What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?

Answer:

2x(x+y)(x-y)

Step-by-step explanation:

Given the expression;

(x+y)² + 2(x+ y)(x- y) + (x– y)²

Factorize

(x+y)² + (x+ y)(x- y) +   (x+ y)(x- y) + (x– y)²

= (x+y)[x+y+(x-y)] +(x-y)[(x+y)+(x-y)]

= (x+y)(x-y)(x+y+(x-y))

= (x+y)(x-y)(x+y+x-y)

= (x+y)(x-y)(2x)

hence the expanded form is 2x(x+y)(x-y)

Answer:

The algebraic equation for the given sentence is

3x - 8 = 25

The system of equations are solved and the value of x and y are -4 and 12 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

4x + 3y = 20   be equation (1)

3x + 2y = 12   be equation (2)

Multiply equation (1) by 3 and equation (2) by 4 , we get

12x + 9y = 60   be equation (3)

12x + 8y = 48   be equation (4)

Subtracting equation (4) from equation (3) , we get

y = 12

Substituting the value of y in equation (2) , we get

3x + 2 ( 12 ) = 12

Subtracting 24 on both sides , we get

3x = -12

Divide by 3 on both sides , we get

x = -4

Hence , the system of equations are solved

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It has been proved that the lines MN and PR are parallel because they have the same slope.

We are given the coordinates of the points P, Q and R as:

P(-3, -6)

Q(1, 4)

R(5, -2)

Since M is the midpoint of PQ, we have:

M = (-3 + 1)/2, (-6 + 4)/2

M = (-1, -1)

N is the midpoint of QR and so:

N = (1 + 5)/2, (4 - 2)/2

N = (3, 1)

Slope of MN = (1 + 1)/(3 + 1) = 1/2

Slope of PR = (-2 + 6)/(5 + 3)

Slope of QR = 4/8 = 1/2

Both slopes are equal and as such they are parallel lines

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The total number of different possible sequences of heads and tails when a coin is flipped 10 times is 1024.

According to the given question.

A coin is flipped 10 times.

As we know that a sample space or sequence is a collection or a set of possible outcomes of a random experiment.

If a coin is flipped once, then the number of possible sequences or outcomes will be 2 (either head or a tail).

Since, the coin is flipped 10 times in a row.

Thereofore,

The number of different possible sequences of heads and tails

= 2^10

= 1024

Where, 2 is the number of possible sequences when a coin is flipped once and 10 is the number of trials.

⇒ 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 ×2 × 2 = 1024

Hence, the total number of different possible sequences of heads and tails when a coin is flipped 10 times is 1024.

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The if statement assigns a value of 10000 to the variable "bonus" if the value of the variable "goodssold" exceeds 500000.

To achieve this, we can use an if statement in programming. An if statement allows us to conditionally execute a block of code based on a specified condition. In this case, the condition is whether the value of the variable "goodssold" is greater than 500000. If the condition evaluates to true, the code inside the if statement will be executed, and the variable "bonus" will be assigned a value of 10000.

Here's an example of how the if statement can be written in Python:

if goodssold > 500000:

   bonus = 10000

In this code snippet, the variable "goodssold" represents the number of goods sold, and we compare its value to 500000 using the greater than operator (>). If the condition is true, the code inside the if statement is executed, and the variable "bonus" is assigned a value of 10000. If the condition is false, the code inside the if statement is skipped, and the variable "bonus" retains its previous value (if any).

By using this if statement, we can dynamically assign a bonus of 10000 to the variable "bonus" based on the value of the variable "goodssold" being greater than 500000. This allows for flexible and conditional handling of the bonus calculation in the program.

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When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is   \(\\26 \frac{2}{5}\).

What is improper fractions?

