Find the composition of transformations that
map ABCD to EHGF.
Reflect over the [? ]-axis, then translate
(x+[],y+[]).
Note: Enter x or y for axis.
4
7.
B C
o
Y
D
-1
3
2
0
2
3
H
4

Help

Find The Composition Of Transformations Thatmap ABCD To EHGF.Reflect Over The [? ]-axis, Then Translate(x+[],y+[]).Note:

Answers

Answer 1

the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).

What is axis reflection ?

An axis reflection is a transformation in geometry that involves reflecting a point, a line, or an object across a given axis. In two dimensions, there are two axes of reflection: the x-axis and the y-axis.

When reflecting over the x-axis, all points stay in the same horizontal position but change their vertical position, so a point (x,y) is reflected to (x,-y).

When reflecting over the y-axis, all points stay in the same vertical position but change their horizontal position, so a point (x,y) is reflected to (-x,y).

Axis reflections can be used to transform geometric shapes such as polygons, circles, or lines. These transformations have important applications in various fields, including physics, engineering, computer graphics, and art.

To find the composition of transformations that map ABCD to EHGF, we first need to determine the individual transformations that are needed.

Reflecting over the y-axis will change the x-coordinates of the points, but leave the y-coordinates unchanged. So, to reflect over the y-axis, we negate the x-coordinates of the points.

The translation (x+4, y+7) will move each point 4 units to the right and 7 units up.

Therefore, the composition of transformations is:

Reflect over the y-axis by negating the x-coordinates:

A'(-2, 3), B'(-4, 2), C'(-4, 0), D'(-2, -1)

Translate by (4,7):

A''(2, 10), B''(0, 9), C''(0, 7), D''(2, 6)

Therefore, the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).

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Related Questions

What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.

a cylinder with a radius labeled 2.6 meters and height labeled 6.1 meters

82 square meters
91 square meters
96 square meters
142 square meters

Answers

Answer:

142 square meters

Step-by-step explanation:

To find the Surface Area of a Cylinder you have to use the formula [tex]A= 2\pi rh+2\pi r^2[/tex]

Plug in the radius, height, and pi to get

[tex]A=(2*3.14*2.6*6.1)+(2*3.14*2.6^2)\\A= (99.6008)+(42.4528)\\A= 142.0536\\[/tex]

You can round the answer to 142

solve the equation x^3 - x^2 - 8x + 12=0

Answers

The root of this given equation is 2, -3.

What is a quadratic equation?

Any equation that can be written in standard form as where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation.

Here, we have

Given:  x³ - x² - 8x + 12 = 0

We have to solve this equation and find the roots.

x³ - x² - 8x + 12 = 0

= (x-2)(x²+ x - 6) = 0

= (x-2)(x² + 3x - 2x - 6)

= (x-2)(x(x+3)-2(x+3))

= (x-2)(x+3)(x-2) = 0

x = 2, -3

Hence, the root of this given equation is 2, -3.

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After solving  [tex]x^3 - x^2 - 8x + 12 = 0[/tex] we get x = 1,  x = √8, and x = -√8.

The equation[tex]x^3 - x^2 - 8x + 12 = 0.[/tex]

Identify the given equation.

The given equation is [tex]x^3 - x^2 - 8x + 12 = 0.[/tex]

Look for possible factorization.

In this case, we can factor the equation by grouping:

[tex]x^3 - x^2 - 8x + 12 = (x^3 - x^2) + (-8x + 12)[/tex]

Factor out the common terms in each group.

[tex]x^3 - x^2 - 8x + 12 = x^2(x - 1) - 8(x - 1)[/tex]

Factor out the common binomial.

[tex]x^3 - x^2 - 8x + 12 = (x^2 - 8)(x - 1)[/tex]

Solve the factors for x.

Set each factor to zero and solve for x:

[tex]x^2 - 8 = 0[/tex] and x - 1 = 0

[tex]x^2 = 8[/tex], x = 1

x = ±√8

The solutions to the equation [tex]x^3 - x^2 - 8x + 12 = 0[/tex] are x = 1, x = √8, and x = -√8.

