How to Use a Table to Multiply Two Polynomials
Step 1: Use the __________ in one polynomial to label the columns (one term per column).

Step 2: Label the _________ with the terms in the other polynomial (one term per row). Step 3: Multiply each __________ label by each row label to fill in all the entries.

Step 4: __________ all the products in the entries.

Step 5: __________ the sum, if possible.

6. The costs are given as follows:

4 kites - $28.

7 kites  - $34.

10 kites - $40.

7. The linear function is defined as follows:

y = 20 + 2x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, the intercept b is given as follows:

b = 20.

When x increases by one, y increases by two, hence the slope m is given as follows:

m = 2.

Then the function is given as follows:

y = 2x + 20.

The costs are given as follows:

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A. Superman's average rate is = 104 m/s

B. The distance flew in 10 seconds =  1040 m.

C. After 18 seconds, Superman is 1164 meters away from Lois.

For B, To find the distance flown in 10 seconds, we can use the average rate calculated in part A and multiply it by the time elapsed:

104 m/s * 10 s = 1040 m

In this scenario, we have used the formula for average speed, which is given by:

To calculate the average speed, we found the difference between the two distances and divided it by the difference in time. To find the distance flown in 10 seconds, we simply multiplied the average speed by the time elapsed. The final answer to how close to Lois Superman is after 18 seconds is 1164 meters.

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Complete Question:

Superman needs to save Lois from the clutches of Lex Luthor. After flying for 14 seconds, he is 1372 meters from her. Then at 18 seconds he is 1164 meters from her.

A. What is Superman's average rate? _____ meters per second

B. How far does Superman fly every 10 seconds? _________meters

C. How close to Lois is Superman after 18 seconds? ________meters.

The height of the tree is 38 feet.

Trigonometry is a topic the requires determination of length/ distance or measure of angle of the position of an object from a reference point. Thus the trigonometric functions are required.

In the given question, let distance from Woody's eyes to the top of the tree be represented by x. Then applying the appropriate trigonometric function, we have;

Tan θ = opposite/ adjacent

Tan 70 = x/ 12

x = 12 * Tan 70

  = 12(2.7475)

x = 32.97

x = 33 feet

Thus,

the height of the tree = woody's eyes from the ground + distance from Woody's eyes to the top of the tree

                                    = 5 + 33

                                    = 38 feet

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The cost of each shirt Bobby and Davonte bought if they both spent $145.20 on 11 shirts is $13.2

Total number of shirts bobby and Davonte bought = 11

Amount Bobby spent on shirts= $92.40

Amount Davonte spent on shirts= $52.80

Total amount both spent= $92.40 + $52.80

= $145.20

Cost of each shirt= Total amount both spent / Total number of shirts bobby and Davonte bought

= $145.20 / 11

= $13.2

Therefore, each shirt Bobby and Davonte bought cost $13.2

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Answer:

Step-by-step explanation:

It seems we are looking for a math expression that is the same as English expression you wrote.The sum is what we get when we add numbers. Therefore, we could restate the English expression as what do we get when we add 5 to the number x? While we do not know what specific number x represents, we do know that if we add 5 to the number x we get 5 plus x. Now the question can be restated as, "How do we write 5 plus the number x?" Do you know the answer now? Does 5 + x sound right? How about x + 5? Both of these expressions are correct as they both represent the sum of 5 and the number x.

The simplified form of the expression [tex]\frac{-8.97\times10^1}{-3.00\times10^3}[/tex] is 2.99×10⁻².

In scientific notations numbers are written in the form of a base that is

0  ≤ b < 10 and multiplied by 10ⁿ where n represents integers.

We write large standard numbers in scientific form in a compact manner.

The rational expression given is  [tex]\frac{-8.97\times10^1}{-3.00\times10^3}[/tex].

First, we'll solve for the base which is,

- 8.97/- 3.00.

= 2.99 and we know 10¹/10³ = 10¹⁻³ = 10⁻².

