what is the slope?

Khan Academy ​

Answer:

x = 2

Step-by-step explanation:

[tex]\frac{5(x-2)}{3} = -x + 2[/tex]

expand left side:

[tex]\frac{5(x-2)}{3} = -x + 2\\\\\frac{5x-10}{3} = -x + 2[/tex]

multiply both sides by 3:

[tex]3(\frac{5x-10}{3}) = 3(-x + 2)\\\\ =5x - 10 = -3x + 6[/tex]

Add 3x to both sides:

5x - 10 + 3x = -3x + 6 + 3x

8x - 10 = 6

add 10 to both sides:

8x - 10 + 10 = 6 + 10

8x = 16

divide both sides by 8:

8x/8 = 16/8

x = 2

Answer:

[tex]y=3x^2+12x+17[/tex]

Step-by-step explanation:

The equation in vertex form is [tex]y=a(x+2)^2+5[/tex].

We can use the point [tex](1,32)[/tex] to solve for [tex]a[/tex].

[tex]32=a(1+2)^2+5 \\ \\ 27=9a \\ \\ a=3 \\ \\ \\ \therefore y=3(x+2)^2 + 5 \\ \\ =3(x^2+4x+4)+5 \\ \\ =3x^2+12x+12+5 \\ \\ =3x^2+12x+17[/tex]

Corresponding angles theorem states that parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

To prove m∠  = m∠2.

Then,

The corresponding angles theorem states that If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Corresponding angles are formed when a transversal passes through two lines.

As we know that line segment m is parallel to the line segment n.

m || n .

Hence,

m∠3 + m∠2 = 180 (same interior angles)

Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.

Same side interior angles are supplementary.

m∠1 + m∠3 = 180(sum of angles on a straight line)

Angles on a straight line is supplementary.

So, by transitive property of equality, we get:

m∠  = m∠2

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Answer:

G

Step-by-step explanation:

[tex]x^4-x^3-x^2-x-2=0 \\ \\ (x+1)(x^3+x-2x^2-2)=0 \\ \\ (x+1)(x(x^2+1)-2(x^2+1))=0 \\ \\ (x+1)(x-2)(x^2+1)=0 \\ \\ (x+1)(x-2)(x-i)(x+i)=0 \\ \\ x=-1, 2, i, -i[/tex]

The required height of the tub is given as 7.32 inches.

As mentioned in the question, Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 387.79 square inches, and the diameter of the tub is 10 inches.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,
The surface area of the cylinder = 2πrh + 2πr²
Substitute the values,
387.79 = 2 × 3.14 × 5 [h + 5]
h = 7.32 inches

Thus, the height of the cylindrical gallon tub is given as 7.32 inches.

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Answer:

7.35 inches

Step-by-step explanation:

I took the test and got it right :)

Using sample standard deviation formula and the provided sample mean value, The test statistic are $8,080(sample mean) and 125 (sample standard deviation).

Large-scale numerical data collection and analysis, especially with the aim of extrapolating proportions in the total from those in a representative sample.

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait.

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

Sample mean= $8,080

population standard deviation= $1,000

number of sample=64

sample standard deviation = [tex]\frac {1000}{\sqrt {64}}[/tex]

=1000/8

=125

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The provision of a necessary raw material for industrial production by industrial revolution benefitted for slavery.

Agrarian and handicraft economies were replaced by industrial and machine production during the Industrial Revolution in modern history. These technical developments brought about new methods of working and living that dramatically altered civilization.

the provision of a necessary raw material for industrial production by industrial revolution benefitted for slavery.

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The linear function for Line L3 is given as follows:

y = -2/3x + 8/3.

The lines L1 and L2 are given as follows:

The x-coordinate of intersection is obtained as follows:

-2/3x + 8/3 = -2/9x - 4/9.

Multiplying everything by 9, the expression is given as follows:

-6x + 24 = -2x - 4.

4x = 28

x = 7.

