Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:

A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 6 feet..

Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)

Part B: The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)

Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

From the question we can say that the Hexagon has three shapes inside it,

Also it is given that,

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.

From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.

A pentagon is shown inside a regular hexagon.

An equilateral triangle is shown inside a square.

The expression for total shaded region would be written as,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,        

⇒ Shaded area  = area of the hexagon – area of the pentagon + area of the  square – area of the equilateral triangle.

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Answer:

Regular Hexagon

Regular Pentagon

Square

Equilateral Triangle

Step-by-step explanation:

E2020 Geometry B!! :3

If Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party and he divided the pizza evenly among his 4 students, each student will get 5/3 pizzas.

Given the data in the question;

First we convert the mixed fraction into an improper fraction.

6 2/3 = ( 6×3 + 2 )/3 = 20/3

Since McConnell divides the pizza evenly among his 4 students.

We will divide 20/3 by 4

20/3 ÷ 4

20/3 × 1/4

(20 × 1) / (3 × 4 )

20/12

5/3

Therefore, if Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party and he divided the pizza evenly among his 4 students, each student will get 5/3 pizzas.

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Profit function in terms of x = 33x + 390.

What is a profit in business?

Given that revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial

[tex]2x^{3} + 30x - 130[/tex]

The cost, in dollars, of producing the skateboards can be modeled by

[tex]2x^{3} -3x - 520[/tex]

Profit function = Revenue - cost

                         = [tex]2x^{3} + 30x - 130 - ( 2x^{3} - 3x - 520)[/tex]

                          = 33x + 390

Therefore, profit function in terms of x = 33x + 390

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Answer: x = 2

Step-by-Step Solution:

Given:

OH = WO = LW

OH = 2x + 1

WO = 3x - 1

LW = 5

To Find:

The value of 'x'

Solution:

We know, OH = WO = LW

So, equate any two of the values given :-

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, x = 2.

An example of the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

This is the term that is used to refer to the fraction that is represented by the use of a rational fraction. That is there is denominator and a numerator.

The denominator must have a variable and this variable has to be of degree 1. Hence the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

First you have to know if it is an inequality or not. Then you have to assign x and y variables to numbers. From here you form an equation. This equation is plotted on a graph.

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Recall the Pythagorean identity,

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

Use it to rewrite the equation in terms of cos only.

[tex]12 (1 - \cos^2(x)) + \cos(x) - 6 = 0[/tex]

[tex]-12 \cos^2(x) + \cos(x) + 6 = 0[/tex]

Factorize the left side.

[tex]-(3\cos(x) + 2) (4\cos(x) - 3) = 0[/tex]

Solve the two cases for [tex]\cos(x)[/tex].

[tex]3 \cos(x) + 2 = 0 \text{ or } 4\cos(x) - 3 = 0[/tex]

[tex]\cos(x) = -\dfrac23 \text{ or } \cos(x) = \dfrac34[/tex]

From the first equation, we get one family of solutions:

[tex]\cos(x) = -\dfrac23[/tex]

[tex]x = \cos^{-1}\left(-\dfrac23\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(-\dfrac23\right) + 2n\pi[/tex]

From the second equation, we get another family:

[tex]\cos(x) = \dfrac34[/tex]

[tex]x = \cos^{-1}\left(\dfrac34\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(\dfrac34\right) + 2n\pi[/tex]

where [tex]n[/tex] is an integer.

We get solutions in the given domain for

[tex]n = 0 \implies \boxed{x = \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = \cos^{-1}\left(\dfrac34\right)}[/tex]

[tex]n=1 \implies \boxed{x = 2\pi - \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = 2\pi - \cos^{-1}\left(\dfrac34\right)}[/tex]

Answer:

Step-by-step explanation:

the graph is down below

The total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

Elsa + 3(her friends) ≤ Total

145 + 3(110) ≤ x

145 + 330 < x

475 ≤ x

Therefore, the total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

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The expression, written as the sine of an angle is sin (7π/10)

From the question, we are to write the given expression as the sine or cosine of an angle.