Therefore, The expression [tex]\frac{-8.97\times10^1}{-3.00\times10^3}[/tex] can be written as 2.99×10⁻².

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Answer:

1050 feet

Step-by-step explanation:

We know

A cheetah runs 420 feet in 6 seconds

Find how many feet the cheetah runs in 1 second by taking

420 / 6 = 70 feet

How many feet could a cheetah run in 15 seconds?

70 x 15 = 1050 feet

So, the cheetah could run 1050 feet in 15 seconds.

The equation of the line in slope-intercept form is y = 1/4x + 4, with slope 1/4, and passes through the point (-4,3).

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

Given the slope, m = 1/4, and the point (-4,3), we can use the point-slope form of a line to find the y-intercept:

y - 3 = 1/4 × (x - (-4))

y - 3 = 1/4x + 1

We can simplify this equation:

y = 1/4x + 4

This is the equation of the line in slope-intercept form.

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The value of [tex]i^5[/tex] is i.

The correct option is (A).

Complex Numbers in Maths. Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.

Given:

[tex]i^5[/tex]

Now, we have to expand the complex number

[tex]i^5[/tex] = i x i x i x i x i

   = (i)² x (i)² x i

As, the value of i² = -1

[tex]i^5[/tex] = (i)² x (i)² x i

   = (-1) x (-1) x i

   = 1 x i

   = i

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Answer: (f∘g)(x)=15x

Step-by-step explanation:

The expression of (f∘g)(x) in the simplest form is (f∘g)(x)=15x and this can be determined by using the arithmetic operations.

Given :

f(x)=3x

g(x)=5x

The following steps can be used in order to determine the expression of (f∘g)(x):

Step 1 - Write the given function.

f(x)=3x

g(x)=5x

Step 2 - Now, replace 'x' with g(x) in order to determine the expression of (f∘g)(x).

(f∘g)(x)=3g(x)

(f∘g)(x)=3x5x

Step 3 - Simplify the above expression.

(f∘g)(x)=15x

The expression of (fog)(x) in the simplest form is (f∘g)(x)=15x

A declared limit to the number of impressions that will be made from a particular plate (or matrix) is known as an "impression limit".

An "impression limit" is a predetermined maximum number of times that a printing plate (also known as a matrix) can be used to make an impression on the printing material before it becomes worn and less effective. The purpose of setting an impression limit is to ensure consistent, high-quality printing results.

A printing plate is typically made of metal, plastic, or rubber and is used to transfer an image or text onto paper or another printing surface. Each time the plate makes an impression on the printing material, a small amount of wear and tear occurs, causing the plate to degrade over time.

To prevent this degradation, an impression limit is set for each plate. This limit specifies the maximum number of times that the plate can be used before it needs to be replaced. The impression limit helps to ensure that each plate is used for a specific number of impressions only and then replaced, which helps to ensure consistent, high-quality printing results.

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Literally nothing occurs. On the off chance that the two terminals are at an equivalent voltage, no ongoing streams, any more than if you contacted two impartial bits of metal together.

Cases 1 and 3 are basically something very similar. There's a voltage difference, so current normally streams. In any case, you don't have a circuit, so when electrons stream from the lower positive voltage (which is zero assuming it's released) to the higher positive terminal, the electrons develop and make a static charge that balances the voltages. This occurs in a small part of a second, so the current is negligible, and voltage promptly stops.

The standard metric unit on electric potential difference is the volt, truncated V and named to pay tribute to Alessandro Volta. One Volt is identical to one Joule per Coulomb. In the event that the electric potential difference between two areas is 1 volt, one Coulomb of charge will acquire 1 joule of potential energy when moved between those two areas. In the event that the electric potential difference between two areas is 3 volts, one coulomb of charge will acquire 3 joules of potential energy when moved between those two areas.

