Triangle P is rotated 180° about (0, 0) to give triangle Q.
Triangle Q is translated by 5 -2
to give triangle R.
(a) Describe fully the single transformation that maps triangle P onto triangle R.

The values of x and y in the given figure are 10.5 and 15 respectively in the quadrilateral

We have to find the values of x and y in quadrilateral

4y+14+7y+1=180

Combine like terms

11y+15=180

Subtract 15 from both sides

11y=180-15

11y=165

Divide both sides by 11

y=15

The value of y is 15

Now 7x+1+105=180

7x+106=180

Subtract 106 from both sides

7x=180-106

7x=74

Divide both sides by 7

x=10.5

Hence, the values of x and y in the given figure are 10.5 and 15 respectively

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Answer:

32

Step-by-step explanation:

m∠S = tan⁻¹(5/8) = 32⁰

Answer: The regular price of the sofa is $705.71.

Step-by-step explanation:

Regular price = Sale price / (1 - Discount rate)

* 65% = 0.65

Regular price = $247 / (1 - 0.65) = $247 / 0.35 = $705.71

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Answer:Let's use the formula for the area of a sector to find the radius of the sector:

Area of sector = (1/2) * radius^2 * angle in radians

We know the area of the sector is 75pi/16 and the angle in radians is 3pi/8, so we can plug those values in and solve for the radius:

75pi/16 = (1/2) * radius^2 * 3pi/8

Simplifying:

75pi/16 = (3/16) * radius^2 * pi

Multiplying both sides by 16/3pi:

25 = radius^2

Taking the square root of both sides:

radius = ±5

Since a radius can't be negative, we have:

radius = 5

Therefore, the radius of the sector is 5 units.

Yes, an answer can be incorrect even if it looks reasonable

Yes, an answer can be incorrect even if it looks reasonable. This is because an answer might seem reasonable on the surface but may not be correct due to various reasons such as calculation errors, incorrect assumptions, or misinterpretation of the problem.

For instance, in a math problem that involves converting units of measurement, a student may have calculated the answer and arrived at a number that seems reasonable.

However, if the student used the wrong conversion factor or made an error in calculations, the answer would be incorrect despite appearing reasonable.

Similarly, in a word problem, an answer may seem reasonable but might not take into account all the given information, resulting in an incorrect solution.

Therefore, it is important to double-check answers and verify that they make sense in the context of the problem and that all the given information has been taken into account to ensure accuracy.

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The area of the irregular pentagon is determined using it's coordinates. Its area is: 30.5

First indicate the coordinates:

A (1,4)

B(4, 3)

C(4, -3)

D(-1-2)

E(-1.5, 2)

Using the shoe lace formula:

Area = (1/2) | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |

where n is the number of vertices, and

(x1,y1), (x2,y2), ..., (xn,yn) are the coordinates of the vertices in clockwise or counterclockwise order.

Plugging in the values,

Area = Area = (1/2) | (1*3 + 4*(-3) + 4*2 + (-1.5)*(-2) + (-1)*4) - (4*3 + 4*(-1.5) + (-1)*(-3) + 3*2 + (-2)*1) |

Area = 30.5

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The value of the quotient of 4 1/2 ÷ 2/3 is,

⇒ 27/4

We have to given that;

The expression is,

⇒ 4 1/2 ÷ 2/3

Now, We can simplify as;

⇒ 4 1/2 ÷ 2/3

⇒ 9/2 × 3/2

⇒ 27/4

Thus, The value of the quotient of 4 1/2 ÷ 2/3 is,

⇒ 27/4

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Every subgroup of Z is cyclic and is generated by a unique nonnegative integer. This property makes Z a particularly simple and well-behaved group for studying group theory.

Group theory is a branch of abstract algebra that studies mathematical structures called groups. Group theory provides a powerful framework for studying symmetry, structures, and transformations in various areas of mathematics, physics, chemistry, and other fields of science. It has applications in cryptography, coding theory, crystallography, quantum mechanics, and many other areas of science and engineering.

The set of integers subject to addition, or Z, is an example of an abelian group in group theory. A subset that also forms a group by addition is referred to as a subgroup of Z. It turns out that every Z subgroup is cyclic, i.e., created by a single element.

