Figure ABC has vertices A(-3,3), B (1,-1), and C (0,5). Sketch ABC and draw its image after the translation (x,y) (x+4, y + 2).

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{22\% of 72}}{\left( \cfrac{22}{100} \right)72}\implies 15.84~\hfill \underset{ new~price }{\stackrel{ 72~~ + ~~15.84 }{\text{\LARGE 97.84}}}[/tex]

The measures of the angles, obtained using circle theorems are;

a = 90°, b = 12°, c = 64°, d = 54°, e = 54°, f = 48°, g = 66°, h = 32°, i = 36°, and j = 20°

Circle theorems are theorems that specify the relationships between the chords, tangents, sectors, and angles in a circle.

The linear pair angles ∠a indicates;

a + a = 2·a = 180°

a = 180°/2 = 90°

The 78° angle in the inscribed right triangle indicates;

∠b = 90° - 78° = 12°

The 32° angle at the circumference of one of the circles indicates;

Angle at the center, which nis a base angle of the large triangle = 2 × 32° = 64°

A base angle of the large triangle = 64°

∠C = A base angle of the large triangle = 64°

2·c + d = 180° (Properties of a cyclic quadrilateral)

Therefore;

2 × 64° + d = 180°

d = 180° - 2 × 64° = 54°

d = 54°

Angle ∠e = Angle ∠d = 54°

The vertex angle of the inscribed isosceles triangle in the circle with angle ∠f is; 4·b

Therefore;

The vertex angle = 4 × 12° = 48°

An angle formed between a chord and a circle is equivalent to the angle in the segment that is in the alternate side or area, therefore;

Circle theorem indicates; ∠f = The vertex angle = 48°

The base angles of the isosceles triangle = (180° - 48°)/2 = 66°

Angle ∠g = 66°

The  chord which is the base of the isosceles triangle in the circle with the angle h forms an isosceles triangle with the sides of the large triangle, such that the base angles are also ∠c = 64°

Circle theorem indicates that the vertex angle of the triangle with angle h is also 64°

Therefore, according to circle theorem; 2·h = 64°

h = 64°/2 = 32°

The vertex angle of the quadrilateral with angle 2·f is; 180° - 2·f

The vertex angle is therefore; 180° - 2 × 48° = 84°

The angle at the center is therefore; 2 × 84° = 168°

Angle ∠i is therefore;

i = 360° - 5·b - 2·f - 168°

i = 360° - 5 × 12° - 2 × 48° - 168° = 36°

5·b + 2·h + i + j = 180°

Therefore; j = 180° - (5·b + 2·h + i)

j = 180° - (5 × 12° + 2 × 32° + 36°) = 20°

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Therefore, the types of transformation and the value of k for each equation are: Horizontal compression by a factor of 1/2, k = 0. Vertical stretch by a factor of 2, k = 0. Horizontal stretch by a factor of 2, k remains the same as in f(x). Vertical compression by a factor of 1/2, k = 0.

Given by the question.

We can use the given table of values for f(x) and the transformed function g(x) to determine the type of transformation and the value of k for each equation.

g(x) = f(2x):

This is a horizontal compression by a factor of 1/2. The value of k is not affected by this transformation, so k remains the same as in f(x).

g(x) = 2f(x):

This is a vertical stretch by a factor of 2. The value of k is also multiplied by 2, so k = 2(0) = 0.

g(x) = f(1/2x):

This is a horizontal stretch by a factor of 2. The value of k is not affected by this transformation, so k remains the same as in f(x).

g(x) = 1/2 f(x):

This is a vertical compression by a factor of 1/2. The value of k is also divided by 1/2, so k = (0)/(1/2) = 0.

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The equation for the least squares regression line is y = 0.488x + 8.543.

Least squares regression line is the line of best fit formed when the relationship is linear for the given data points.