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10. Patrick is walking around an amusement park looking at the following map. Use the following diagram
and the following information to calculate the desired distances. Sides of grid squares represent 500 feet.
(HINT: The statement in bold will be important when calculating your answers.) Round your answers to the
nearest hundredth.
Bumper Cars
-654-3 -2 -1
Water Slide
JA
1
-1-
23
3
Ferris Wheel
Rollercoaster
1 2 3 4 5 6
Restrooms.
a) How far must she travel from the Bumper Cars to the Ferris Wheel?
b) What is the distance from the Water Slide to the Rollercoaster?
c) How far is it from the Bumper Cars to the Restrooms?
feet
d) If Sasha gets a direct distance from the Water Slide to the Ferris Wheel, how far is it?

Answers

a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet or 1.5 miles. b)  1000 feet or 1 mile. c)  2000 feet or 2 miles. d) 2500 feet or 2.5 miles.

What is  distance?

Distance is the measurement of how far apart two points are on a surface.

a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet. To calculate this, we can count the number of squares (3) from the Bumper Cars to the Ferris Wheel. Each square represents 500 feet, so the total distance is 1500 feet or 1.5 miles.

b) The distance from the Water Slide to the Rollercoaster is 2 squares or 1000 feet.

To calculate this, we can count the number of squares (2) from the Water Slide to the Rollercoaster. Each square represents 500 feet, so the total distance is 1000 feet or 1 mile.

c) The distance from the Bumper Cars to the Restrooms is 4 squares or 2000 feet.

To calculate this, we can count the number of squares (4) from the Bumper Cars to the Restrooms. Each square represents 500 feet, so the total distance is 2000 feet or 2 miles.

d) The direct distance from the Water Slide to the Ferris Wheel is 5 squares or 2500 feet.

To calculate this, we can count the number of squares (5) in a straight line from the Water Slide to the Ferris Wheel. Each square represents 500 feet, so the total distance is 2500 feet or 2.5 miles.

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rational functions v and w both have a point of discontinuity at x=7 which equation could represent function w ?

Answers

Answer: The answer is C.

Step-by-step explanation:

The equation that could represent a rational function is answer C.

I hope this helped! A brainilist would be amazing! <3

Is 5:10 and 15:30 equivalent

Answers

Yes, 5:10 and 15:30 are equivalent ratios because they simplify to the same ratio of 1:2.

Ratios represent the relationship between two or more quantities or values. When two ratios have the same simplified form, they are considered equivalent because they represent the same relationship between the quantities being compared.

In the given example, the ratios 5:10 and 15:30 can be simplified to the same ratio of 1:2. This means that both ratios represent the same relationship between the quantities being compared. Specifically, both ratios represent a comparison between two quantities where the second quantity is twice as large as the first quantity.

To simplify a ratio, we divide both the numerator and denominator by their greatest common factor (GCF). The GCF is the largest number that divides evenly into both the numerator and denominator. In this case, the GCF of 5 and 10 is 5, and the GCF of 15 and 30 is 15. Dividing both ratios by their respective GCFs results in a simplified ratio of 1:2 for both ratios.

Therefore, 5:10 and 15:30 are equivalent ratios because they represent the same relationship between quantities, and have the same simplified form.

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Find the length of the segment indicated. Round your answer to the nearest tenth if necessary. (Please show step by step on how to figure this out! I want to understand!)

Answers

The length segment of the circle indicated is 6 units.

How to find the radius of a circle?

A circle is a round-shaped figure that has no corners or edges. Therefore, let's find the length segment of the circle.

Therefore, the diameter of a circle is the line that passes through the centre and meets the circumference at opposite ends.

Therefore, the radius of a circle is the distance from the centre of the circle to any point on it's circumference.

The radius is half of a diameter.

Therefore, the length x is the radius of the circle and it is 6 units.

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A square is graphed in a coordinate plane, with vertices at S(−3,0)
, H(2,0)
, A(2,5)
, and Q(−3,5)
. The square is then reflected across the x-axis to form the image S′H′A′Q′
.

Which statement is true?
S′H′¯¯¯¯¯¯¯¯¯¯¯
is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯
.

