Consider trapezoid SODA

The height of the isosceles triangle is  h = [tex]\sqrt{a^{2}-\frac{c^{2} }{4} }[/tex]

Given,

Isosceles triangle;

An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

Follow these procedures to determine an isosceles triangle's height:

That is,

Height, h = [tex]\sqrt{a^{2}-\frac{c^{2} }{4} }[/tex]

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The equation that makes relationship between width, length and area of a room is Area of room = length of room × width of room and perimeter of room = 2× (length of room + width of room)

The size of a room is either square or rectangle in shape. Whenever a room is rectangle shaped, we need to measure all the side lengths and finally area is found by product of two unequal side length. Besides, we can determine the perimeter of room by adding the two unequal side length and finally 2 is multiplied with it.

We stated earlier that the size of a room is either rectangle or square.

area of square shaped room = (side length× side length)

area of rectangle shaped room = (bigger side length × smaller side length)

perimeter of square shaped room = 4 × side length = 4√(area of room)

perimeter of rectangle shaped room = 2(bigger side length + smaller side length)

hence, the above equations make relationship among the width, length, area and perimeter of a room.

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The sample size is more than 30 and according to the central limit theorem, with a sample size of more than 30, approximately normal distribution.

What is the central limit theorem?

The central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.

We have,

the shape of the sampling distribution of the (mean of members - mean of non-members):

A. It's exactly normal because both populations are normally distributed.

B. It's approximately normal because both sample sizes are at least 30.

C. It's skewed, because the populations are skewed, and both sample sizes are at least 30.

D. The shape cannot be determined since we don't know the shape of either population distribution.

Option (B) is true, as the sample size is more than 30 and according to the central limit theorem, with a sample size of more than 30, approximately normal distribution.

Hence, the sample size is more than 30 and according to the central limit theorem, with a sample size of more than 30, approximately normal distribution.

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Answer:

the answer it's No, it is not proportional because 2.3 over 9.2 does not equal 13.6 over 3.4.

Answer: The answer is C!

Step-by-step explanation:

Answer:

Miyo can make 30 origami figures in 18 minutes

Step-by-step explanation:

tbh, i just counted up by 5's until i reached 18

Answer: 3

Step-by-step explanation: Because we know Miyo can make 5 origami figures in 3 minutes. and we want to know How many origami figures can Miyo make in 18 minutes? so, we know 5*3 is 15. right? well, then we take 18-15 and get 3 so, Miyo can make 3 origami figures in 18 mins.

Yes, Purple math is a completely free online math resource for students and teachers.

What is purple math?

Purple math is an online resource that provides comprehensive math lessons and problem-solving tools for students of all ages.

It offers step-by-step instructions for solving math problems, interactive tutorials, and helpful study guides.

The website also features practice tests, quizzes, and a variety of other learning resources to help students improve their math skills.

Purple math makes learning math fun and accessible to everyone, no matter their age or learning level.

According to the given question:

It provides comprehensive math lessons and tutorials, as well as interactive practice questions with instant feedback. It is an invaluable tool for students of all levels as it is free, from middle school to college, who are looking to improve their math skills and better understand mathematical concepts.

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In order to solve a inverse function question we switch the coordinates  of x with that of y and the perform the required  calculations.

The result which we get as is considered as a relation and not as a function.

We an calculate inverse for functions which are one to one .

A function is known as a one to one function only when every second element matches the first value.

The inverse question is a type of function , when we solve this function we get another function which is represented as , ‘g’  and is known as the inverse of function .

y = f(x) then,

x = g(y)

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3x - 1 = 0 is not a quadratic equation.

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

In the given equation: 3x - 1 = 0 , no ax² term is given, so it is not a quadratic equation.

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The complete question is as follows:

Is 3x - 1 = 0 a quadratic equation?

Answer:

A

Step-by-step explanation:

To compare the initial out-of-pocket cost for the lease and loan options, we need to calculate the total cost for each option.

