Suppose the dimensions of a rectangular pyramid are doubled. How does this affect its volume?

The volume is 4 times the original volume.

The volume is 2 times the original volume.

The volume is 9 times the original volume.

The volume is 8 times the original volume.

Answer:

what is that thing? where is the question

The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.

In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.

First, write the complete expression:

2 · tan² θ - 7 · sec θ + 8 = 0

Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:

2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0

2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0

2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0

6 · cos² θ - 7 · cos θ + 2 = 0

Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:

6 · u² - 7 · u + 2 = 0

u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]

u = - 7 / 12 ± (1 / 12) · 1

u = - 7 / 12 ± 1 / 12

There are two possibilities:

u₁ = - 2 / 3, u₂ = - 1 / 2

Fourth, find the angles associated to roots by inverse trigonometric functions:

u₁ = - 2 / 3

θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°

u₂ = - 1 / 2

θ₂₁ ≈ 120°, θ₂₂ ≈ 240°

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Answer:

0.65

Step-by-step explanation:

The r-value option (B) 0.65 represents the strongest correlation.

The correlation coefficient is a quantitative method of calculating correlation. It is a statistical concept, which helps in establishing a relation between predicted and actual values obtained in a statistical experiment.

For the given situation,

We need to determine the r-value that represents the strongest correlation.

The relationship between two variables is generally considered strong when their r value is larger than 0.7.

Among the options, 0.65 is near to 0.7, so it has strongest correlation.

Hence we can conclude that the r-value option (B) 0.65 represents the strongest correlation.

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Answer:

Volume of pyramid =1/3× Area of base × height

Since the base is a square

Area of base = l²

l = length

= 6²

= 36ft²

Height of pyramid = 5ft from the diagram above

Volume = 1/3× 36ft² × 5ft

= 60ft³

On solving the provided question we can say that - here in trigonometry [tex]sinx(2cosx - 1) = 0\\[/tex] =>  sinx = 0 and 2 cosx -1 =0

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin 2x - sinx = 0\\-sinx + 2cosx sinx=0\\sinx(2cosx - 1) = 0\\[/tex]

sinx = 0 and 2 cosx -1 =0

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i dont see an =, so imma assume u meant

5x - 12 + 3x=28

8x -12 = 28

8x = 40

x=5

Answer:

Step-by-step explanation:

(x+8)(x-1)(x-3)

The table with values for x or y that make this equation true : 3x + y = 15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

What is solving an equation?

One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side.

Consider, the given equation: 3x + y = 15

We have to complete the given table for the values of x and y.

Plug x = 2 in the given equation.

⇒  3(2) + y = 15

        6 + y = 16

              y = 9

Plug y = 3  in the given equation.

3x + 3 = 15

     3x = 12

       x = 4

Plug x = 6  in the given equation.

3(6) + y = 15

 18 + y = 15

        y = -3

Plug x = 0  in the given equation.

3(0) + y = 15

         y = 15

Plug x = 3  in the given equation.

3(3) + y = 15

  9 + y = 15

        y = 6

Plug y = 0  in the given equation.

3x + 0 = 15

     3x = 15

       x = 5

Plug y = 8  in the given equation.

3x + 8 = 15

3x = 7

x = 7/3

Hence, the table with values for x or y that make this equation true : 3x+y=15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

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Answer:

Step-by-step explanation:

Use formula:

Given

Find the amount:

draw a line from the starting point of the segment to the endpoint using the same angle and length.

1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.

2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.

3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.

The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.

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An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

Interval notation is a simplified way of describing a particular interval. Let’s see how it’s done.

Step 1: We write the first and last number of the interval, which are the endpoints of the interval. For example, if the interval is from 6 to 20, we write 6, 20.

Step 2: We use a round or square bracket on each side of the two numbers. We use:

A square bracket [ ], if we want to include the endpoints

A round bracket ( ), if we don’t want to include the endpoints

So in this example, we use:

So, we can see that some intervals include the endpoints, some partially include them, and some do not include them. Based on this, there are three types of intervals

These are:

This type of interval does not include the endpoints. For example, (5, 10) does not include endpoints 5 and 10.