H′A′¯¯¯¯¯¯¯¯¯¯¯
is parallel to H′S′¯¯¯¯¯¯¯¯¯¯¯
.

A′Q′¯¯¯¯¯¯¯¯¯¯
is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯
.

Q′S′¯¯¯¯¯¯¯¯¯¯
is parallel to A′H′¯¯¯¯¯¯¯¯¯¯¯
.

Answers

The statement "S′H′ is parallel to S′Q′" is true.

How to find the correct statement?

To find the image of the square after reflection across the x-axis, we need to flip each point of the square over the x-axis. The coordinates of the reflected points will have the same x-coordinate, but the y-coordinate will have the opposite sign.

The coordinates of the original square are:

S(−3,0)

H(2,0)

A(2,5)

Q(−3,5)

The coordinates of the reflected square are:

S′(−3,0)

H′(2,0)

A′(2,−5)

Q′(−3,−5)

Now, we can find the slopes of the sides of the reflected square to determine which sides are parallel.

S′H′¯¯¯¯¯¯¯¯¯¯¯: The slope of S′H′¯¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the x-axis.

S′Q′¯¯¯¯¯¯¯¯¯¯: The slope of S′Q′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, S′Q′¯¯¯¯¯¯¯¯¯¯ is also parallel to the x-axis.

H′A′¯¯¯¯¯¯¯¯¯¯¯: The slope of H′A′¯¯¯¯¯¯¯¯¯¯¯ is undefined, since the two points have the same x-coordinate. Therefore, H′A′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the y-axis.

H′S′¯¯¯¯¯¯¯¯¯¯¯: The slope of H′S′¯¯¯¯¯¯¯¯¯¯¯ is also undefined, since the two points have the same x-coordinate. Therefore, H′S′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the y-axis.

A′Q′¯¯¯¯¯¯¯¯¯¯: The slope of A′Q′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, A′Q′¯¯¯¯¯¯¯¯¯¯ is parallel to the x-axis.

Q′S′¯¯¯¯¯¯¯¯¯¯: The slope of Q′S′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, Q′S′¯¯¯¯¯¯¯¯¯¯ is also parallel to the x-axis.

Based on these calculations, we can see that S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯ (both are parallel to the x-axis). Therefore, the statement "S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯" is true.

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Explain how you would organize your step-by-step calculations in evaluating the order of operations problem below. (Remember PEMDAS!) There should be five steps in this calculation. For full credit you must provide a step-by-step explanation as well as computation for the correct answer.


8÷2 (1+3) - 2^3

Answers

The steps that should be taken to evaluate the order of operations given are:

Solve for the brackets Solve for the exponents Solve the division Multiply by the result of the bracket Subtract the result of the exponents

How to solve with PEMDAS ?

To solve with PEMDAS, you first need to solve what is in the brackets in the order of operations given which is 8÷2 (1+3) - 2^3.

= 8÷2 (1+3) - 2^3

= 8÷2 x 4 - 2^3

Then solve for the exponents :

= 8÷2 x 4 - 2^3

= 8÷2 x 4 - 8

Then because the division comes first, you solve for that:

= 8÷2 x 4 - 8

= 4 x 4 - 8

You then solve for the multiplication as this takes precedence over subtraction:

= 4 x 4 - 8

= 16 - 8

Then solve the subtraction:

= 16 - 8

= 8

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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B is 95% salt. She wants to obtain 120 ounces of a mixture that is 75% salt. How many ounces of each solution should she use?

Answers

The number of ounces in solution A= 16, and the number of ounces in the solution B = 104

let x be the number of ounces of solution A

let y be the number of ounces of solution B

x+y=120

Substitute the value of y,

y=120-x

Solution A is 70% salt and B is 95% salt,

then

0.7x+.95y=.75(120)

0.7x+.95y=90

multiply both sides of the equation by 100 to remove the decimal points,

70x+95y=900

70x+95(120-x)=900

70x+1140-95x=900

-15x=900-1140

15x=240

x=16

and y=120-16

y=104

The number of ounces in solution A= 16

and the number of ounces in solution B = 104

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bob left his grandmothers house at 5:00 he drove for 2 hours and 22 minutes

Answers

Answer:

7:22

Step-by-step explanation:

Given: 2 hours and 22 minutes

5:00 + 2 hours

5 + 2 = 7

7:00 + 22 minutes

7:22

help pls show ur work

Answers

21. The trainer raised the end of the treadmill from the floor by 0.62 ft or 7.4 in.

22. The ramp needs to be 1.19 ft tall at the highest point.

23. The springboard is 6.21 in long.

What is  trigonometric ratio?