For the loan option, we can calculate the total cost as follows:

Total cost = MSRP + down payment + interest

= $15,000 + $1,500 + $1,050 (7% of MSRP)

= $17,550

For the lease option, we can calculate the total cost as follows:

Total cost = (MSRP x money factor x 36) + acquisition and documentation fees + security deposit

= ($15,000 x 0.00271 x 36) + $1,250

= $5,925 + $1,250

= $7,175

Since the total cost for the lease option is less than the total cost for the loan option, the initial out-of-pocket cost is less for the lease. Therefore, the correct statement is:

a. The initial out-of-pocket cost is less for the lease.

With the help of Algebra the correct function is C(t) = 0.10t+25.

What is Algebra?

Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating them. It is used to solve a variety of equations and problems by using formulae, equations and graphs. Algebra is primarily used to find unknown values, such as the unknown side of a triangle or the value of a variable in an equation. It can also be used to solve problems that involve more than one variable, such as those involving linear equations and systems of equations. Algebra is a powerful tool for problem-solving and can be used in various scientific fields, such as physics, chemistry and engineering. It is essential for developing a good understanding of mathematics and is an important part of any mathematics curriculum.

Assuming that :  y = kx + b

plug in : ( 0, 25 ) and  ( 50, 30)

25 = b

30 = 50k + 25

so, k = 0.10 after solving this equation

y =  0.10t+25

Hence the function is C(t)=  0.10t+25

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Answer:

9

Step-by-step explanation:

vertical angles are congruent

110=13x-7

110+7=13x

117=13x

divide

9=x

x=9

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is  52!/(47! * 5!).

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.

The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.

Order is irrelevant, therefore we utilize a combination (instead of a permutation)

We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)

so we obtain:

n C r = r!*(n-r)!/(n!)

52 C 5 = (52!)/(5!*(52-5)!)

52 C 5 = (52!)/((52-5)!*5!)

The complete question is:-

Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?

a) (52-5)! / 52!5!

b) 52! / (52-5)!

c) 52! / (52-5)!5!

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Answer:

C. [tex]3[/tex]

Step-by-step explanation:

[tex]y=-2x^2 + 8x-5 \\ \\ =-2(x^2 -4x)-5 \\ \\ =-2(x^2-4x+4-4)-5 \\ \\ =-2((x-2)^2 -4)-5 \\ \\ =-2(x-2)^2 +8-5 \\ \\ =-2(x-2)^2 + 3[/tex]

The nature of the roots of the equation 5x² + 3x + 2 = 0 are x = -7.123 and x = 0.878.

The equation 5x² + 3x + 2 = 0 has two solutions, or roots, which can be found using the quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

Where a = 5, b = 3 and c = 2,

x = [-3 ± √(3² - 4(5)(2))] / 2(5)

x = [-3 ± √17] / 10

x = (-3 ± 4.123) / 10

x = (-7.123) / 10,  0.878

The roots of the equation 5x² + 3x + 2 = 0 are x = -7.123 and x = 0.878.

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To display the distribution of the lengths in inches of a sample of brook trout, the graph you should use is histogram. (Option A)

A histogram refers to a graphical representation of data points organized into user-specified ranges. It is an approximate representation of the distribution of numerical data. It is similar in appearance to a bar graph; however, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins. It is used to summarize discrete or continuous data that are measured on an interval scale. The histogram is represented by a set of rectangles, adjacent to each other, where each bar represents a type of data. Hence, in order to display the distribution of the lengths in inches of a sample of brook trout, the appropriate graph to use is histogram.

Note: The question is incomplete. The complete question is probably is: To display the distribution of the lengths in inches of a sample of brook trout, what graph should you use? A) histogram B) bar chart C) scatterplot D) pie chart E) line graph.

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Step-by-step explanation:

remember some of the angle theorems inside a circle.

first of all, arc angles are the angles of the corresponding circle segments at the center of the circle (the angle between the lines from the points on the arc to the center).

and, of course, all the arc angles together around a circle are therefore 360°.

so,

(8x + 20) + 104 + arc angle KJP = 360

and then :

the opposite angle is half of the arc angle for the same points on the circle arc.

angle L = 5x + 1 is the opposite angle of K and P, and that is therefore half of the arc angle KJP.