This type of interval includes the endpoints. For example, [4, 9] includes the endpoints 4 and 9.

This type of interval includes only one of the endpoints.

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So, y = ab^x and y = ac^x are the exponential functions to represent the spread of Ben's and Carter's social media posts respectively.

An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).

For Ben's social media posts:

y = ab^x

For Carter's social media post:

y = ac^x

Please note that the value of a, b, and c will be different for Ben and Carter's post, as it will depend on the number of shares, likes, views, etc., and the rate of spread of the post.

This is an exponential function that represents the spread of Ben's social media posts and  Carter's social media post.

Complete Question:

1. Write an exponential function to represent the spread of Ben's social media post 2. Write an exponential function to represent the spread of Carter's social media post. 3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology. 4. Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers 5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is   . How does this graph compare with the original graph of Amber's photo share? 6. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions? 7. If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions

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The coordinates of vertex D in the parallelogram ABCD are (7,-3).

In a parallelogram, opposite sides are parallel and congruent. Therefore, the vector that goes from vertex A to vertex B is the same as the vector that goes from vertex C to vertex D, and the vector that goes from vertex B to vertex C is the same as the vector that goes from vertex D to vertex A.

The vector from vertex A to vertex B is [tex]< 5-(-3), 7-1 > = < 8,6 >[/tex]

So, the vector from vertex C to vertex D is also [tex]< 8,6 >[/tex]

The vector from vertex B to vertex C is [tex]< 6-5, 2-7 > = < 1,-5 >[/tex]

So, the vector from vertex D to vertex A is also [tex]< 1,-5 >[/tex]

To find the coordinates of vertex D, we can add the vector from vertex C to vertex D to the coordinates of vertex C.

The coordinates of vertex C are (6, 2)

So, the coordinates of vertex D are [tex](6+1, 2-5) = (7, -3)[/tex]

Therefore, the coordinates of vertex D in the parallelogram ABCD are (7,-3).

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Answer:

3: x = 22.5

4: x = 3.75

Step-by-step explanation:

1/7 is the probability that the product is an odd number.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                   Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Total Cards are 7

2 cards out of 7 cards can be selected in ⁷C₂   = 21  ways

Product would be odd if both cards are odd

3 , 5 , 7  are odd cards

2 cards out of 3 Can be selected   in ³C₂  = 3  ways

( 3 , 5) , ( 3 , 7) , ( 5 , 7)

Hence probability  the product of the numbers on the 2 cards  is odd number

= 3/21

= 1/7

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Answer:

x = 2

y = 4

Step-by-step explanation:

Answer:

1. a

2. 422

3. 156.06

Step-by-step explanation:

We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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The values of x and y could be 25 and 113

What are parallel lines ?

parallel lines can be stated as , they both are equi distant from each other and which never intersect.

From the given figure,

y+12 = 3x + 50

as both are parallel to each other.

y-3x = 38

and 5x  = y + 12

as vertically opposites are always equal .

y = 3x + 38

y = 5x - 12

hence,

5x - 12 = 3x +38

2x = 50

x = 25

put x = 25 in y = 3x + 38

y = 3 * 25 + 38

y = 113

hence the values of x and y are 25 and 113 respectively.

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Answer:

y = -x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise / run or (y2 - y1) / (x2 - x1)

Let's pick 2 points ( -6, 0) (-5, -1)

We see the y decrease by 1 and the x increase by 1, so the slope is

m = -1

The y-intercept is located at (0,-6)

So, our equation is

y = -x - 6

Answer:

5 ; 12 ; 13

Step-by-step explanation:

Let :

Shorter leg = x

Other leg = x + 7

Hypotenus = x + 8

Recall:

Hypotenus² = opposite² + adjacent²

(x+8)² = x² + (x+7)²

x² + 16x + 64 = x² + x² + 14x + 49

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x(x - 5) +3(x - 5) = 0

(x + 3) = 0 ; x = - 3

(x - 5) = 0 ; x = 5

Side can't be negative ;