Trigonometric ratio is the ratio of two sides of a right triangle to each other, or the ratio of the sine, cosine, or tangent of an angle in a right triangle.

21: Incline = 7°

Length of walking surface = 5 ft

We need to calculate the change in height of the treadmill.

Let x be the height of the end of the treadmill from the floor.

We can use the trigonometric ratio, tangent (tan), to solve the problem.

tan(7°) = Opposite/Adjacent

=> x/5 = tan(7°)

=> x = 5tan(7°)

=> x = 5×0.124

=> x = 0.62 ft

22: Angle = 20°

Length of board = 3.5 ft

We need to calculate the height of the ramp at the highest point.

Let y be the height of the ramp at the highest point.

We can use the trigonometric ratio, sine (sin), to solve the problem.

sin(20°) = Opposite/Hypotenuse

=> y/3.5 = sin(20°)

=> y = 3.5sin(20°)

=> y = 3.5×0.342

=> y = 1.19 ft

23: Angle = 14.5°

Length of springboard coils = 6 in

We need to calculate the length of the springboard.

Let z be the length of the springboard.

We can use the trigonometric ratio, cosine (cos), to solve the problem.

cos(14.5°) = Adjacent/Hypotenuse

=> 6/z = cos(14.5°)

=> z = 6/cos(14.5°)

=> z = 6/0.966

=> z = 6.21 in

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22. Morality In a recent poll, the Gallup Organization found
that 45% of adult Americans believe that the overall state of
moral values in the United States is poor. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that

(a) exactly 250 of those surveyed feel the state of morals is poor.
(b) no more than 220 of those surveyed feel the state of morals is poor.
(c) more than 250 of those surveyed feel the state of morals is poor.
(d) between 220 and 250, inclusive, believe the state of morals is poor.
(e) at least 260 adult Americans believe the overall state of
moral values is poor. Would you find this result unusual? Why?

Answers

The probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.

(To find the probability that exactly 250 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.

Then, we can standardize the value of 250 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.

z = (250 - 225) / 10.42 ≈ 2.4

Using a standard normal table or calculator, we find that the probability of z being less than or equal to 2.4 is approximately 0.9918.

Therefore, the probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.

(b) To find the probability that no more than 220 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.

Then, we can standardize the value of 220 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.

z = (220 - 225) / 10.42 ≈ -0.48

Using a standard normal table or calculator, we find that the probability of z being less than or equal to -0.48 is approximately 0.3146.

Therefore, the probability that no more than 220 of those surveyed feel the state of morals is poor is approximately 0.3146.

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Suppose on your 21st birthday you begin saving $500 quarterly into an account that pays 12% compounded quarterly. If you continue the savings until your 51st birthday (30 years), how much money will be in the account?

Answers

Answer:$386,711.70

Step-by-step explanation:

To solve the problem, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value

PMT = payment per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

First, we need to find the number of compounding periods and the interest rate per quarter:

n = 4 (quarterly compounding)

r = 0.12 / 4 = 0.03 (3% quarterly interest rate)

Next, we can plug in the values:

PMT = $500

n = 4

r = 0.03

t = 30

FV = $500 x [(1 + 0.03/4)^(4*30) - 1] / (0.03/4)

FV = $500 x [(1 + 0.0075)^120 - 1] / 0.0075

FV = $500 x [6.3207 - 1] / 0.0075

FV = $500 x 773.4234

FV = $386,711.70

Therefore, if you save $500 quarterly into an account that pays 12% compounded quarterly from your 21st to your 51st birthday, you will have approximately $386,711.70 in the account.

