Suppose that some resource x is necessary to produce some good y. If the price of x rises.

APUQ = ASUR, which proves that the two triangles are congruent.

To prove that APUQ = ASUR, we can use the concept of parallel lines and corresponding angles.

Since PQ || RS and PQ = RS, we can conclude that corresponding angles are equal.

In the figure, angle APU and angle ASR are corresponding angles and are therefore equal.

Also, angle UQP and angle USR are corresponding angles and are therefore equal.

Since the angles APU and UQP add up to 180 degrees (because they form a straight line), we can conclude that angle APU = 180 - UQP.

Similarly, angle ASR = 180 - USR.

Therefore, APU + UQP = ASR + USR

So, APUQ = ASUR, which proves that the two triangles are congruent.

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a. The line of the best fit is ŷ = -8.55485X + 118.39451.

b. The value of the correlation coefficient is  -0.8619.

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Sum of X = 117.4

Sum of Y = 298

Mean X = 10.6727

Mean Y = 27.0909

The sum of squares (SSX) = 0.8618

The sum of products (SP) = -7.3727

Regression Equation = ŷ = bX + a

b = SP/SSX = -7.37/0.86 = -8.55485

a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451

ŷ = -8.55485X + 118.39451

X Values

∑ = 117.4

Mean = 10.673

∑(X - Mx)² = SSx = 0.862

Y Values

∑ = 298

Mean = 27.091

∑(Y - My)² = SSy = 84.909

X and Y Combined

N = 11

∑(X - Mx)(Y - My) = -7.373

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -7.373 / √((0.862)(84.909)) = -0.8619

Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451

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the slopes would look like this

The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

c represents the constant.

Next, we would solve the above quadratic function by using the factorization method;

x² + x - 72 = 0

x² - 8x + 9x - 72 = 0

x(x - 8) + 9(x - 8) = 0

(x + 9)(x - 8) = 0

(x + 9)(x - 8) = (x + a)(x - b).

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80 times, the house should be cleaned to buy the car.

Equation for the amount is y = 50t + 500

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Given,

Amount in the savings = $500

Amount to get the car = $4500

Grandma pays $50 for every time after cleaning

then, after t times, the amount will be

y = 50 t + 500

here, y is the total amount after working

t is number of times of cleaning the house

For $4500

4500 = 50t + 500

50t = 4500 - 500

50t = 4000

t = 4000/50

t = 80

Hence, we have to clean the house 80 times to have $4500.

equation for the amount is y = 50t + 500

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The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.

Let the two lines be ax + by + c₁ = 0 and ax + by + c₂ = 0. Then the distance between the lines is given as,

d = |c₂ - c₁| / √(a² + b²)

Let the distance between Line AB and A'B' be d and the equation of the line AB be ax + by + c₁ = 0. Then the value of c₂ is given as,

d = |c₂ - c₁| / √(a² + b²)

d√(a² + b²) = c₂ - c₁

c₂ = d√(a² + b²) + c₁

Then the equation of the line A'B' is given as,

ax + by + c₂ = 0

ax + by + d√(a² + b²) + c₁ = 0

The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.

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250 in the function given represents the exponential constant.

Given is the exponential function as -

y = 250(2.3)ˣ

In the exponential function given, 250 represents the exponential constant.

An exponential function is of the form -

y = A(B)ˣ

Therefore, 250 in the function given represents the exponential constant.

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Answer: I guess its 10?

Step-by-step explanation:

Answer:28

Step-by-step explanation:

4x/7=24

x=42(total workers)

male workers=42-24=28

The equation that determines how many text messages Bria sent is given as follows:

t/4 = 20.

The number of messages that Bria sent is obtained applying the proportions in the context of the problem.

The amount sent by April is given as follows:

20 messages.

20 is one fourth of the amount t sent by Bria, hence the equation is given as follows:

t/4 = 20.

The number of messages sent by Bria is then given as follows:

t = 20 x 4

t = 80 messages.

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The area of the given triangle is approximately 204.2 square inches.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

To calculate the area of a triangle with given side lengths, we can use Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.