5x + 1 = (arc angle KJP)/2

arc angle KJP = 2×(5x + 1)

and by using this in the first equation we get

(8x + 20) + 104 + 2×(5x + 1) = 360

8x + 124 + 10x + 2 = 360

18x + 126 = 360

18x = 234

x = 234/18 = 13

The factor of  [tex]x^3 -7x + 6[/tex] is (x - 1) (x +3) (x -2).

Now, According to the question:

The given expression to be factorized is :

[tex]x^3 -7x + 6[/tex]

This can be written in the form:

[tex]x^3 -7x + 6[/tex] = [tex]x^3[/tex] - (1 + 6)x + 6

[tex]x^3 -7x + 6[/tex] = [tex]x^3[/tex] -x - 6x + 6

Take common 'x' from the first two terms and -6 from the last two terms. Then we have,

[tex]x^3 -7x + 6[/tex] = x([tex]x^2 -1[/tex]) -6 (x -1)

                  = x{ [tex](x)^2 - (1)^2[/tex] } - 6(x -1)

                  = x(x +1) (x -1) - 6(x -1)

Finally, Take common (x -1) from the above expression:

[tex]x^3 -7x + 6[/tex] = (x -1) {x(x +1) - 6}

                 = (x -1) [tex](x^{2} +x-6)[/tex]

                 = (x -1)([tex]x^{2}[/tex]+3x -2x -6)

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

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

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The complete question is this:

Which is the factor of [tex]x^3 -7x + 6[/tex]

1. x(x -6) (x -1)

2. [tex](x^{2} -6)[/tex] (x -1)

3. (x + 1) (x + 2) (x +3)

4. (x - 1) (x +3) (x -2)

The mean of the set of numbers 23, 45, 87, 40, and 50 is 49. This is the average value of the set, and it is affected by all the values in the set.

The mean, also known as the arithmetic mean, of a set of numbers is found by adding up all the numbers in the set and dividing by the total number of numbers in the set. In this case, the set of numbers is 23, 45, 87, 40, 50. When we add up all the numbers in the set, we get a total of 245. There are 5 numbers in the set, so the mean is 245 / 5 = 49.

To find the mean, we first need to add up all the numbers in the set. Then, we divide that sum by the total number of numbers in the set. This gives us the average value of the set.

In summary, the mean of the set of numbers 23, 45, 87, 40, 50 is 49. This is the average value of the set, and it is affected by all the values in the set.

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The space among contour lines are known as Sharp slopes which is closely spaced contour lines. Gently sloping or comparatively flat regions are shown by widely spaced contour lines.

Contour lines link places with the same elevation; if they are close together (they never intersect), the terrain is steep and the elevation changes quickly over a short distance. The elevation changes gently where the contour lines are far apart, indicating a moderate slope.

The areas between the contour lines are filled with colors when using the layer tinting technique. A particular height is indicated by each color. Contours are shown as lines. A hilltop is indicated by a contour line that creates a closed loop with no other contour lines inside. Sharp slopes are indicated by closely spaced contour lines. Gently sloping or comparatively flat regions are shown by widely spaced contour lines.

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The size and shape of things are preserved by stiff transformations (reflections, translations, and rotations). As a result, archetypes and visuals are always compatible.

The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped. When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.

c + 18 + 10 = 42//

[tex]c = 42 -(18 + 10) cm = 14 cm\\s = 21 cm//[/tex]

Area = [tex]\sqrt{s(s - a)(s - b)(s - c) }[/tex]

and, here s = half the perimeter,

[tex](a + b + c)/2.[/tex]

A = [tex]21\sqrt{11}[/tex]

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Answer:

The answer is a = w + 4 - 3b/2

Step-by-step explanation:

w = 3(2a + b) - 4

add 4 both sides we get,

w + 4 = 3(2a + b) - 4 + 4

w + 4 = 3(2a + b)

w + 4 = 6a + 3b

Subtract 3b from both sides we get,

w + 4 - 3b = 6a + 3b - 3b

w + 4 - 3b = 2a

Now, Divide both sides by 2 we get,

w + 4 - 3b/2 = 2a/2

a = w + 4 - 3b/2

Thus, The answer is a = w + 4 - 3b/2

From the concepts and properties of triangles, m∠BDC is 26°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is equal to 180°.