In this case, we have:
P = $500
r = 0.12 (12% as a decimal)
n = 4 (since interest is compounded quarterly)
t = 30 (the number of years)

Plugging in the values, we get:

A = $500(1 + 0.12/4)^(4*30)
A = $500(1 + 0.03)^120
A = $500(1.03)^120
A = $500(15.5919)
A = $7,795.96

Therefore, after 30 years of quarterly savings at a 12% interest rate compounded quarterly, there will be approximately $7,795.96 in the account.

Fran and Jill made a new years resolution to ride bikes. Fran rode 40 miles last week
and plans to ride 55 miles per week. Jill rode 70 miles last week and plans to ride 45
miles per week. Predict the week in which Fran and Jill will have ridden the same
number of miles.

A.) 4 weeks

B.) 3 weeks

C.)They will never ride the same number

D.) 5 weeks

Answers

If Fran and Jill made a new years resolution to ride bikes.  it will take 3 weeks for Fran and Jill to have ridden the same number of miles..

How to find the number of weeks?

Let's assume that it takes "x" number of weeks for Fran and Jill to ride the same number of miles.

In the first week, Fran rides 40 miles, and Jill rides 70 miles.

In the "x"th week, Fran will have ridden a total of 40 + 55x miles.

In the "x"th week, Jill will have ridden a total of 70 + 45x miles.

For Fran and Jill to ride the same number of miles in "x" weeks, we need to solve the following equation:

40 + 55x = 70 + 45x

Simplifying this equation, we get:

10x = 30

x = 3

Therefore, it will take 3 weeks for Fran and Jill to have ridden the same number of miles.

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(13 points)
A gardener would like to add to their existing garden to make more flowers available for the butterflies that visit the garden. Her current garden is 45 square feet. If she added another rectangular piece with vertices located at (−21, 7), (−23, 7), (−21, 12), and (−23, 12), what is the total area of the garden?

A: 10 ft2
B: 55 ft2
C: 225 ft2
D: 450 ft2

no image

Answers

Total area of garden after adding rectangular piece will be 55 ft² i.e. B.

What exactly is a rectangle?

A rectangle is a two-dimensional geometric shape that is characterized by having four sides and four right angles. Opposite sides of a rectangle are parallel and equal in length, while opposite angles are equal. The area of a rectangle can be calculated by multiplying its length by its width, while its perimeter is the sum of the lengths of all its sides. Rectangles are commonly used in many fields, such as architecture, engineering, and mathematics.

Now,

The rectangle has a length of |-21 - (-23)| = 2 and a width of |7 - 12| = 5. Therefore, the area of the new rectangular piece is 2 x 5 = 10 square feet.

Adding this to the area of the existing garden gives a total area of 45 + 10 = 55 square feet.

Therefore, the answer is (B) 55 ft².

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A street that is 186 m long is covered in snow. City workers are using a snowplow to clear the street. A tire on the snowplow has to turn 31 times in traveling the length of the street. What is the diameter of the tire? Use the value 3.14 for PI . Round your answer to the nearest tenth. Do not round any intermediate steps.

Answers

Answer:

The number of times the tire will have to turn in travelling the length of the street is 30.9 times.

To determine the number of times the tire will have to turn in travelling the length of the street, we will first calculate the circumference of the tire.  

Since the tire is circular, the circumference of the tire can be calculated from the formula for calculating the circumference of a circle.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 1.7m and π = 3.14

∴ C = 3.14 × 1.7

C = 5.338 m

Therefore, the circumference of the tire is 5.338 m

Now, for the number of times the tire will have to turn in travelling the length of the street, we will divide the length of the street by the circumference of the tire.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 165 m ÷ 5.338 m

Number of times the tire will have to turn = 30.91045 times

Number of times the tire will have to turn ≅ 30.9 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 30.9 times

Simplify the following expression. Write your answer using positive exponents.

Answers

After simplifying the given expression we can write answer using positive exponent [tex]7^3 * 6^30[/tex].

What is expression?

In mathematics, an expression is a combination of numbers, variables, and symbols that are grouped together to represent a mathematical relationship or quantity. It can be a single term, or a combination of terms separated by mathematical operations such as addition, subtraction, multiplication, and division.