Number of data points, N = 5

x : 35         39         63         86         93        Σx = 316

y : 38         20         28         55         56        Σy = 197

x² : 1225   1521    3969    7396     8649       Σ(x²) = 22,760

xy : 1330   780     1764     4730     5208       Σ(xy) = 13,812

Slope of the line, m = [N Σ(xy) - Σx Σy] / [N Σ(x²) - (Σx)²]

                                 = [ (5 × 13812) - (316 × 197) ] / [(5 × 22760) - (316)²]

                                 = 6808/13944

                                 = 0.488

Intercept, b = [Σy - (m Σx)] / N

                   = [197 - (0.488 × 316)] / 5

                   = 8.543

Equation of the line is y = mx + b

y = 0.488x + 8.543

Hence the equation of the line is y = 0.488x + 8.543.

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Lim initially had $5145, and he withdrew an additional $1040 from his bank account, so he had a total of:

$5145 + $1040 = $6185

Lim divided this total amount equally among his 5 sons, so each son would receive:

$6185 ÷ 5 = $1237

Therefore, each son would receive $1237.

There are only one solution  x= 1/2 in the expression.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.\

Given that;

The expression is,

⇒ 8x - 4 = 3 - 6x

Now, We can simplify the expression as;

⇒ 8x - 4 = 3 - 6x

Add 6x both side,

⇒ 8x + 6x - 4 = 3 - 6x + 6x

⇒ 14x - 4 = 3

Add 4 both side,

⇒ 14x - 4 + 4 = 3 + 4

⇒ 14x = 7

Divide by 14;

⇒ x = 7/14

⇒ x = 1/2

Thus, There are only one solution  x= 1/2 in the expression.

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As a resuIt, 10 (181)/181 is the sin vaIue that cοmes cIοsest tο 10 √(181)/√181. B is the apprοpriate answer, sο.

The cοst οr price οf sοmething, aIsο knοwn as its mοnetary vaIue.

The right-angIed triangIe fοrmed by the angIe's terminaI side and the pοints (-9, 10) can be caIcuIated using the Pythagοrean Theοrem tο determine the Iength οf a hypοtenuse:

h = √((-9)² + 10²) = √(81 + 100) = √(181)

Sin is pοsitive because the pοsitiοn (-9, 10) οccupies the secοnd quadrant. We are abIe tο determine the actuaI amοunt οf sin that use the definitiοn οf sin:

sin(theta) = οppοsite/hypοtenuse = 10/√(181)

We can cοmbine the twο parts οf this fοrmuIa by √181 tο οbtain the fοIIοwing resuIt:

sin(theta) = 10 × √(181)/√(181)√(181) = 10√(181)/181

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Answer:

To find the percent increase in price, we need to calculate the difference between the original price and the new price, and then express that difference as a percentage of the original price.

The original price of the sweatshirt was $40, and the new price is $65, so the difference is:

$65 - $40 = $25

To express this as a percentage of the original price, we divide the difference by the original price and multiply by 100:

($25 / $40) x 100% = 62.5%

Therefore, the percent increase in the price of the sweatshirt is 62.5%.

Answer:

A. (1,2), (2,4), (3,6), (4,8)

Step-by-step explanation:

The 1st number in parenthesis is the number of boxes of popcorn. The 2nd number is the cost.

Step-by-step explanation:

Please when you come across any questions including two equations of two variables, please solve that question by using the simultaneous method.

To go about that, since you would be given two equations, name one equation as "equation one" (eq 1) and the other, "equation two" (eq 2).

Right after that, make any of the variables a subject ( make it stand alone or be on one side of the equal to sign). Now, substitute that variable you've made the subject into the other equation which you didn't make any variable the subject. Solve for that, by grouping all like terms and you would realize that the final result would be the answer of one of the variables.

After getting that value, substitute that value in place of its variable. (For instance, x = 1, substitute the value which is 1 in place of x in the equation you made a variable the subject at the beginning). Solve for that equation too, and finally you would arrive at an answer or a value.

To verify that your answers are right, substitute the values in their respective variables. ( For instance, if x = 1 and y = 2, put 1 in place of x and 2 in place of y in the first equation then do same for the second equation as well). The answer would be the same as the number it has been equated to.