The y-coordinate is given as follows:

y = -2/3(7) + 8/3 = -2.

Then the points on line L3 are given as follows:

(7,-2) and (1,2).

Given two points, the slope is calculated by the division of the change in y by the change in x, hence:

m = (-2 - 2)/(7 - 1)

m = -2/3.

Then:

y = -2/3x + b

When x = 1, y = 2, then the intercept b is calculated as follows:

2 = -2/3 + b

b = 2 + 2/3

b = 8/3.

Thus:

y = -2/3x + 8/3.

The problem asks for the definition of the line L3, which passes through the intersection of the linear L1 and L2 and through point (1,2).

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Answer:

y = - [tex]\frac{1}{4}[/tex] x - 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x - 2 ← is in slope- intercept form

with slope m = 4

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex] , then

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute (4, - 11 ) into the partial equation

- 11 = - [tex]\frac{1}{4}[/tex] (4) + c = - 1 + c ( add 1 to both sides )

- 10 = c

y = - [tex]\frac{1}{4}[/tex] x + (- 10) , that is

y = - [tex]\frac{1}{4}[/tex] x - 10 ← equation of line

The roots of the quadratic equation 2x^2 + 5x + 3 are the two values of x that make the equation equal to 0. These two values are x = -3 and x = -1/2.

The roots of a quadratic equation are the two values of x that make the equation equal to 0. To find the roots of the equation 2x^2 + 5x + 3, we need to set the equation equal to 0 and solve for x. We can do this by using the Quadratic Formula, which states that the two roots of a quadratic equation ax^2 + bx + c = 0 are x = [-b +/- sqrt(b^2 - 4ac)] / 2a. In this equation, a = 2, b = 5, and c = 3. We can plug these values into the formula to get x = [-5 +/- sqrt(25 - 24)] / 4. Simplifying this expression gives us x = -3 and x = -1/2, which are the two roots of the equation 2x^2 + 5x + 3.

x = [-5 +/- sqrt(25 - 24)] / 4

x = [-5 +/- sqrt(1)] / 4

x = [-5 +/- 1] / 4

x = -3 and x = -1/2

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Answer:

The rate of change/cost per mile driven can be calculated by finding the slope of the line that connects the points (1,10.70) and (0,10). The slope is the change in the y-value divided by the change in the x-value, so the slope of the line is (10.70-10)/(1-0) = $0.70/mile.

The point (0, 10) represents the cost of the driving service when 0 miles are driven. In other words, the service costs $10 for no miles driven.

The equation that models the function in the table is C(m) = $10 + $0.70m. The first term represents the cost of the service when no miles are driven and the second term represents the cost per mile driven.

The arrangement of the rooms in increasing order of their areas:

Drawing Room = 72m²

Balcony = 87.5 m²

T.V Room = 156m²

Hallway = 216m²

Bedroom = 225m²

Kitchen = 250m²

What is the area of a shape called?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. Draw a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

We have,

kitchen:

40 feet × 10 feet

bedroom

15 feet × 15 feet

hallway

15 feet

TV room

12 feet × 13 feet

balcony:

5 feet × 12 feet × 12 feet

drawing room:

8 feet × 13 feet

Areas of the various spaces in the house:

Drawing Room = 72m²

Balcony = 87.5 m²

T.V Room = 156m²

Hallway = 216m²

Bedroom = 225m²

Kitchen = 250m²

Hence, the arrangement of the rooms in increasing order of their areas:

Drawing Room = 72m²

Balcony = 87.5 m²

T.V Room = 156m²

Hallway = 216m²

Bedroom = 225m²

Kitchen = 250m²

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With the Application of normal distribution conclusion can be All students missed at least one day of school per semester

what is normal distribution?