In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:

s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5

Now we can plug in these values into the formula and simplify:

Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16

Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.

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The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.

We can start with the equation AB = AC and multiply both sides by A^-1 on the left:

A^-1(AB) = A^-1(AC)

Using the associative property of matrix multiplication, we can simplify the left-hand side:

(A^-1A)B = (A^-1A)C

Using the fact that A^-1A = I (the identity matrix), we get:

IB = IC

Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:

B = C

Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.

The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.

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Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

Answer: 6 and 1/3

Step-by-step explanation:

Assuming that sweet generous little Marcus here wants some muffins too, he has to share 19 blueberry muffins between 3 people (Marcus + friend 1 + friend 2.)

Most unfortunately, 19 isn't divisible by 3 to create a whole number (ie. a whole muffin).

Therefore you have 2 options:

Option 1:

19/3 = 6.333....

This means that each person will get 6 and 1/3 of a muffin

Option 2:

19/3 = 6 (and 1 remainder)

This means that each person will get 6 muffins each, but there will be a leftover muffin to feed the birds or something.

(I personally prefer option 2, but I think your teacher is looking for option 1.)

The graph represents a function because the graph passes the vertical line test option (A),

Yes, the graph that passes the vertical line test is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Here, The graph is attached to the picture, please refer to the picture.

Now, We have a graph shown in the picture.

The graph represents the parabola.

As we know, if the graph passes the vertical line test then it can be a function.

Thus, the graph represents a function because the graph passes the vertical line test option (C) Yes, the graph that passes the vertical line test is correct.

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Answer:

bottom-right

Step-by-step explanation:

the points on the graph are scattered and have no correlation whereas the others all remain in a relatively similar shape

Rounding to the nearest whole number, we get that the score a student would need to have a 30th percentile score on the SAT is 1345.  Correct option is B.

To find the score corresponding to the 30th percentile, we need to use the standard normal distribution with a mean of 0 and a standard deviation of 1. We can convert the SAT score to a standard normal score using the formula:

z = (x - μ) / σ

where x is the SAT score, μ is the mean score (1509), and σ is the standard deviation (312).

To find the score corresponding to the 30th percentile, we need to find the z-score that has an area of 0.30 to its left. Using a standard normal table or calculator, we can find that the z-score corresponding to a 30th percentile is approximately -0.52.

Now we can use the formula to find the corresponding SAT score:

-0.52 = (x - 1509) / 312

Solving for x, we get:

x = -0.52 * 312 + 1509 = 1345.36

Therefore, the answer is (b) 1345.

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The expression 14/20 is equivalent to 7/10

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Given the expression:

14/20

The common term between the numerator and denominator is 2. Hence:

= 7/10

The expression 14/20 is equivalent to 7/10

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The solution is, a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements are,

x+ y ≥ 330

y≥ 30

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

given that,

One such airline requires that each passenger and his bag weighs no more than 330 lbs.

On this airline, each passenger is allowed to bring exactly one bag that weighs at most 30 lbs.

let, the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements.

so, a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements are,

x+ y ≥ 330

y≥ 30

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The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.

The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :

The mean formula is written thus :

Population mean = Σx / N

Sample mean = Σx / n

Where, x = set of values.

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Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

The length of the guy wire, to the nearest foot, is 109 feet.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

From the diagram.

ΔABE is similar to ΔCDE.

CD = 9 ft

DE = 1 ft

BD =11 ft

And we know,

ΔABE ~ ΔCDE.

So, the corresponding sides of similar triangles,

AB/CD = BE/DE

AB/9 = (11 + 1)/1

AB/9 = 12

AB = 12 x 9

AB = 108 feet.

To find AE:

Applying Pythegoras' theorem,

we get,

AE = √(AB² + BE²)

AE = √(108² + 12²)

AE = 108.67

Therefore, AE = 109 feet.

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The factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).