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

12 times 120% + 12

12*120%+12

\($$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$\)

Follow the PEMDAS order of operations

Multiply and divide (left to right) \($12 \times \frac{6}{5}: \frac{72}{5}$\)

\(=\frac{72}{5}+12$$\)

Add and subtract (left to right) \($\frac{72}{5}+12: \frac{132}{5}$\)

\(=\frac{132}{5}$$\)

Convert improper fractions to mixed numbers: \($\frac{132}{5}=26 \frac{2}{5}$\)

\(=26 \frac{2}{5}$$\)

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Answer:

The cost C, of hosting the banquet with the services of Caterer One is;

C = $ 45·n

The cost C, of hosting the banquet with the services of Caterer Two is;

C = $250 +  $ 28·n

The cost C, of hosting the banquet with the services of Caterer Three is;

C = $500 +  $ 20·n

Step-by-step explanation:

The information includes;

The amount available to the group for the banquet = $120

The number of people attending the banquet = n

The cost incurred in hosting the banquet = C

The major costs in hosting the banquet are hall rental and caterer

The cost per caterer are as follows;

Caterer One

The cost per person including the hall = $45

Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;

C = n × $45 = $ 45·n

Caterer Two

The hall rental = $250

The cost per person = $28

Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;

C = $250 +  n × $28 = $250 +  $ 28·n

Caterer Three

The hall rental = $500

The cost per person = $20

Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;

C = $500 +  n × $20 = $500 +  $ 20·n.

Answer:

The cost C, of hosting the banquet with the services of Caterer One is;

C = $ 45·n

The cost C, of hosting the banquet with the services of Caterer Two is;

C = $250 +  $ 28·n

The cost C, of hosting the banquet with the services of Caterer Three is;

C = $500 +  $ 20·n

Step-by-step explanation:

The information includes;

The amount available to the group for the banquet = $120

The number of people attending the banquet = n

The cost incurred in hosting the banquet = C

The major costs in hosting the banquet are hall rental and caterer

The cost per caterer are as follows;

Caterer One

The cost per person including the hall = $45

Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;

C = n × $45 = $ 45·n

Caterer Two

The hall rental = $250

The cost per person = $28

Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;

C = $250 +  n × $28 = $250 +  $ 28·n

Caterer Three

The hall rental = $500

The cost per person = $20

Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;

C = $500 +  n × $20 = $500 +  $ 20·n.

Answer:

Step-by-step explanation:

9

The angles are vertically opposite. Vertically opposite angles are equal.

12x - 5 = 10x + 1           Add 5 to both sides.

12x = 10x + 5 + 1          Combine

12x = 10x + 6                Subtract 10x from both sides.

12x - 10x = 6                Combine

2x = 6                          Divide by 2

x = 6/2

x = 3

10

Adjacent angles to each other when sharing a side are supplementary

4x + 7 + 2x + 5 = 180             Combine like terms on the left

6x + 12 = 180                          Subtract 12 from both sides

6x = 180 - 12                          Combine

6x = 168                                  Divide by 6

x = 168 / 6

x = 28

Answer:

Day 13

Step-by-step explanation:

If you add on both side 13 time you get 90

Answer:

ye that is the correct answer

The ways that the exercise can be expressed such that for every 6 squares there are 3 circles include:

This question is asked in Spanish on an English site so the answer will be provided in English for better learning by other students.

The ratio of squares to circles is 6:3 or simplified, 2:1. This means for every 2 squares, there is 1 circle.

You could also use a proportional statement such that the number of squares is twice the number of circles. For every 6 squares, there are 3 circles.

There is also equation form where we can say, if S is the number of squares and C is the number of circles, the relationship could be expressed as S = 2C. This means the number of squares is twice the number of circles.

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The translated question is:

How to express this exercise for every 6 squares there are 3 circles.

Answer:11 kids were at the party

Step-by-step explanation:24 slices in all , 22 were eaten so that means 22 divided by 11 is 2 so there was 11 kids

Answer:

11 children

Step-by-step explanation:

First you have to do 8 times 3 to get the number of slices of pizza there were.

Then you have to divided that by 2. But remember, there are 2 slices left.

So, you have to take away one child to get the answer: 11 children

I feel bad for that last child. I hope this helped ;)

The reasonable solution for the number of buttons of each color in one sack is (20, 11), meaning there are 20 black buttons and 11 white buttons in one sack.

Let's solve the system of equations based on the given information:

Let b be the number of black buttons in one sack and w be the number of white buttons in one sack.