Answer:

C:  constant of proportionality is 5

Step-by-step explanation:

x       k       y

3       5        15

5       5        25

8       5        40

10      5        50

12      5        60

constant of proportionality (k) is 5.  All the rows check out.

y = kx = 5x

Therefore , the solution of the given problem of equation comes out to be w + x + y + z = 35 optian A is correct.

The same letter is frequently used in mathematical formulas to attempt to enforce uniformity among two variable assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using the outcome y + 6 = 12 as an example, the normalise divides the numbers 12 and b + 6 into 2 parts. The relationship between each symbol component and the amount of lines can be found. A symbol's meaning typically runs counter to itself.

Here,

In order to remove variables and obtain an expression for w + x + y + z, we can begin by adding the four equations. As a result, we get:

=> (5w + 3y + 7x -2z) + (3z - w + y -3x) + (-2x -2y + 3z - 2w) + (3x + 3y + z + 3w)

=>  17 - 4 + 9 + 13

By condensing both parts, we obtain:

=> 4x + 4y + 4z + 5w = 35

By separating it on one side, we can finally find the solution for

=> w + x + y + z:

=> w + x + y + z = 35

As a result, w + x + y + z = 35

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As a result, 198 small bags and 92 big bags of popcorn were sold at the movie theatre.

An equation in mathematics is a claim that two statements are equivalent. It usually has two sections: a left and a right, separated by an equals sign in the middle. For instance, the statement that the expression 2x Plus 3 equals the expression 7 is represented by the equation 2x + 3 = 7. The equation can be used to determine the number of x that causes the equation to hold true when the variable x is unknown. Equations, such as linear equations, quadratic equations, trigonometric equations, and many others, can be used to explain a broad range of mathematical relationships.

given

Let x represent the quantity of big popcorn bags sold and y represent the quantity of small popcorn bags sold.

Based on the knowledge provided, we can create the following system of two equations:

x + y = 290 (the total amount of bags distributed) (the total number of bags sold)

4x + y = 566 (the entire revenue from popcorn sales) (the total revenue from popcorn sales)

We have two options for resolving the equation for x and y: substitution or removal. Here, we'll apply the replacement technique:

Y = 290 - x is the result of solving equation 1. We can enter the following formula in place of y in equation 2:

4x + (290 - x) = 566

If we simplify, we get:

3x + 290 = 566

290 from both parts are subtracted, giving us:

3x = 276

3 divided gives us:

x = 92

Thus, 92 big bags of popcorn were sold. We can change x = 92 into equation 1 to determine how many small packages were sold:

92 + y = 290

92 is subtracted from both parts to arrive at:

y = 198

Thus, 198 small packages of popcorn were sold.

As a result, 198 small bags and 92 big bags of popcorn were sold at the movie theatre.

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From the given situation of equation Diamond worked 24 overtime hours that week.

The hourly rate that is paid for the typical hours worked within a pay period is known as regular pay. For full-time employees in the US, this is typically referred to as 40 hours a week. On the other hand, overtime pay is the hourly rate paid for any additional hours worked. Most businesses give time-and-a-half (1.5 times the usual pay rate) or double-time (two times the regular pay rate) for extra hours, which is often more than regular compensation.

Let us suppose the number of hours = x.

Let us suppose the overtime hours = y.

From the given situation we have:

7.5x + 11.25y = 352.5 (equation 1)

x + y = 35 (equation 2)

Substituting equation 2 into equation 1 and simplifying:

7.5x + 11.25(35 - x) = 352.5

7.5x + 393.75 - 11.25x = 352.5

-3.75x = -41.25

x = 11

Substitute the value of x = 11.

11 + y = 35

y = 24

Hence, Diamond worked 24 overtime hours that week.

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The length of the radius and diameter are 10.5 and 21 respectively

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

The area of the sector = tetha/360 × πr²

= 72/360 × 3.14 × r²

= 0.628r²

area of the circle = area of the shaded part + area of sector

3.14r² = 277 + 0.628r²

3.14r²-0.628r² = 277

2.512 r² = 277

r² = 277/2.512

r² = 110.3

r = √ 110.3

r = 10.5

d = 2r

d = 10.5 × 2

= 21

therefore the radius and diameter are 10.5 and 21 respectively

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After simplificatiοn οf the given expressiοn the factοr is 11. Thus, οptiοn b is cοrrect.

