students in Ms. Vitals Wednesday night aerobics class.

Aerobics is a form of physical exercise that combines rhythmic aerobic exercise with strength and stretching training routines with the goal of improving all elements of fitness ( cardio-vascular fitness, flexibility and muscular strength ).

The percentage  can be  found by  dividing the  value by the total value and then multiplying the  result by 100. The formula  used to  calculate  the  percentage is: [tex]\frac{value}{total value}[/tex]×100%.

To find out  how many of the  students in Ms.  Vitals aerobics class are Hispanic,

first of all to determine  the percentage of students  are not African American or Caucasian.

The percentage  of students are African American is 30%, and the percentage are Caucasian is 45%. Therefore, the percentage of students are not African American or Caucasian is;

100% - 30% - 45% = 25%

So, 25% of  the students in the aerobics class are Hispanic.

To find the number of students are Hispanic,  we need to calculate 25% of the total number of  students;

25% of 40 students = [tex]\frac{25}{100}[/tex] x 40 = 0.25×40=10 students

Therefore, there are 10 Hispanic students in Ms. Vitals Wednesday night aerobics class.

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The scale of the drawing is 1 cm = 4.5 m. This means that each centimeter in the drawing represents 4.5 meters in the actual field. The length of the field in the drawing is 7.2 cm, so the actual length of the field is 7.2 cm × 4.5 m/cm = 32.4 m. The width of the field in the drawing is 3 cm, so the actual width of the field is 3 cm × 4.5 m/cm = 13.5 m. The area of a rectangle is found by multiplying its length by its width, so the area of the actual field is 32.4 m × 13.5 m = 437.4 m²

Note :- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √[tex](b^2 - 4ac)[/tex]) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √[tex]((-12)^2 - 4(2)(20)))[/tex] / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √[tex](144 - 160)[/tex]) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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If Natalia paid $12 for the necklace, then Each t- shirt cost $7.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

We are given that Natalia paid $40 for 4 t-shirts and a necklace.

If Natalia paid $12 for the necklace, then;

We need to find the cost of each shirt.

Therefore,

cost of 4 t- shirt + 1 neclace = 40

40 - 12 = 28

Cost of 4 t- shirt = 28

Cost of 1 t- shirt = 28/4 = 7      

Hence, the cost of each t shirt is $7.

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Answer: The group size is 32 friends.

Step-by-step explanation:

We will consider the total number of friends as x

The total expenditure can be broken down into the following equation:

85*x + 35 + 26*x = 3587

111x = 3587-35

111x = 3552

x = 3552/111

x = 32

95$

Step-by-step explanation:

Based on the given conditions, formulate ( 1100 - 720 ) ÷ 4

Calculate the sum or difference = 380/4

Cross out the common factor = 95

Answer:

C. 9 times larger

Explanation:

where, r = radius of a cylinder and h = height of the cylinder. This means that the volume of a cylinder will be 9 times larger if the radius is multiplied by 3.

The total surface area of diagram is 119.1 unit

A rectangular pyramid is a three-layered strong item that comprises of a rectangular base and four three-sided faces that meet at a typical point, called the summit.

In the figure below is a cuboid and upside is Square Pyramid;

Surface area of cuboid = 2 (l×h + l×w+ h×w)

Surface area of cuboid = 2 (6×3 + 6×3+ 3×3)  = 2 (18+18+9)

Surface area of cuboid = 90 unit²

The slant height is the hypotenuse of a right triangle whose height is 3 inches and half the base of the triangular (3/2 = 1.5 inches). Using the Pythagorean theorem,

slant height = [tex]\sqrt{3^2 + 1.5^2}[/tex]   [tex]= \sqrt{11.25}[/tex]

slant height = 3.35 unit

Surface Area of a Square Pyramid = base² + 2×base×slant height

Surface Area of a Square Pyramid = 3² + 2×3×3.35

Surface Area of a Square Pyramid = 9 + 20.1

Surface Area of a Square Pyramid = 29.1 unit²

The total area of these two faces =  Surface area of cuboid + Surface area of pyramid.

The total Surface area = 90 + 29.1 = 119.1 unit²

Therefore total area of diagram is 119.1 unit²

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Answer:

B.

Step-by-step explanation:

Since the line is from the top left to bottom right it's negative but if it was the opposite it would be positive.

The probability of selecting a car from the rental parking lot is 0.6 or 60%.

Probability of selection refers to the likelihood or chance of selecting a particular item or event from a group or population. It is a mathematical concept used in statistics, mathematics, and science to describe the likelihood of an event occurring, given the set of possible outcomes.

The probability of selecting a car from the rental parking lot can be found by dividing the number of cars by the total number of vehicles:

P(Car) = Number of Cars / Total Number of Vehicles

In this case, there are 5 trucks, 9 cars, and 1 van, so the total number of vehicles is:

Total Number of Vehicles = 5 + 9 + 1 = 15

Number of Cars = 9

Therefore, the probability of selecting a car from the rental parking lot is:

P(Car) = Number of Cars / Total Number of Vehicles

           = 9 / 15

           = 3 / 5

            = 0.6

So the probability of selecting a car from the rental parking lot is 0.6 or 60%.

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The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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