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The probability of choosing a three digit number whose sum is 3 is given by the equation P = 0.00666

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the number of three digits number be represented as n

Let the probability of choosing a three digit number whose sum is 3 be P

Now , the number of three digits number whose sum is 3 is given by set A

Set A = { 102 , 120 , 111 , 201 , 210 , 300 }

Now , the total number of 3 digits numbers is n = 900

So , the probability of choosing a three digit number whose sum is 3 P = number of three digits number whose sum is 3 / total number of 3 digits numbers

The probability P = 6/900

On simplifying the equation , we get

The probability P = 1/150

The probability P = 0.00666

Hence , the probability is P = 0.00666

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The time it takes for gaussian elimination to work on a system of equations is directly related to the number of equations in the system.

Gaussian elimination is a method used in linear algebra to solve systems of linear equations. It involves manipulating the coefficients of the equations in a specific way so that the solution is easier to find.

When comparing a system of 1000 equations to a system of 500 equations, the time it takes for gaussian elimination to work on the larger system is significantly longer.

This is because the number of operations required to solve the system increases as the size of the system increases.

To be more specific, the number of operations required for gaussian elimination is proportional to the square of the number of equations in the system.

This means that if a system of 500 equations requires 1000 operations, a system of 1000 equations would require 2000 operations.

So, we can expect gaussian elimination to take about twice as long to work on a system of 1000 equations compared to a system of 500 equations.

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The variables for this problem are classified as follows:

a) The number of songs on a randomly chosen ipod is discrete.

b) The number of people in line at the bank at a randomly chosen time is discrete.

c) The time it takes to drive to the airport is continuous.

d) The amount of rain during the next thunderstorm is continuous.

Variables are classified as continuous or discrete depending if they can assume decimal values, as follows:

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6.08 ounces of Ceylon tea and 1.92 ounces of Formosa tea must be mixed to produce a mixture of 8 oz worth $1.62/oz.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

Ceylon tea = x

Cost = $1.50

Formosa tea = y

Cost = $2

Now,

To produce a mixture of 8 oz worth $1.62/oz.

We can make two equations:

x + y = 8 _____(1)

1.50x + 2y = 12.96 ______(2)

From (1),

x = 8 - y

Substituting in (2).

1.50x + 2y = 12.96

1.50 (8 - y) + 2y = 12.96

12 - 1.50y + 2y = 12.96

0.50y = 12.96 - 12

y = 0.96/0.50

y = 1.92

And,

x = 8 - 1.92

x = 6.08

Thus,

6.08 ounces of Ceylon tea.

1.92 ounces of Formosa tea.

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Yes, the data provided can be used to provide convincing evidence that the true proportion of teens who think highly of their mother is greater than 0.84.

To determine if the data provides convincing evidence that the true proportion of teens who think highly of their mother is greater than 0.84, we need to perform a hypothesis test. Here is the basic process:

State the null and alternative hypotheses:

Null Hypothesis: The true proportion of teens who think highly of their mother is equal to 0.84 (p = 0.84)

Alternative Hypothesis: The true proportion of teens who think highly of their mother is greater than 0.84 (p > 0.84)

Select the level of significance: A commonly used level of significance is 0.05, meaning that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is true).

Compute the test statistic and p-value: The test statistic is the z-score and can be calculated using the formula:

z = (x - p) / sqrt(p(1-p) / n)

where x = number of positive responses in the sample = 135

p = proportion claimed in the statement = 0.84

n = sample size = 150

Make a decision: Compare the calculated p-value with the level of significance. If the p-value is less than the level of significance (0.05), reject the null hypothesis. If the p-value is greater than the level of significance, fail to reject the null hypothesis.

Draw a conclusion: If the null hypothesis is rejected, conclude that the data provides convincing evidence that the true proportion of teens who think highly of their mother is greater than 0.84. If the null hypothesis is not rejected, conclude that the data does not provide convincing evidence that the true proportion is greater than 0.84.

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The first case given is a deigned experiment and the second case is an observational study.

i. This is a designed experiment because the tunas were randomly assigned to two different treatments (polluted and non-polluted water) in an attempt to determine the effect of the treatment (methyl mercury) on the outcome (survival times). The experiment was intentionally designed and carried out to test a hypothesis.

ii. This is an observational study because the data was collected by simply observing the natural occurring relationship between increasing amounts of phosphorus in the lake and decreasing number of lake trout over time, without any manipulation or intervention by the biologist. The purpose is to describe or understand the relationship between two variables rather than to test a hypothesis.