The given expression is

sin(π/5)cos(π/2) + sin(π/2)cos(π/5)

Let A = π/5

and

B = π/2

Thus, we get

sinA cosB + sinB cosA

From the given information, we have that

sin(A ± B) = sinA cos B ± cosA sinB

∴ sin(A + B) = sinA cos B + cosA sinB

Now,

sinA cosB + sinB cosA = sinA cosB + cosA sin B

∴ sinA cosB + sinB cosA = sin (A + B)

Put A = π/5

and

B = π/2

sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)

sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)

Hence, the expression, written as the sine of an angle is sin (7π/10)

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Answer:

  (2, 2) ⇒ (-2, 2)

  (-5, 6) ⇒ (-6, -5)

  (2, 6) ⇒ (-6, 2)

  (-5, 2) ⇒ (-2, -5)

Step-by-step explanation:

The new coordinates can be found using the transformation function for figures rotated 90° about the origin.

Rotation 90° (counterclockwise) about the origin can be described by ...

  (x, y) ⇒ (-y, x)

The end points of the diagonal that comes closest to the origin will be transformed to ...

  (2, 2) ⇒ (-2, 2)

  (-5, 6) ⇒ (-6, -5)

The other diagonal end points will be on the same horizontal and vertical lines as these.

  (2, 6) ⇒ (-6, 2)

  (-5, 2) ⇒ (-2, -5)

Answer:

y = 3x + 4

Step-by-step explanation:

Substituting into point-slope form and converting to slope-intercept form,

[tex]y+5=3(x+3) \\ \\ y+5=3x+9 \\ \\ \boxed{y=3x+4}[/tex]

Answer:

=========================

Triangle with:

As per definition of midsegment, it is connecting the midpoints of two sides and its length is half the length of the opposite side of the triangle.

So we have:

Solve it for n:

Correct choice is D.

The solutions to the given quadratic equation are as follows:

x = 1.10, x = 10.9.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

For this problem, the equation in item D is:

-x² + 12x - 12 = 0

x² - 12x + 12 = 0

Hence the coefficients are:

a = 1, b = -12, c = 12.

Then the solutions to the equation are found as follows:

The solutions are:

x = 1.10, x = 10.9.

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The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.

Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.

The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.

So, each term is ⁿCₓaˣbⁿ⁻ˣ.

Comparing (a + b)ⁿ with (2t + s)⁷,

So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ

= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ

So, the coefficient term is ⁷Cₓ(2)ˣ

Now for the term t²s⁵, x = 2.

So, the coeficient term is  ⁷Cₓ(2)ˣ =  ⁷C₂(2)²

= 7!/2!(7 - 2)! × 4

= 7!/2!5! × 4

= 7 × 6 × 5!/(2! × 5!) × 4

= 7 × 6/2 × 4

= 7 × 3 × 4

= 84

So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

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The given condition on the basis of truth table is true.

According to the statement

we have given that the some condition p and q. and we have to find that  the given condition is true or false on the basis of the truth table.

So, The given conditions are:

If 3 + 2 = 5, Then 5 + 5 = 10

Now,

The Truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It is a mathematical table that shows all possible outcomes that would occur from all possible scenarios that are considered.

So, the given conditions are properly verified with the truth table. So, it is true.

So, The given condition on the basis of truth table is true.

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Answer:

Zero

Step-by-step explanation:

The sampling method used is classified as Systematic.

Samples may be classified as:

In this problem, every 4th element is taken, which is a systematic sample with k = 4.

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The expected error between the sample mean and the population mean is 3.

In this problem, we have been given :

population mean (μ) = 80,

standard deviation (σ) = 24,  

sample size (n) = 64

We know that,

The Central Limit Theorem states that, for a normally distributed random variable X, with mean μ and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation, which is also called standard error [tex]s=\frac{\sigma}{\sqrt{n} }[/tex]

We need to find the error between the sample mean and the population mean.

standard error

= σ /√n

= 24 /√64

= 24 / 8

= 3

Therefore, the expected error between the sample mean and the population mean = 3

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Answer:

following the (x,y) coordinate system,

(0,4) ; (1,1) ; (2,-2)

Step-by-step explanation:

youre given the value of the x variable in the table, so all you need to do is substitute x and follow pedmas!! hope this helps<3

Answer:

The length of the diagonal of a rectangle is 10m

Step-by-step explanation:

There is a visual below,

The diagonal of a rectangle has formed 2 right triangles.

This diagonal is called hypotenuse side length of a triangle

To find the hypotenuse, we can use the Pythagorean Theorem

a² + b² = c²

we are given the length of a and b, where a = 6 and b = 8

(6)² + (8)² = c²

36 + 64 = c²

100 = c²

√100 = c

10 = c

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The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)

When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.

Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;

(10x^(0.5) - 8)(5x^(0.5) + 4)

The output will retain the same thing.