Let H be a subgroup of Z to be more precise. H is closed under addition since Z is an additive group, and it includes the identity element (0). We can demonstrate that H is produced by a, which means that every element in H can be written as a multiple of a, by looking at the lowest positive integer in H (if any), indicated as a. Thus, H becomes a cyclic subgroup with an as its generator.

Moreover, this generator a is exclusive to H. Assume that H contains a second positive integer b that likewise yields H. We can demonstrate that the set of multiples of a and b is indeed the same set, which suggests that a and b produce the same subgroup H. As a result, a = b, and H has a unique generator.

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The restrictions on the expression are x = -9/5 and x = -4 and the simplified expression is (2x - 1)/(x + 4)

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

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36}[/tex]

When the above expressions are factorized, we have

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]

To calculate the restrictions, we set the denominator to 0

So, we have

(5x + 9)(x + 4) = 0

Evaluate

x = -9/5 and x = -4

So, the restrictions are x = -9/5 and x = -4

Next, we simplify the expression

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]

Cancel out the common factors

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{2x - 1}{x + 4}[/tex]

Hence, the simplified expression is (2x - 1)/(x + 4)

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Answer: 2x

Step-by-step explanation: Separate variables from numbers, 4x-2x=2x, and 1-1=0. Therefore, the answer is 2x.

Answer:

2(x+1)

Step-by-step explanation:

Add you 1s together, than take a 2x out and that vies you 2 on the outside 2x/2= x and 2/2= 1 which gives you your answer.

Answer:

To find the gross profit, we need to subtract the cost of the dolls sold from the gross sales revenue (after returns have been deducted).

First, we need to calculate the net sales revenue, which is the gross sales revenue minus the returns:

Net sales revenue = Gross sales revenue - Returns

Net sales revenue = ₱42,356 - ₱3,479

Net sales revenue = ₱38,877

Next, we can calculate the gross profit:

Gross profit = Net sales revenue - Cost of goods sold

Gross profit = ₱38,877 - ₱27,212

Gross profit = ₱11,665

Therefore, the gross profit from the sale of the dolls is ₱11,665.

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Answer:

D. The data has an outlier, therefore the range will be much greater than it would be without the outlier.

Step-by-step explanation:

The given data consists of six values, ranging from 187 to 1984. The numbers are not listed in order. There is an obvious outlier value, 1984, which is potentially impacting the spread and central tendencies of the data. However, without calculating the range or interquartile range, it is difficult to determine the extent of its impact.

Answer:

d got it right in edge.

The number of parents you have to sample is calculated as: 5918

The formula for the margin of error here is:

E = z(σ/√n)

where:

E is margin of error

σ is standard deviation

n is sample size

We are given:

E = 2

σ = $78.5

At 95% Confidence Level, z = 1.96

Thus:

2 = 1.96(78.5/√n)

Square both sides to get:

4 = 23672.9/n

n = 23672.9/4

n = 5918

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The end behavior of f(x) is described as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The function for this problem is given as follows:

f(x) = 4(5/7)^x.

It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:

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Answer:

y = - [tex]\frac{1}{5}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 1 ← is in slope- intercept form

with slope m = 5

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex]

the y- intercept c = 6 , then

y = - [tex]\frac{1}{5}[/tex] x + 6 ← equation of line A

The expansion will be:

a) (x-6) (x+7) = x² + x - 42

b) (2x-3)(5x-4) = 10x² - 23x + 12

c (x+3)(x+5) = x² + 8x + 15

The factorization will be:

a) 2(x+3)

b) 3x(3x-4)

c) 2(12x² + 8x-1)

An equation simply has to do with the statement that illustrates the variables given.

In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Therefore, the expansion will be:

a) (x-6) (x+7) = x² + x - 42

b) (2x-3)(5x-4) = 10x² - 23x + 12

c (x+3)(x+5) = x² + 8x + 15

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Answer:

V = 16155.3 cubic feet

Step-by-step explanation:

The formula for volume (V) of a cone is

[tex]V=1/3\pi r^2h[/tex], where r is the radius and h in the height.