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The expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right))[/tex].

If there are N top applicants and M schools to choose from, then the expected number of schools that will be attended by at least one top applicant is [tex]\frac{M \choose N}{M^N}[/tex]. This is because each of the N top applicants can choose any of the M schools independently, and the probability of any one top applicant attending any given school is[tex](\frac{1}{M})[/tex]. Thus, the probability of at least one top applicant attending any given school is[tex](1 - \left( \frac{M-1}{M} \right)^N)[/tex]. Therefore, the expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right)).[/tex]

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The  total distance traveled by the "super ball" is 49 meters.

1. First bounce: The ball drops from 16 meters above the ground and rises to [tex]\(\frac{3}{4}\)[/tex] of that height.

Distance traveled in the first bounce:

[tex]\[16 + \frac{3}{4} \times 16\][/tex]

2. Second bounce: The ball drops from the new height and rises to [tex]\frac{3}{4}\)[/tex] of that height.

Distance traveled in the second bounce:

[tex]\[\left(\frac{3}{4} \times 16\right) + \frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\][/tex]

3. Third bounce: The ball drops from the new height and rises to [tex]\(\frac{3}{4}\[/tex] ) of that height.

Distance traveled in the third bounce:

[tex]\[\left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right) + \frac{3}{4} \times \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)\][/tex]

Now, the total distance traveled

[tex]\[ \text{Total distance traveled} = \left(16 + \frac{3}{4} \times 16\right) + \left(\frac{3}{4} \times 16 + \frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)[/tex]

                                         [tex]+ \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right) + \frac{3}{4} \times \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)\right) \][/tex]

[tex]\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{27}{4} + \frac{81}{16}\][/tex]

[tex]\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{27}{4} + \frac{81}{16}[/tex]

                                       [tex]= 16 + 12 + 9 + \frac{108}{16} + \frac{81}{16} \][/tex]

[tex]\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{108 + 81}{16}[/tex]

                                    [tex]= 16 + 12 + 9 + \frac{189}{16} \][/tex]

Add the whole numbers and fractions separately:

[tex]\[\text{Total distance traveled} = 37 + \frac{189}{16}\][/tex]

Now, convert the improper fraction to a mixed fraction:

[tex]\[ \frac{189}{16} = 11\frac{13}{16} \][/tex]

Finally, add the whole number and the mixed fraction:

[tex]\[ \text{Total distance traveled} = 37 + 11\frac{13}{16} \][/tex]

So, the total distance traveled by the "super ball" is :

[tex]\[ \text{Total distance traveled} = 37 + 12 = 49 \text{ meters} \][/tex]

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Answer:

Divide 192 (students) by 3 ( buses).

192/ 3 = 64

Step-by-step explanation:

hsjdiwkdhd jdindid odj

The  values of x is (4,-8) he two vectors will be orthogonal.

Let u=(x+4) i-4 j

x=x i+8 j

Now, U and v are orthogonal.

A number of vectors that are mutually perpendicular to each other, meaning they form an angle of 90° with a magnitude of one unit with each other, are called orthogonal unit vectors.

Therefore, u.v=0

⇒[tex]((x+4) i-4 j) \cdot(x i+8 j)=0 \\[/tex]

⇒[tex]x(x+4)-32=0 \\[/tex]

⇒[tex]x^2+4 x-32=0 \\[/tex]

⇒[tex]x^2+8 x-4 x-32=0 \\[/tex]

⇒[tex]x(x+8)-4(x+8)=0 \\[/tex]

⇒x=4, x=-8

Therefore, the value of x=4 and x=-8 the two vectors will be orthogonal.