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Answer:

8.5 g/cm^3

Step-by-step explanation:

Density = mass/volume

          = 34 g / 4 cm^3 =  8.5 g/cm^3

Answer:

8.5 grams per cubic centimeter.

Step-by-step explanation:

Density = mass / volume

             =  34 / 4

             = 8.5 grams / cubic centimeter.

Answer:

Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession.  He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point.  It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.

Step-by-step explanation:

We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods.  The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.

Differentiate

y = -16x² +85x

The first derivative produces an equation that gives us the slope of the line at any point x.  At the ball's top height, it stops and reverses direction, a point at which the slope is zero.

y = -16x² +85x

d(y)/d(x) = -32x + 85

0 = -32x + 85

32x = 85

x = 2.66 feet horizontal distance when the ball reaches its peak.

At x = 2.66, y is 112.9 feet high

When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.

Graph:

See attached plot of the function.

Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.

After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.

Answer:

22480.000

Step-by-step explanation:

Cost of 1km²=6000

So,

Cost of 4.08km²=6000x4.08

=22480.000

I don't know what nearest $100 means tho maybe nearest hundredth but I'm not sure.

The total cost nearest 100 is = $22500.

Modern mathematics heavily relies on the concept of area. The area is the quantity that shows the amount of space occupied by a two-dimensional figure or shape or planar lamina in the plane. Simply put, the area is the amount of cloth or other material with the specified thickness needed to build a model of the form or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint.

Cost of 1km2 = 6000

So,

Cost of 4.08km2 = 6000 * 4.08

                              =  22480.000

Rounding off to 100;

Cost = 22500.00

Hence,

Total cost of the land nearest 100 is = $22500.

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Answer:

Let m be the number of muffins.

a) 4m <= 30

b) m <= 7.5, so the maximum number of muffins to buy is 7.

c) $4 × 7 = $28, so $2 will be left over.

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

⨠ use the distributive property

[tex]\sf{7x-3(x-6)=30}[/tex]

[tex]\sf{7x-3x+18=30}[/tex]

⨠ combine like terms

[tex]\sf{4x+18=30}[/tex]

⨠ subtract both sides by 18

[tex]\sf{4x=30-18}[/tex]

[tex]\sf{4x=12}[/tex]

⨠ divide both sides by 4

[tex]\boxed{\sf x=3}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Answer:

The answer is 3

Step-by-step explanation:

25% of 2.40 equals 0.6

so 3 will be the total price and he will get 0.6 profit.

William bought canned goods at 2.40 per can. he wants to increase the price per can so that he makes a 25% profit,  the selling price per can be, 3.00

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

William bought canned goods at 2.40

He wants to increase the price per can so that he makes a 25% profit

The selling price per can be =?​

Percentage = Amount he wants to increase/previous amount×100

25 = x/2.40×100

x = 0.60

new selling price = 2.40+0.60

                             = 3.00

Therefore, The new selling price is 3.00 per can

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The area of the given semicircle is 56.574 sq. units. Half of the area of the circle is the area of the semicircle.

The area of the semicircle is

A = [tex]\frac{1}{2}[/tex] πr² sq. units

Where r - radius

A semicircle is nothing but half part of the circle. So, its area is also half of the circle's area.

It is given that,

The radius of the semicircle is

r = 6

So, its area in terms of π is

A = [tex]\frac{1}{2}[/tex] πr²

   =  [tex]\frac{1}{2}[/tex] × π × 6²

   = 18π sq. units

On substituting π = 3.143, we get

A = 18 × 3.143 = 56.574 sq. units

Thus, the area of the given semicircle in terms of π is 18π or in terms of π =3.143 is 56.574 sq. units.

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Applying the knowledge of fractions, the number of cups of water that will fill a bottle of 3 liters is calculated as: 13.5 cups.

Fractions are numbers that indicate a part of whole numbers. For example, 2/9 of a liter means 2/9 of a part of 1 liter.

In math, a proportion is simply and equation that sets to ratios equal to each other.

To solve the problem given, create a proportion then use cross product to find the wanted value, which is the number of cups of water that can be filled into a 3-liter bottle.

Let x represent the cups of water we are looking for.

1 cup = 2/9 liter

x = 3 liters

We would have:

(1)(3) = (2/9)(x)

3 = 2x/9

(3)(9) = 2x

27/2 = x

x = 13.5

The number of cups of water to fill a 3-liter bottle is: 13.5.

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