The point where the graphs of two equations intersect has y-coordinate 2. One equation is y=3x+5. Find the other equation if its graph has a slope of 1.

The required distance between each pair of numbers on a number line is below in the solution part.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

1. The distance between 5 and -2 on a number line is |5-(-2)| = 7 units.

2. The distance between -8 and -17 on a number line is |-17-(-8)| = 9 units.

3. The distance between 28 and -12 on a number line is |28-(-12)| = 40 units.

4. The distance between -17 and 15 on a number line is |15-(-17)| = 32 units.

5. The distance between 33 and -2 on a number line is |33-(-2)| = 35 units.

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The three lengths 8, 9 and 10 form a triangle.

In Euclidean geometry stating that any two triangle sides added together must be greater than or equal to the third side; represented by the symbols a + b ≥c. The basic tenet of the theorem is that a straight line connects any two places.

Given:

Sides: 8, 9, 10

As from Triangle Inequality the sum of two sides are greater than the third side of triangle.

So, 8 + 9 > 10

9 + 10 > 8

10+ 8> 9

Since the triangle inequality satisfied.

Thus, the triangle can form using sides 8, 9, 10.

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The solution of the system of equation is , x= -4 & y= -8.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

from the given graph we get,

one line is passing through the points (0,10) , ( 4,28)

so, the equation of the line can be,

4y= 18x + 40

and, second line is passing through the points (0,8) , (1,12)

so, the equation of the line can be,

y= 4x+8

solving the equations we get,

x= -4

y= -8

Hence, The solution of the system of equation is , x= -4 & y= -8.

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The sine function with the values in the table is defined as follows:

y = 5sin(πx/2) - 1.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a maximum value of 4 and a minimum value of -6, for a difference of 10 units, hence the amplitude is obtained as follows:

A = [4 - (-6)]/2

A = 10/2

A = 5.

Without vertical shift, a function with amplitude of 2 would oscillate between -5 and 5, while this one oscillates between -6 and 4, hence the vertical shift is given as follows:

D = -1.

The shortest distance between repetitions can be given by 4 - 0, hence the period is of 4 units and the coefficient B is given as follows:

2π/B = 4

B = 2π/4.

B = π/2.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 5sin(πx/2) - 1.

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Answer:

80 divded by 10 is c c=8

Answer:

no linear relationship exists between the two variables being compared

Step-by-step explanation:

A reduced row echelon form of a matrix is a way to solve a system of linear equations. A reduced row echelon matrix has the following properties:

For a system of three equations and three variables with no solution, the reduced row echelon form of the augmented matrix would be in the form:

\begin{bmatrix}

1 & a & b & c \

0 & 0 & 0 & d \

0 & 0 & 0 & e

\end{bmatrix}

where a, b, c, d and e are constants and d and e are non-zero.

This form indicates that the system has no solution because the bottom row represents an equation that is false (0 = non-zero).

The reduced row echelon form of a matrix is a way to determine whether a system of linear equations has a solution. A system of linear equations has no solution if and only if the reduced row echelon form of the augmented matrix contains a row in the form of 0 = k, where k is non-zero.

In this case, the reduced row echelon form of the augmented matrix has the bottom row with the form 0 = d, and d is non-zero. This means that the equation is false, indicating that the system has no solution.

So, the fact that the bottom row of the reduced row echelon form has the form 0 = k, where k is non-zero, allows us to determine that the system of linear equations has no solution.

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Answer:

$6.50

Step-by-step explanation:

25 - 6.25 = 18.75

18.75 - 3.75 = 15

15 - 8.50 = 6.50

The expression in simplest form that represents the

total amount that Andrew spent would be = $8d

The simple forms of representation of expression shows that all the values of that expression are in its simplest form.

In Andrew cans of ping pong balls,

Last week he bought = 4 cans

This week he bought = 2 cans

The cost of ping pong balls = d dollars per

can..

The total amount that Andrew spent would be;

= d × ( 4+2)

= $8d

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Answer:  x= - 9/4

Step-by-step explanation:

1. Move the variable to the left, and change its sign.

-4x+8+2x=17

2. Collect like terms

-2x=17-8

3. Divide each side by -2

-2x=9

Answer: x= - 9/2

Answer: 2/3

Step-by-step explanation: 1/3+1/3 is 2/3.