When we raise a power to another power, we need to multiply the exponents. So we can simplify the expression as follows:

[tex]7^3(6^6)^5 = 7^3 * 6^(6*5) = 7^3 * 6^30[/tex]

so we write the answer using positive exponents as:

[tex]7^3 * 6^30[/tex]

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Find the area of a rectangular park whose perimeter is 320m and length is 90m.

Answers

First, 90 + 90 = 180

Second, 320 - 180 = 140

Third, 140 / 2 = 70.

|                                90 * 70 = 6,300
|
|
| 90
|
|____________

         70

calculo del incremento %
se tiene 5430 y se gasto 1150
¿que porcentaje de dinero se gasto?​

Answers

21.12%

1150/5430=0.21178631
0.21178631(100)=21.12%

Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2

Answers

The first second and last are equivalent

Integers a and b are such that
[tex](a + 3 \sqrt{5} ) {}^{2} + a - b \sqrt{5} = 51 [/tex]
Find the possible values of a and the corresponding values of b.
(Answers are a= -3 , 2 and b= -18 , 12. But I don't know how to show the working so please help, thx)​

Answers

The possible values of a and the corresponding values of b are; a= -3, 2 and b= -18, 12.

How to calculate possible and the corresponding values?

Expanding the left-hand side of the equation:

(a + 3√5)² + a - b√5 = a² + 6a√5 + 45 + a - b√5

Combining like terms:

2a² + (2a - b)√5 + 45 = 51

Simplifying further:

2a² + (2a - b)√5 = 6

Now, since √5 is irrational, the only way the left-hand side can equal 6 is if both the rational and irrational parts are equal to 0. Therefore two equations:

2a² + 2a - b = 0 (Equation 1)

2a - b = 0 (Equation 2)

Solving Equation 2 for b:

b = 2a

Substituting this into Equation 1:

2a² + 2a - 2a = 0

Simplifying:

2a² = 0

Thus, a = 0 is a solution. However, a = 0 does not satisfy the original equation, since the left-hand side would be 45, which is not equal to 51. Therefore, we can divide both sides of Equation 1 by 2a to get:

a + 1 - b/2a = 0

Multiplying both sides by 2a:

2a² + 2a - b = 0

Substituting b = 2a:

2a² + 2a - 2a = 0

Simplifying:

2a² = 0

Thus, a = 0 is a solution. However, as noted above, a = 0 does not satisfy the original equation. Therefore, we must consider the case where a ≠ 0. Dividing both sides of Equation 2 by 2:

a - b/2 = 0

Solving for b:

b = 2a

Substituting into the original equation:

(a + 3√5)² + a - 2a√5 = 51

Expanding:

a² + 6a√5 + 45 + a - 2a√5 = 51

Combining like terms:

a² + 7a√5 - 6 = 0

Using the quadratic formula:

a = (-7√5 ± √(7²√5² - 4(1)(-6))) / 2(1)

Simplifying:

a = (-7√5 ± 13) / 2

Therefore, the possible values of a are -3 and 2. For each value of a, we can use b = 2a to find the corresponding value of b. Thus, the possible values of b are -18 and 12.

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What’s the interest?

Answers

Amount Due at Maturity a. $102,000, b. $30,100, c. $62,620, d. $42,930, e. $40,700.

Describe Interest?

Interest is the cost of borrowing money, typically expressed as a percentage of the borrowed amount, called the principal. It is the amount charged by a lender to a borrower for the use of money over a certain period of time. Interest can also refer to the amount earned on money that is invested, such as in a savings account or a bond. The rate of interest depends on factors such as the level of risk associated with the loan, the length of the loan period, and the market rate of interest at the time of borrowing. The amount of interest paid or earned can be calculated using various formulas, including simple interest and compound interest.