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The probability of getting an no head is 1/8 or 12.5%

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space / total outcome

The total outcome of tossing a coin thrice is 8

The sample space of getting no head i.e (TTT) is 1

Therefore the probability of getting no head = 1/8

in percentage; 1/8 × 100 = 100/8 = 12.5 %

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Answer:

Step-by-step explanation:

i know

The inverse of the linear equation is:

y = x - 3

And its graph can be seen on the image at the end.

The dashed line is the parent linaer equation:

y = x

And it is its own inverse, so we ignore that one.

The other line is:

f(x) = x + 3

Now, remember that the inverse of f(x) will be a function g(x) such that:

f( g(x)) = x

         = g(x) + 3 = x

Solving that for g(x) we will get:

g(x) =x - 3

The graph of that lineis on the image at the end.

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The height of the tree is 5.4 meters.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

The picture shows a man next to a tree.

The man has a height of 1.8 meters.

The man and the tree are drawn to the same scale.

The height of the tree = 1.8 x 3 = 5.4 meters

Therefore, the height is 5.4 meters.

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Answer:7.2

Step-by-step explanation: as the man is 1.8 you can see that if you add on top of him 4 more in total that would be the height of the tree so the calculation would be 1.8x4 which would be 7.2

Answer: Your answer is 2x2√7 (Please Mark Branliest)

Step-by-step explanation:

Step 1: Rewrite 28x4 as (2x2)2⋅7

Step 1.1: Factor 4 out of 28 which should get you √4(7)x4

Step 1.2: Rewrite 4 as 22 which should get you √22⋅7x4

Step 1.3: Rewrite x4 as (x2)2 which should get you √22⋅7(x2)2

Step 1.4: Move the 7 which should get you √22(x2)2⋅7

Step 1.5: Rewrite 22(x2)2 as (2x2)2 which sould get you √(2x2)2⋅7

Step 2: Pull terms out from under the radical to get yourself 2x2√7

The image point is located at (16, 4).

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that, a point (8, 2) is dilated using a scale factor of 2.

A point (x, y) when dilated by a scale factor of k changes to (kx, ky).

Point (8, 2) will become,

(8 × 2, 2 × 2) = (16, 4).

Hence the dilated point is (16, 4).

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The correct answer is B) the graph of g is a 1/3 horizontal shrink of the graph of f.

A mathematical transformation is the movement of a geometric object or function from one space to another. This new space may be a new quadrant in a Cartesian coordinate system, or it could be a whole new plane or number set. When we translate, we move a figure in any direction. When we flip a figure over a line, we call this reflection. When we rotate a figure a given amount around a point, we call this rotation. Transformations are classified into four types: translation, rotation, reflection, and dilation. Rotation, translation, and reflection are examples of stiff transformations.

Here,

The function g(x) = f(3x) is defined as the transformation of f(x) by replacing x with 3x in the argument of f. This means that each x-value of f(x) is replaced with 3 times its original value in g(x). As a result, the graph of g(x) will be a horizontal shrink of the graph of f(x) by a factor of 1/3. The horizontal axis will be compressed, making the graph appear narrower than the graph of f(x).

The correct answer is B) the graph of g is a horizontal shrink of the graph of f by a factor of 1/3.

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Using the distance formula, the most precise classification of LMNP is a parallelogram.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is given by the following formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²],

where d is the distance between the points (x₁, y₁) and (x₂, y₂).

we shall evaluate the distance between each points as follows:

distance between L and M = √[[-2 - (-5)]² + (14 - 8)²]

distance between L and M= √(3³ + 6²)

distance between L and M= √45

distance between M and N = √[[12 - (-2)]² + (7 - 14)²]

distance between M and N = √[14² + (-7)²]

distance between M and N = √245

distance between N and P = √[(9 - 12)² + (1 - 7)²]

distance between N and P = √[(-3)² + (-6)²]

distance between N and P = √45

distance between P and L = √[(-5 - 9)² + (8 - 1)²]

distance between P and L = √[(-14)² + 7²]

distance between P and L = √245.

Therefore, using the distance formula, the most precise classification of LMNP is a parallelogram.

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