Answer:

Exact form:2/3

decimal form:       _

                           0.6

Step-by-step explanation:

You can form 56,800 possible teams from a pool of 16 eligible engineers by selecting a total of 3 team members.

The total number of teams can be calculated using combination formula. The combination formula is nCr where n is the total number of items and r is the number of items you want to choose.

In this case, n = 16 and r = 3. Hence, the number of possible teams:

This means you can form 56,800 unique teams by choosing 3 engineers out of 16 eligible engineers. The combination formula helps in finding the number of possible combinations when the order does not matter, which is the case here as the order of engineers in a team does not matter.

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If we change the 0's to negative numbers then the average, median and SD. The average would b) decrease.

The average value calculated within a specific data set is referred to as the "mean.". This calculation can be used in any situation where knowing a data set's average value, such as its cost or income, may be deemed as useful.

By being aware of the average cost or income within a given data set, you can better position yourself to increase your profits or savings.

A normal distribution can have a mean that is negative in nature. When only some of the data points have negative values, this is both a possibility and a foregone conclusion;

however, if all of the data points have negative values as nature it should be noted that if a normal distribution has a negative mean, at least half of the data points in the distribution must also have a negative mean.

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Note that the full question is:

some of the girls with 0 weight gain actually lost weight. if we changed their 0's to negative numbers how would the average, median and sd change? the average would

a) increase

b) decrease

c) stay the same

Answer:

20% of 11 is 2.2

Step-by-step explanation:

11 x .20 = 2.2

The kind of discontinuous measurement procedure that is used is partial interval recording

Given that,

A client frequently shouts things out loud. You break up the session into shorter timed segments in order to get data on this. You record an event if the behavior happens at any time throughout the interval.

To find : which discontinuous measuring technique are you employing?

An interval recording technique is partial interval recording. An interval recording approach involves watching to see if a behaviour happens or not within predetermined intervals of time. After determining the duration of an observation session, the time is divided into shorter segments that are all of the same length.

So, partial interval recording is the type of discontinuous measuring technique that is applied.

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If a trapezoid has an area of 100 square units, the scale factor that would be required to dilate the trapezoid to have each area is:

sqrt(A / 100)

To find the scale factor required to dilate a shape, you need to determine what ratio of the new area to the original area you want to achieve.

Let's call the scale factor "k". If the original area of the trapezoid is 100 square units, and the new area is "A", the relationship between the two areas can be expressed as:

So to find the scale factor required to achieve a specific new area, you can solve for k by dividing the new area by 100 and taking the square root:

Note that: This equation assumes that the dilation is proportional, meaning that all dimensions of the trapezoid are scaled by the same factor.

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The linear function rule for the given data is y = 6x + 6.

A linear function is defined as an equation in which the highest exponent of the variable is always one.

The rule for the data in the given table:

x:  1   2   3   4

y: 12 18 24 30

The linear function rule for the given data can be found using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Let's use the first and second points: (1,12) and (2,18).

The slope can be found using the formula:

m = (18 - 12) / (2 - 1) = 6

Next, we can use the slope and one point from the table to find the y-intercept:

b = y - mx = 12 - m × 1 = 12 - 6 × 1 = 6

So the linear function rule for the given data is:

y = 6x + 6

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Hence, the standard deviation is more affected by skewness compared to the IQR.

Skewness is a metric for a distribution's asymmetry. When the left and right sides of a distribution are not mirror reflections, it is asymmetrical. Right (or positive), left (or negative), or zero skewness can all apply to a distribution.

Skewness refers to the degree of asymmetry in a distribution and a skewed distribution has more observations on one side than the other. In a skewed distribution, the standard deviation is a better measure of spread as it takes into account the deviation of each data point from the mean. On the other hand, the interquartile range (IQR),

which is the difference between the 75th and 25th percentile, is less affected by skewness as it only considers the middle 50% of the data. Hence, the standard deviation is more affected by skewness compared to the IQR.