To determine the due date and amount of interest due at maturity for each note, we can use the following formula:

Interest = Principal x Rate x Time

where Principal is the face amount of the note, Rate is the annual interest rate, and Time is the time in years (based on a 360-day year).

a. January 5, $100,000, 6%, 120 days

Due Date: May 5

Time: 120/360 = 1/3 year

Interest = $100,000 x 0.06 x 1/3 = $2,000

Amount Due at Maturity = Principal + Interest = $100,000 + $2,000 = $102,000

b. February 15, $30,000, 4%, 30 days

Due Date: March 17 (assuming non-leap year)

Time: 30/360 = 1/12 year

Interest = $30,000 x 0.04 x 1/12 = $100

Amount Due at Maturity = Principal + Interest = $30,000 + $100 = $30,100

c. May 19, $62,000, 8%, 45 days

Due Date: July 3

Time: 45/360 = 1/8 year

Interest = $62,000 x 0.08 x 1/8 = $620

Amount Due at Maturity = Principal + Interest = $62,000 + $620 = $62,620

d. August 20, $42,400, 5%, 90 days

Due Date: November 18

Time: 90/360 = 1/4 year

Interest = $42,400 x 0.05 x 1/4 = $530

Amount Due at Maturity = Principal + Interest = $42,400 + $530 = $42,930

e. October 19, $40,000, 7%, 90 days

Due Date: January 17

Time: 90/360 = 1/4 year

Interest = $40,000 x 0.07 x 1/4 = $700

Amount Due at Maturity = Principal + Interest = $40,000 + $700 = $40,700

Therefore, the due date and amount of interest due at maturity for each note are as follows:

a. Due Date: May 5, Interest: $2,000, Amount Due: $102,000

b. Due Date: March 17, Interest: $100, Amount Due: $30,100

c. Due Date: July 3, Interest: $620, Amount Due: $62,620

d. Due Date: November 18, Interest: $530, Amount Due: $42,930

e. Due Date: January 17, Interest: $700, Amount Due: $40,700

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What is the probability of Meikel wearing khakis and sandals?Help.



3/21

1/4

4/8

1/2

Answers

Step-by-step explanation:

The probability of Meikel wearing khakis and sandals is

3 ÷ 12 which will give us

1/4

Find the area of the parallelogram.

Answers

Answer: 33.34

Step-by-step explanation: first we have to cut this shape up like you would a pizza

2 triangles and 1 rectangle, we know that the rectangle is 10 by 3 cm, but we don't have all the measurements for the triangle.

Find the last side using this equation:
3.2 squared = 10.24
3 squared = 9
subtract
1.24
square root of 1.24 = 1.11

Area of rectangle:
10 x 3 = 30
Area of triangle:
1.11 x 3 ≈ 1.67

Final Area:
30 + 1.67x2 = 33.34

9.6 because for area, you multiply the 2 numbers in this case 3 x 3.2 = 9.6

Police plan to enforce speed limits by using radar traps at four different locations within the
national limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated
40%, 20%, 30%, and 40% of the time. A person who is speeding on her way to work has
probabilities of 0.3, 0.1, 0.4, and 0.2 respectively, of passing through these locations.
Let S be the event that radar traps was set and Li be the locations i, i = 1, 2, 3 or 4.
If the person received a speeding ticket on her way to work, what is the probability
that she passed through the radar trap located at L2?Draw a tree diagram with the notation and probabilities provided

Answers

Using Bayes theorem, the probability that the person passed through the radar trap located at L2 given that she received a speeding ticket is 0.059 or 5.9%.

What is the probability that the person passed through the radar trap located at L2

We can solve this problem using Bayes' theorem. Let A be the event that the person received a speeding ticket, and Bi be the event that the radar trap was set at location Li, for i = 1, 2, 3, or 4. Then we want to find the conditional probability of B22 given A, which is:

[tex]P(B_2 | A) = P(A | B_2) * P(B_2) / P(A)[/tex]

We can compute each of the probabilities on the right-hand side using the given information.

First, we have:

[tex]P(B_1) = 0.4, P(B_2) = 0.2, P(B_3) = 0.3, P(B_4) = 0.4[/tex]

Next, we have:

[tex]P(A | B_1) = 0.3, P(A | B_2) = 0.1, P(A | B_3) = 0.4, P(A | B_4) = 0.2[/tex]

Finally, we have:

[tex]P(A) = P(A | B_1) * P(B_1) + P(A | B_2) * P(B_2) + P(A | B_3) * P(B_3) + P(A | B_4) * P(B_4)\\= (0.3 * 0.4) + (0.1 * 0.2) + (0.4 * 0.3) + (0.2 * 0.4)\\= 0.34[/tex]

Plugging these values into Bayes' theorem, we get:

[tex]P(B_2 | A) = P(A | B_2) * P(B_2) / P(A)\\= (0.1 * 0.2) / 0.34\\= 0.059\\[/tex]

Therefore, the probability that the person passed through the radar trap located at L2 given that she received a speeding ticket is 0..059 or 5.9%.