In the diagram, we're shown that the radius is 21 feet and the height is 35 feet.  Thus, we can plug everything into the formula including 3.14 instead of the entire pi number:

[tex]V=1/3(3.14)(21)^2(35)\\V=16155.3[/tex]

The area of the rhombus by decomposition is

The rhombus is decomposed into simpler elements which are

Area of 2 triangles

= 2 * 1/2 * base * height

= 2 * 1/2 * x * h

= 2 * 1/2 * 3 * 4

= 12 square units

Area of a parallelogram

= base x height

= y * h

= 5 * 4

= 20 square units

Area of the rhombus

= 20 square units + 12 square units

= 32 square units

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Answer:

B. chocolate-peanut butter cups and chocolate-caramel bites

Step-by-step explanation:

Chocolate-peanut butter cups cost $11.46 per pound, so one-half pound costs $5.73.

Chocolate-caramel bites cost $9.62 per pound, so one-half pound costs $4.81.

$5.73 + $4.81 = $10.54, so B is the correct answer.

Answer:

-1.75

Step-by-step explanation:

12.5 - (31 / 2) + 1 1/4 = -1.75

Answer:

D. 67 square inches

Step-by-step explanation:

The area of a 16-inch pizza is:

A = πr^2 = π(8)^2 = 64π

Since the pizza was cut into 12 equal slices, each slice has an area of:

64π / 12 = 16π/3

Each boy ate 4 slices, so the total area of pizza each boy ate is:

4(16π/3) = 64π/3

Rounding to the nearest whole square inch, we have:

64π/3 ≈ 67 square inches

Therefore, the answer is D. Each boy ate approximately 67 square inches of pizza.

Hope this helps!

Therefore the 95% confidence interval is,

(219.25, 534.75)

Here sample standard deviation is given but the sample size is large. Therefore we use z table to find the critical value.

Therefore the 90% confidence interval for the mean GPA for students at the University who are employed and who are not employed is,

(0.112, 0.308)

For the next problem,

We follow the same procedure as we have done in the first problem.

And here the data is different and we construct 95% confidence interval.

Therefore the 95% confidence interval is,

(219.25, 534.75)

And we interpret this confidence interval as,

We are 95% confident that the true difference in the mean daily caorie intake for teens who do eat fast food on a typical day and those who do not falls within this interval.

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Answer:

Katherine needs 1 unit of insulin for 15 g of carbohydrates.

Step-by-step explanation:

To find out how many units of insulin Katherine should inject for her lunch which has 60 g of carbohydrates, we can use the following proportion:

1 unit : 15 g = x units : 60 g

where x is the number of units of insulin Katherine should inject.

To solve for x, we can cross-multiply:

1 unit * 60 g = 15 g * x units

60 = 15x

x = 4

Therefore, Katherine should inject 4 units of insulin for her lunch.

To find MR, we take the derivative of the demand curve with respect to Q:

MR = dP/dQ = 900 - 0.06Q

To find MC, we need to take the derivative of the quadratic cost function with respect to Q:

C(Q) = 500 + 10Q + 0.005Q^2

MC = dC/dQ = 10 + 0.01Q

To find AC, we divide the total cost by the quantity:

AC = C(Q)/Q = (500 + 10Q + 0.005Q^2)/Q = 500/Q + 10 + 0.005Q

To find P, we use the demand curve and solve for Q:

P = 900 - 0.03Q

Q = (900 - P)/0.03

Explanation:

To find P, we use the demand curve and solve for Q:

P = 900 - 0.03Q

Q = (900 - P)/0.03

To find MR, we take the derivative of the demand curve with respect to Q:

MR = dP/dQ = 900 - 0.06Q

Now we can graph MC, AC, P, and MR:

|

P  |        /MR

  |       /

  |      /

  |     /

  |    /

  |   /

  |  / AC

  | /

MC |/

  |------------- Q

Note:

The graph is a rough sketch and not drawn to scale. The MC curve is upward-sloping, the AC curve is U-shaped, the P curve is downward-sloping, and the MR curve lies below the P curve and is also downward-sloping.

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The expressions B and C are equivalent to the given expression:

A logarithmic function is the inverse of an exponential function. In other words, if we have an exponential function that takes a base, b, and raises it to a power, x, to get a result, y, then the logarithmic function is the inverse of that process.

Simplify the expression using logarithmic property,

log m + log n = log (m.n)

Expression can be written as,

log₂(2) + log₂(8) = log₂(2x8)

                         = log₂ 16

simplify further,

log₂16 = log₂(2)⁴

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