In the given ΔABD, line segment AD and BD are equal and hence it is an isosceles triangle.

Therefore,

x° + x° + 70° = 180°.

2x° = 110°.

x = 55°.

So, m∠DAB = m∠DBA = 55°.

We know the sum of linear pair of angles is 180°.

Therefore, m∠ABD + m∠DBC = 180°.

55° + m∠DBC = 180°.

m∠DBC = 125°.

Now,

m∠BDC + m∠DCB + m∠CBD = 180.

m∠BDC + 29° + 125° = 180°.

m∠BDC = 26°.

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Examples of perpendicular slope are the sides of a fixed square, a window, and the Red Cross emblem.

Lines that are vertical and horizontal are perpendicular to one another. In this instance, the perpendicular line's slope would be equal to a horizontal line's slope, which would be 0. The slope of the perpendicular line is zero, but the slope of the parallel line is unknown. By taking the negative reciprocal of the slope of the provided line, one can determine the slope of a perpendicular line from that line. We obtain m2 = -1/m1 if the slope of the provided line is m1 and the slope of a perpendicular line is m2.

Given

There are a lot of perpendicular lines that we may see in reality. The corners of the chalkboard, the arms of a clock at specific times of the day, the sides of a fixed square, a window, and the Red Cross emblem are a few examples.

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Sets of points connected by typical lines or curves form graphs.

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Answer:

  1598.9 ft

Step-by-step explanation:

You want the distance between points A and B when observers at each point find the angle of elevation to a lighthouse beacon to be 15° and 6°, respectively. Point A is 1032 ft horizontal distance from the lighthouse.

The tangent relation for sides in a right triangle is ...

  Tan = Opposite/Adjacent

This can be rearranged to ...

  Opposite = Tan × Adjacent

If d is the distance in feet from A to B, two expressions for the same lighthouse height can be written:

  height = tan(15°)(1032)

  height = tan(6°)(1032 +d)

Equating these values of height, we have ...

  tan(6°)(1032 +d) = tan(15°)(1032)

  d = 1032(tan(15°) -tan(6°))/tan(6°) = 1032(tan(15°)/tan(6°) -1)

  d ≈ 1598.946 . . . . feet

The distance from A to B is about 1598.9 feet.

The inequality x² + 8x - 238 <= 0 represents the situation in which the area of the cake is at least 254 square inches.

The width of the cake is 4 inches more than the width of the photo, so the width of the cake can be represented by the expression x+4.

The length of the cake is two times its width, so the length of the cake can be represented by the expression 2(x+4).

The area of the cake is the product of its length and width, so it can be represented by the expression (x+4)(2(x+4)).

To represent the situation in which the area of the cake is at least 254 square inches, we can set the expression for the area equal to 254 and solve for x:

(x+4)(2(x+4)) >= 254

2x² + 16x + 16 >= 254

x² + 8x - 238 <= 0

The inequality x² + 8x - 238 <= 0 represents the situation in which the area of the cake is at least 254 square inches.

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Answer:

x=4.04 y=7.66

Step-by-step explanation:

Hence,the company should produce 12 pieces of Model A and 6 pieces of Model B to get the maximum profit i.e. 168000.

Let x be the number of pieces of model A and y be the number of pieces of model B.

Let total profit be Z

Then, Total profit =8000x+12000y

                         Z=8000x+12000y .............. (i)

Now we have the following mathematical model for the given problem 

Max Z=8000x+12000y

Subject to constraints 

9x+12y≤180 .......... (Fabricating constraints)

3x+4y≤60   .......... (ii)

x+3y≤30   (Finishing constraints)........ (iii)

Let us evaluate the objective function Z at each point as shown below

At C(0,10),  Z=8000×0+12000×10=120000

Maximum value of Z is 168000 at B(12,6)

Hence, the company should produce 12 pieces of Model A and 6 pieces of Model B to get the maximum profit i.e. 168000.

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Answer:

Step-by-step explanation:

x= -3  

y= 3