There is a need fοr mathematical οperatiοns like multiplying, splitting, adding, and even deleting. They wοuld result in the fοllοwing assertiοn if cοmbined: A mathematical fοrmula, sοme data, and an equatiοn A declaratiοn οf truth is made up οf values, elements, and mathematical οperatiοns like additiοns, erasures, algebraic expressiοns, and divisiοns. It is pοssible tο rate and analyze wοrds and sentences.

Here,

When we replace these in the statement, we get:

=[tex]\dfrac{(2^{10} \times 3^{10})(5^3 \times 11^3)(3^2 \times 5^2) }{(2^{10} \times 5^5)(3^{12})(11^{20})}[/tex]

= [tex]\dfrac{(11 \times 15^2) } {15^2}[/tex]

= 11

After simplificatiοn of the given expressiοn the factor is 11. Thus, οption b is correct.

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Using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.

What is a system of equations?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system.

1) y = -3 and x = -6

This system of equations has only one solution as the variables have only a constant as their value.

2) y = 2x and y = -2x

    There is only one solution to this system of equations. It is x =0 and y = 0. This solution only satisfies these equations.

3) y = -x -2

   y = -x -6

  There is no solution to this system of equations as the mathematical operation on two numbers will not give two values.

4) y = 3x + 4

2y = 6x + 8

There is an infinite number of solutions as the second equation when divided by 2 becomes y = 3x + 4, which is the same as the first equation.

5) y = 9x -1

   y = x + 9

 There is only one solution for this system of equations.

Therefore using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.

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Answer:

Step-by-step explanation:

One possible solution to the linear equation −5x+y=−10 is:

x = 2

y = 0

To check if this solution is valid, we can substitute the values of x and y into the equation and see if it satisfies the equation:

(-5)(2) + (0) = -10

-10 = -10

Since the equation is true, we have found a valid solution.

Answer:

Step-by-step explanation:

to write the proportion is a number of the girl in intramural sport is [tex]\frac{x}{y} 2/3=230[/tex]

and find the number a girl in intramural sport is 90

The inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is 202.5 + 36.39x ≤ 480.

What is an inequality?

An inequality is a comparison between two or more mathematical expressions. It can be of the form ≤, ≥, < or >.

We are given per day charges as $36.39 and the charges per mile as $0.90.

Also, it is given that in total 225 miles have been driven.

So, the charges of 225 miles are:

⇒225 x 0.90

⇒$202.5

It is given that he can spend maximum $480.

So, for the maximum number of x days, we get the inequality as

202.5 + 36.39x ≤ 480

Hence, the inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is

202.5 + 36.39x ≤ 480.

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The height of the skyscraper is 201.49 meters.

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, Sadie is seeing a skyscraper making an angle of the elevation of 36°, she is 275 meters away from the skyscraper, we need to find the height of the skyscraper,

Using the concept of height and distance and trigonometric ratios,

Tan 36° = x / 275 [please refer to the figure attached]

x = 275 × Tan 36°

x = 199.80 meters

Therefore, the height of the skyscraper is x+1.69 = 199.80+1.69 = 201.45 m

Hence, the height of the skyscraper is 201.49 meters.

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The complete question is :-

From her eye, which stands 1.69 meters above the ground, Sadie measures the angle of elevation to the top of a prominent skyscraper to be 36. If she is standing at a horizontal distance of 275 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

The graph of the piecewise function is added as an attachment

Let c(x) be the cost of an automotive ad with x lines.

For the first 4 lines, the cost is $34, so:

c(x) = 34, for 1 ≤ x ≤ 4

For each additional line beyond the first 4, the cost is $3.50, so:

c(x) = 34 + 3.50(x - 4), for x > 4

When these two cases are put together, we get the piecewise function:

c(x) = 34, for 1 ≤ x ≤ 4

c(x) = 34 + $3.50(x - 4), for x > 4

This function represents the cost of an automotive ad as a piecewise function that depends on the number of lines in the ad.