To factor the trinomial 2x² - 2x - 3x + 9 using the box method, we first draw a box and divide it into four sections:

   | 2x  -3 |

   |--------|

   | -2x  9 |

Then, we fill in the top left section with the coefficient of the leading term, 2x, and the bottom right section with the constant term, 9.

   | 2x  -3 |

   |--------|

   | -2x  9 |

Next, we find two numbers that multiply to 2x * 9 = 18 and add to the coefficient of the middle term, -2x - 3x = -5x.

One way to do this is to factor out 2 from the leading two terms, giving 2x² - 2x - 3x + 9 = 2x(x - 1) - 3(x - 3), and then finding the product of (x - 1) and (x - 3) using the AC method:

AC method:

2x(x - 1) - 3(x - 3) = 2x(x - 1) - 3x + 9 - 3(-1)

We can then place these two numbers in the remaining two sections of the box:

   | 2x  -3 |

   |--------|

   | -2x  9 |

   | 2x  -3 |

   |--------|

   | -2x  9 |

   |--------|

   | -3   1 |

We can now factor the trinomial by taking the common factor out of each row and column of the box:

2x(x - 1) - 3x + 9 - 3(-1)

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

Therefore, the factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).

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The probability that you deal the 7 of Spades followed by a King is 0.1.

Given is that you randomly shuffle a deck of cards and deal two cards from the top.

We can write the probability as -

P{E} = 1/52 + 4/51

P{E} = 0.02 + 0.08

P{E} = 0.1

Therefore, the probability that you deal the 7 of Spades followed by a King is 0.1.

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Answer:

+5&-2

Step-by-step explanation:

The height of the cone in discuss as required to be determined is; 16.38 cm.

Since the height of the cone is three times the length of the diameter of its base;

h = 3d;

d = h/3

Therefore, radius,

r = d/2

r = h/3 ÷ 2

multiply by the reciprocal of 2

r = h/3 × 1/2

r = h / 6.

Volume of a cone, V = (1/3) πr²h

128 = (1/3) × (22/7) × (h³/36)

h³ = 4398.55

h = 16.38 cm.

Ultimately, the height of the cone is; 16.38 cm.

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The solution for f the angle ∠DEF will be 122°.

Geometry is the study of two- and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles.

Symmetry is defined as if the object is cut by its centre line the two cut parts should be the mirror image of each other so that we can call them symmetric to each other.

Given that the angles are:-

∠DCE = (3x + 16)°

∠DEF = (6x - 10)°

∠CDE = (2x - 4)°

In the triangle ΔCDE,

∠DEC = 180 - 3x - 16 - 2x + 4

∠DEC = (-5x + 168)°

∠DEC  + ∠DEF = 180

5x + 168 + 6x - 10 = 180

x = 180 - 158

x = 22

The value of the ∠DEF is,

∠DEF = 6x - 10

∠DEF = 6 x 22 - 10

∠DEF = 122°

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Answer: The coordinates where the two lines intersect are (-5, -8).

Step-by-step explanation:
To find the coordinates where the two lines intersect, we need to solve the system of equations simultaneously. We can do this by substitution or elimination, but we'll use substitution here:

First, we set the two equations equal to each other:

x - 3 = 2x + 2

Next, we solve for x:

x - 2x = 2 + 3

-x = 5

x = -5

Now that we have the value of x, we can substitute it into one of the original equations to find the corresponding value of y. Let's use the first equation:

y = x - 3

y = (-5) - 3

y = -8

The total cost is $76.32.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Juan lives in a state where sales tax is 6%.

The modeled Equation is:

c + 0.06c, where c is the pre-tax price of the item.

If we have the pre-tax price of $72.00.

Total cost = 1.06 c

                 = 1.06 x 72

                 = $76.32

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The milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Thus, option (a) is correct.

The term “passage” refers to the explanation and description of a sentence in relation to a topic. The passage aimed to describe those details related to the theme of the story. The different passage is to justify to the different things as to clarify. The passage is to define the important terms.

The milk bottle sat on the central shelf, as mentioned in the passage. The artifact is a completely empty milk bottle. The section gives information regarding signs. The passage was Sig's refrigerator, which had been opened. A milk bottle sat on the middle shelf, its cap missing and no milk inside.

As a result, the milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Therefore, option (a) is correct.

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