From the first equation, we know that the number of black buttons in one sack is 9 more than the number of white buttons:

b = w + 9

From the second equation, we know that the total number of buttons in one sack is 372 divided by the number of sacks (12):

b + w = 372/12

b + w = 31

We can substitute the value of b from the first equation into the second equation:

(w + 9) + w = 31

2w + 9 = 31

2w = 31 - 9

2w = 22

w = 22/2

w = 11

Substituting the value of w back into the first equation, we can find the value of b:

b = 11 + 9

b = 20

Therefore, the reasonable solution for the number of buttons of each color in one sack is (20, 11), meaning there are 20 black buttons and 11 white buttons in one sack.

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The movement of the particle on the circle is its displacement.

The value of dy/dt at this time is -9/2.

Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

A particle moves on the circle x^2 + y^2=25 in the XY-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6.

The equation of the circle is given as:

\(\rm x^2 + y^2=25\)

Differentiate with respect to time

\(\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\)

Substitute all the values in the equation

\(\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\\\\2(3) \times 6+2(4)\times \dfrac{dy}{dt}=0\\\\ 6 \times 6+8 \times \dfrac{dy}{dt}=0\\\\ 36+8\times \dfrac{dy}{dt}=0\\\\ 8\times \dfrac{dy}{dt}=-36\\\\ \dfrac{dy}{dt}= \dfrac{-36}{8}\\\\ \dfrac{dy}{dt}= \dfrac{-9}{2}\)

Hence, the value of dy/dt at this time is -9/2.

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Answer:

continuous random variable

No, Lydia's assertion that δSTU is a right triangle is not correct.

A right triangle is a triangle in which one of the angles measures 90 degrees (a right angle). To determine if δSTU is a right triangle, we need to examine the angles formed by the given coordinates.

Using the coordinates:

s (-3, 0)

t (0, -3)

u (3, -3)

We can calculate the slopes of the lines formed by connecting these points to see if any of them are perpendicular (indicating a right angle).

The slope of the line connecting points s and t is:

m(st) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (0 - (-3)) = -3/3 = -1

The slope of the line connecting points s and u is:

m(su) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (3 - (-3)) = -3/6 = -1/2

The slope of the line connecting points t and u is:

m(tu) = (y₂ - y₁) / (x₂ - x₁) = (-3 - (-3)) / (3 - 0) = 0/3 = 0

None of the slopes calculated are perpendicular to each other, meaning none of the angles formed by the given coordinates are 90 degrees. Therefore, δSTU is not a right triangle.

In summary, Lydia's assertion that δSTU is a right triangle is incorrect because the angles formed by the given coordinates do not include a 90-degree angle.

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The inputs of the function are -8, 2, 4, and 6.

The input is the number that we put into the given function to get the output function.

x  and y of the function are given below

X    –8      2     4    6

f(x)  –6    –3     1     5  

From the given table, the inputs are given as the set of x values.

outputs are given as the set of y values. here, x is the input value that gives the output f(x).

Since x represents the input values and y represents the output values.

So, inputs of the function are -8, 2, 4 and 6

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Answer:

1/5

Step-by-step explanation:

The Rolle's Theorem cannot be applied to function f on the closed interval [a, b].

What is Rolle's Theorem?

In calculus, Rolle's theorem or Rolle's lemma basically asserts that any real-valued differentiable function that reaches equal values at two different places must have at least one stationary point between them—that is, a position where the first derivative is zero.

As given function is,

f(x) = x^(2/3) - 1

This is basically a cube root of x² in first term.

So, it is continuous for negative numbers even.

So, first condition that is Continuous over [-8, 8] satisfied.

Now differentiate function as follows:

f(x) = x^(2/3) - 1

f'(x) = 2/3 x^(-1/3)

f'(x) = 2/{3x^(1/3)}

Clearly this function is not differentiable at x = 0.

And x = 0 belons to [-8, 8].

So, second condition namely

Differentiable in [-8, 8] does not check out.

Therefore, Rolle's Theorem cannot be applied.

No, because function is not differentiable in the open interval (a, b).