Hence,

x = shorter side = 5

Other side = x + 7 = 5 + 7 = 12

Hypotenus = x + 8 = 5 + 8 = 13

Step-by-step explanation:

From Pythagorean theorem, one of the sides can be determined as x^2 + y^2 =8^2

or y = (8^2 - x^2)^(1/2)

we can write the perimeter P as

P = 2x + 2y ---> 20 = 2x + 2(8^2 - x^2)^(1/2)

Dividing by 2, we get

10 = x + (8^2 - x^2)^(1/2)

Move the x to the other side,

10 - x = (8^2 - x^2)^(1/2)

Take the square of both sides to get rid of the radical sign:

(10 - x)^2 = 8^2 - x^2

Move everything to the left and expand the quantity inside the parenthesis:

x^2 + (100 - 20x + x^2) - 64 = 0

2x^2 - 20x + 64 = 0

or

x^2 - 10x + 32 = 0

Now we can see that a = -10 and b = 32

Answer:

a = -10, b = 18

Step-by-step explanation:

The Pythagorean Theorem is, indeed, involved.  Use it to find an expression (you won't get a number!) for the height of the rectangle.

Using the right triangle, one leg has length  x  and hypotenuse length 8.  for a moment, label the height  h.  Then

[tex]x^2+h^2=8^3\\\\h^2=64-x^2\\\\h=\sqrt{64-x^2}[/tex]

This expression tells the height of the rectangle, so it is the length of the two vertical sides.  The top and bottom sides each have length x.

Perimeter = 20 says that the total length of all the sides is 20.  Set that up and do a heap of algebra!

[tex]x+x+\sqrt{64-x^2}+\sqrt{64-x^2}=20\\\\2x+2\sqrt{64-x^2}=20[/tex]

Divide by 2 (to simplify a bit).

[tex]x +\sqrt{64-x^2}=10[/tex]

Subtract x to get the square root by itself (you'll see why in the next step).

[tex]\sqrt{64-x^2}=10-x[/tex]

Square both sides of the equation.

[tex](\sqrt{64-x^2})^2=(10-x)^2\\\\\\64-x^2=100-20x+x^2\\\\64=100-20x+2x^2\\\\0=36-20x+2x^2[/tex]

Divide by 2 again (because you can)

[tex]0=18-10x+x^2[/tex]

Rearrange terms to match the order in the question.

[tex]x^2-10x+18=0[/tex]

The coefficient of  x  is  a = -10.  The constant is  b = 18.

An open number line can be used to find the amount of cards in three packages for a nurse who collects trading cards.

The relative sizes of numbers are displayed visually on an open number line, which also enables you to execute basic arithmetic operations like addition and subtraction. We can begin by marking the number 0 on the number line to use an open number line to tackle this issue. Then, we can mark the number 3 on the number line using the information from the problem (3 packages).

The total number of cards in the deck can then be determined by counting the units on the number line between 0 and 3. The total number of cards in three packages can then be determined by counting the units on the number line between 0 and 3. If each package has 10 cards, there will be a total of 30 cards in three packages, or 3 × 10 cards. So, after purchasing three packages, the nurse will have 30 trade cards. It's vital to keep in mind that the answer is predicated on the idea that each package contains 10 cards; if the box included a different number of cards, the solution would adjust.

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Answer: 750

Step-by-step explanation:

3000/4= 750

750

Answer:

Step-by-step explanation:Step 1: Remove parentheses by multiplying factors.

= (x * x) + (1 * x) + (2 * x) + (2 * 1)

Step 2: Combine like terms by adding coefficients.

(x * x) = x2

(1 * x) = 1x

(2* x) = 2x

Step 3: Combine the constants.

(2 * 1) = 2

Step 4: Therefore, Simplifying Algebraic Expression is solved as

= x2 + 3x + 2.

Answer:

3y^2 3√3y(end route) if you are simplifying, and (81y^7)^1/3 if you are rewriting it.

Step-by-step:

I know this!

6*12/2

72/2

36

Ans:36

Your welcome