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will give brainliest if both questions are answered

Answers

Answer:

17) x = 23;18) x = 30.

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

Question 17

Angle with the measure of 130° forms a vertical angle pair with the sum of x and 107° angle.

Since vertical angles are congruent we have:

x + 107 = 130x = 23

Question 18

The two angles, x and 2x together form a right angle, since they form a linear pair with another angle, marked as right angle. Therefore, x and 2x are complementary angles:

x + 2x = 903x = 90x = 30

Solve the following inequality.

Negative one-half p less-than negative 16

Which graph shows the correct solution?
A number line going from 27 to 37. An open circle is at 32. Everything to the right of the circle is shaded.
A number line going from 27 to 37. An open circle is at 32. Everything to the left of the circle is shaded.
A number line going from 3 to 13. An open circle is at 8. Everything to the left of the circle is shaded.
A number line going from 3 to 13. An open circle is at 8. Everything to the right of the circle is shaded.

Answers

After answering the prοvided questiοn, we can cοnclude that As a result, the sοlutiοn tο the inequality is p greater than 32.

What is inequality?

In mathematics, an inequality is a nοn-equal relatiοnship between twο expressiοns οr values. As a result, imbalance leads tο inequality. In mathematics, an inequality cοnnects twο values that are nοt equal. Inequality is nοt the same as equality. When twο values are nοt equal, the nοt equal sign is cοmmοnly used ().

Different inequalities, nο matter hοw small οr large, are used tο cοntrast values. Many simple inequalities can be sοlved by mοdifying the twο sides until οnly the variables remain. Hοwever, a number οf factοrs cοntribute tο inequality: Negative values are divided οr added οn bοth sides. Exchange left and right.

We must isοlate the variable p οn οne side οf the inequality sign in οrder tο sοlve it.

-16 negative οne-half p

When bοth sides οf the inequality are multiplied by -2 (and the inequality sign is reversed because we are multiplying by a negative number), we get:

p > 32

As a result, the sοlutiοn tο the inequality is p greater than 32.

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D
Question 3
A mobile home company is new homes with the property of each home
measuring 30 feet wide. If the length of the street is 345 feet, how many
houses can be placed on the street?
1

Answers

The maximum number of homes that can be placed on the street is 11.

To calculate the number of houses that can be placed on the street

first we need to divide the total length of the street by the width of each home.

The length of the street is 345 feet and the width of each home is 30 feet. Therefore, the number of homes that can be placed on the street is:

345 feet / 30 feet per home = 11.5 homes

Since we cannot have a fraction of a home, we need to round down to the nearest whole number.

Therefore, the maximum number of homes that can be placed on the street is 11.

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Statistical measures are shown for the number of hours per week spent doing homework by the students in two classes. Class 1: mean number of hours spent doing homework = 20,mean absolute value deviation = 2. Class 2: mean number of hours spent doing homework = 24, mean absolute value deviation = 2. The difference between the means of the two data sets is ___

Answers

The difference between the means of the two data sets is 4.

How to determine the difference between the means of the two data sets?

Statistical measures are used to describe, analyze, and interpret data. There are several measures that are commonly used in statistics, such as mean, median, mode, standard deviation, etc.

The mean, also known as the average, is the sum of all the values in a dataset divided by the total number of values. It represents the central tendency of the data.

The difference between the means of the two data sets is:

difference between the means = (Class 2 mean) - (Class 1 mean)

difference between the means = 24 - 20 = 4

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. QUESTION 8: You are 765 feet above in the air. You are descending at a rate of 12 feet per minute. Write an equation in slope intercept form to represent this situation. b: Equation:​

Answers

Step-by-step explanation:

You need the line in y = mx + b form:

y = -12x + 765        where x = minutes     y = height in feet

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