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The surface area of the right triangular pyramid is, 269.5 square units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Dimensions of the right triangular pyramid are,

X = 11 units

Y = 10 units

Z = 13 units

Now, The surface area of the right triangular pyramid is,

Area of Lateral triangle = 1/2 × X × Z

                                    = 1/2 × 11 × 13

                                    = 71.5 unit²

And, Area of Base Triangle = 1/2 ·  base ·  height

                                          = 1/2 ·  X ·  Y

                                          = 1/2 ·  11 units · 10 units

                                          = 55 units²

Now, use the method described above to find the surface area of the pyramid.

Surface Area = 3( Area lateral ) + ( Area base )

                    = 3 ( 71.5 square units ) + ( 55 square units )

                   = 269.5 square units

Thus, The surface area of the right triangular pyramid is, 269.5 square units

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Proportionately, if Lexi uses 360 g of flour, the quantity of blueberries she must use is 150 g of blueberries.

Proportion describes the two ratios equated to each other.

Proportions are fractional values between zero and one.

Recipe for making Blueberry Muffins

Ingredient  Quantity

Egg              1

Flour           120 g

Sugar         120 g

Butter          60 g

Blueberries 50 g

120 g of flour = 50 g of blueberries

The Ratio of flour to blueberries = 2.4:1

360 g of flour = 360/120 x 50

= 150 g of blueberries (360/2.4)

Thus, if Lexi uses 360 g of flour, based on the given recipe, she must use 150 g of blueberries.

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The cardinality of (B ⋃ C) will be n(B ⋃ C)=3.

In mathematics, cardinality refers to the size or number of elements in a set. It is a concept used to compare the sizes of sets, regardless of their specific elements. For instance, the cardinality of the set {1, 2, 3} is 3, while the cardinality of the set {2, 4, 6, 8, 10} is 5. Cardinality is typically denoted using vertical bars, such that |S| represents the cardinality of set S.

Now,

The symbol "n(S)" represents the cardinality

To find the cardinality of the sets:

We have to see how many elements are there in (B ⋃ C) and

As we can see from Venn diagram there are 23 elements in (B ⋃ C) i.e.

5+3+1+2+4+8

Hence,

           The cardinality of n(B ⋃ C) will be 23.

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The number of different ways will be 108000.

Permutations are various ways to arrange things in a specific order. It can also be stated as the linear reordering of items in an already ordered set.

A first guess for the number of ways to select a committee consisting of 3 engineers, 2 physicists, and 2 computer scientists from 10 engineers, 5 physicists, and 6 computer scientists could be to simply multiply the number of ways to select each group separately:

10 choose 3 x 5 choose 2 x 6 choose 2

This would give us the number of ways to select 3 engineers out of 10, 2 physicists out of 5, and 2 computer scientists out of 6.

The number of ways can be,

N = ¹⁰C₃ x ⁵C₂ x ⁶C₂

N = 10 x 9 x 8 x 5 x 6 x 5

N = 108000

Therefore, the number of different ways will be 108000.

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Answer:

Below

Step-by-step explanation:

15 point average for 6 games = 90 points total

   for the final 6 games she can score a total of 90 points to maintain her average of 15 points per game

  there are a LOT of possibilities....here is one

   Pts:   16    14    16   14   16  14    = 90 points (with no 15 point games)

We are 95% confident that the true mean hearing loss of senior citizens is between 3.5249 and 4.8751

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most usual, but other levels, such 90% or 99%, are occasionally used to generate a confidence range.

How to calculate:

From the given data:

n= 30

x = 4.2

s = 1.808

d.f = n-1 = 30-1 = 29

At 95% confidence interval:

t[tex]\alpha /2[/tex] = 2.0452

The 95% C.I for the mean is:

x ± t[tex]\alpha /2[/tex]

= 4.2 ± 2.045 [tex]\frac{1.808}{\sqrt{30} }[/tex]

= 4.2 ± 0.6751

( 3.5249, 4.8751)

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