Since Rolle's Theorem cannot be applied, for the value of c.

The Rolle's Theorem cannot be applied to function f on the closed interval [a, b].

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The purchasing power of $3,000 paid to an adjunct faculty member at a local university per course she taught each semester in 2013 is equivalent to $26.06 in 2021.

To determine the purchasing power of $3,000 that was paid to an adjunct faculty member at a local university per course she taught each semester in 2013, using the Annual Average index figures for both 2013 and 2021, we use the following steps:

Step 1: Go to the website of the US Bureau of Labor Statistics and locate the Consumer Price Index (CPI) for 2013 and 2021. The CPI for 2013 is 232.957 and the CPI for 2021 is 268.551. This represents an increase in the CPI over the 8-year period.    

Step 2: Next, we calculate the rate of inflation by dividing the CPI for 2021 by the CPI for 2013 and then multiplying the result by 100. This gives:    

Inflation rate = (CPI 2021 / CPI 2013) x 100

= (268.551 / 232.957) x 100

= 115.25

Step 3: Finally, we determine the purchasing power of $3,000 in 2013 in terms of the dollars needed in 2021 to purchase the same amount of goods and services. This is done by dividing the amount paid in 2013 by the inflation rate calculated above. This gives:    

Purchasing power of $3,000 in 2021 = $3,000 / 115.25

= $26.06 (rounded to the nearest cent)

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Yes, this sample of the trees in the county likely to be representative if each forest is the same size.

Representative sample, the sample must accurately reflect the population studied in demographics and characteristics of the chosen subjects.

For example, a representative sample will reflect only those within the study population and should not extend to those outside the study. If Jose is interested in studying the exercise habits of college athletes, only the population of college athletes should be considered for the selection of a representative sample. Jose will not choose athletes from high school or career athletes as part of his representative sample.

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Answer:

  0.2601

Step-by-step explanation:

There are 19C16 = 969 ways for Lester to choose 16 of the 19 objects.

There are 12C11 = 12 ways to choose 11 vases, and 7C5 = 21 ways to choose a non-vase, for a total of (12)(21) = 252 ways to choose exactly 11 vases in 16 objects.

So, the probability of interest is ...

  252/969 ≈ 0.2601

_____

nCk = n!/(k!(n-k)!) ... the number of ways to choose k objects from n

Answer:

length of side of square = 8 cm

Step-by-step explanation:

Let's first find the area of the triangle, using the formula A = (1/2)(base)(height):

A = (1/2)(16 cm)(4 cm) = 32 cm^2.

Twice the area of the triangle would be 64 cm^2.

The area of the square is then 64 cm^2, which is the square of the length of one side of the square.  Taking the square root of 64 cm^2, we get

length of side of square = sqrt(64 cm^2) = 8 cm

Answer:

Read the explanation

Step-by-step explanation:

Explanation:

When multiplying and dividing more than two positive and negative numbers, use the Even-Odd Rule: Count the number of negative signs — if you have an even number of negatives, the result is positive, but if you have an odd number of negatives, the result is negative. This problem has just one negative sign

Answer:

1/5

Step-by-step explanation:

Answer:

(1/5)

Step-by-step explanation: I did it, got it right.

After adding (-7) to each value in the given data set, the mean is 38.25, the median is 38, the mode does not exist, the range is 24, and the standard deviation is approximately 8.85.

To find the mean of the data set, add all the values together (49, 30, 34, 43, 31, 37, 25, 47) and divide the sum by the total number of values (8). The mean is the average value of the data set.

To determine the median, arrange the values in ascending order (25, 30, 31, 34, 37, 43, 47, 49) and find the middle value. In this case, the median is the average of the two middle values (34 and 37).

The mode refers to the value(s) that appear most frequently in the data set. In this case, there is no mode since no value appears more than once.

The range is calculated by subtracting the smallest value (25) from the largest value (49). Thus, the range is 24.

To calculate the standard deviation, subtract the mean from each value, square the differences, calculate the mean of those squared differences, and finally take the square root of the resulting value. This provides a measure of the dispersion or spread of the data around the mean.

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