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The division of the given expressions gives quotient as x + 6 and the remainder 42.

Synthetic division is the method of division used to divide a polynomial expression with the binomial.

We have to divide x² + x + 12 by x - 5.

Write the coefficients of the dividend in the order of descending powers and the constant term in the binomial as :

 5 |     1    1    12

Write the leading coefficient in the bottom row and then multiply the 1 written on the bottom row with 5 and write it beneath the next coefficient of the dividend.

 5 |     1    1    12

               5    

          1    

Now add 1 + 5 to get 6 and write in the bottom row.

Repeat the process by multiplying 6 with 5 and adding up.

 5 |     1    1    12

               5   30

          1    6   42

Here, 42 is the remainder and 1 and 6 are the coefficients of the quotient.

Quotient = x + 6

Remainder = 42

Hence the quotient and remainder are x+6 and 42 respectively.

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Reduced form of given fraction is (2 + n)/7

An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

Given expression

(2x + nx - 2y - ny)/(7x - 7y)

It can be written as

[(2x - 2y) + (nx - ny)]/(7x - 7y)

Factoring out common factors

[2(x - y) + n(x - y)]/7(x - y)

Again factoring out common factor

(x - y)(2 + n)/7(x - y)

(2 + n)/7

Hence (2 + n)/7 is reduced form of the given expression.

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Answer:

length = 10 inches

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2l + 2w ( l is the length and w the width )

here w = 14 and P = 48 , then

48 = 2l + 2(14)

48 = 2l + 28 ( subtract 28 from both sides )

20 = 2l ( divide both sides by 2 )

10 = l

then length is 10 inches

Standard deviation affects the skewness more.

In data sets containing outliers or skewed distributions, the interquartile range is the most accurate indicator of variability.   It's unlikely to be impacted by outliers because it's based on numbers that come from the center half of the distribution.

A measure of dispersion that demonstrates how closely a set of data's values resemble the mean is called standard deviation.

Outliers in a data set or a skewed data distribution might have an impact on the standard deviation.

Interquartile Range (IQR) is a spread indicator that depicts the variation between a data set's first and third quartiles.

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Nearly 150,000,000 cars were registered in the US as a whole in 2007. China, India, and the United States are the three nations with the largest populations on earth.

Average lifespan and child mortality rate are indeed the two key metrics that most accurately reflect a citizenry's standard of living.

The population of the globe is projected to reach about 10 billion people in 2050. Africa and Asia will see the most expansion in population if indeed the patterns in demographic persist.

Cultural practices, governmental regulations, and monetary support, as well as female employment prospects as well as education levels, all have an impact on the overall birthrate of a community.

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The set describes the zeroes of the function f(x)=6pi sin(4x) is C. {x|x = k/4π} for every integer k

The function has zeroes at the x-intercepts in the graph.

If you look at the graph from 0 to π, you will see that the graph cuts the x-axis at 4 points.

They are at half of π/2, which is π/4, at π/2, at half point between π/2 and π, which is at 3π/4, and at π.

They are basically all multiples of π/4

Looking at the answer choices, option C is correct.

Plugging in k=1, k=2, k=3, and k=4 into the equation, we see that the zeroes are exactly what we saw.

Also, the negative side of the function holds true as well.

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The first step to graph the solution to the system of equations given is option D. Change the inequalities to equalities and solve the resulting system of linear equations.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

1. Given system of inequalities are,

y ≥ x + 3

x < −2

In order to graph the solution, first we have to change the inequality symbols to equality and solve the resulting system of linear equations.

That is, solve y = x + 3 and x = -2

2. The equations of the given line are

y = x - 3

y = -2x

Take the linear equation y = x - 3.

The solution region of both contains the point (-1, 0).

0 = -1 - 3 = -4, correct inequality is 0 ≥ 4.

So the inequality is y ≥ x - 3.

Consider y = -2x

0 = 2, correct inequality is 0 ≤ 2.

So the inequality is y ≤ -2x.

Hence the system of inequalities shown in the graph are option B. y ≥ x - 3 and y ≤ -2x.

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