The normal distribution is a type of probability function that describes the distribution of a variable's values. Since most of the observations cluster around the middle peak of the curve, it is symmetric. When values of the distribution are far from the mean, the probability for those values narrow off evenly in both directions.

solution:

mean - ( standard deviation ) = 4 - 1 = 3

All students missed at least one day of school per semester

Therefore,  conclusion can be All students missed at least one day of school per semester

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Answer:

Mikaela run 10 km in 1hour

Mikaela bikes 25km in 1hour

35km If Mikaela runs for 1 hour and bikes for 1 hour at the rates given

Step-by-step explanation:

Let's solve how many km Mikaela runs in 1 hour.

0.5 hour = 30 minutes

5km = 30 minutes

10km = 60 minute

Let's solve how many km Mikaela bikes in 1 hour.

0.8 hour = 48 minutes

20km = 48 minutes

To get from 48 minutes to 60 minutes, we times 1.25. So, we take 20 times 1.25 = 25km

So, Mikaela bikes 25km in 1 hour.

Let's solve how far she traveled If Mikaela runs for 1 hour and bikes for 1 hour at the rates given

10km+ 25km = 35km

When data are transformed to ranks and the Pearson correlation is performed, the Spearman correlation is what is obtained as a correlation.

Therefore, the correct answer is A)the Spearman correlation

The complete question is:

What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks?

a) the Spearman correlation

b) the point-biserial correlation

c) the phi coefficient

d) it is still called a Pearson correlation

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The required solution of given equation is x = 5, y = 1.

The effective use of substitution relies upon two things: first, given a circumstance in which factors happen, a replacement is just a difference in factor; second, it is just successful if the difference in factor improves on the circumstance and, ideally, empowers one to take care of the worked on issue.

We have,

4x+3y=23---------()1

And

x-5y=0 ⇒ x = 5y

Put the value of x in equation(1)

4(5y) + 3y = 23

20y + 3y = 23

23y = 23

y = 1

Then x = 5y = 5(1) = 5

Thus, solution of equation x = 5, y = 1

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The value of y is -2.

What is coordinate of point?

The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.

Given points are (0,y) and (2,4)​.

The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of the given line is (4 - y)/(2 - 0) =  (4 - y)/2.

Again given that the slope of the line is 3.

Therefore,

(4 - y)/2 = 3

Multiply both sides by 2

4 - y = 6

Subtract 4 from both sides:

-y = 2

Multiply both sides by -1:

y = -2

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The difference between r and p.  is that r represents the sample correlation coefficient while p represents the p-value

Generally, r represents the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between two variables in a sample of data. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

p represents the p-value, which is a measure of the statistical significance of the sample correlation coefficient. It represents the probability that the observed correlation occurred by chance, assuming that there is no true correlation in the population.

A p-value of less than 0.05 is often used as a threshold for determining statistical significance, meaning that the observed correlation is unlikely to have occurred by chance and is likely to reflect a true correlation in the population.

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Answer: 442

Step-by-step explanation: volume is length x width x height

so plug it in to get 17 x 13 x 2 = 442

To solve systems of an infinite equation we need to determine whether the equation is dependent or independent and consistent, or inconsistent.

The number of solutions in an equation depends on the total number of variables contained in it is known as Infinite solutions.

The system of equations contains two or more equations that have two or more variables. It can be any combination such as

If a pair of linear equations have unique or infinite solutions, then the system of equations is said to be a consistent pair of linear equations.

For example, consider two equations in two variables as follows:

a1x + b1y = c1 ——- (1)

a2x + b2y = c2 ——- (2)

The above-given equations are consistent and dependent and have infinitely many solutions.

(a1/a2) = (b1/b2) = (c1/c2)

There are a few conditions for infinite solutions:

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The 10 expressions in Math are:

Math is a subject that can be intimidating to many, but it is a fundamental part of life that is necessary to understand. It is important to have a basic grasp of different expressions in order to be successful in math. This essay will explore the ten expressions of math and provide insight into their importance.

The first expression is the sum. This is the answer you get when adding two or more numbers together. For example, if you have the numbers 5, 7, and 8, the sum would be 20. Sums can also be used to find the total amount of a group of objects.

The second expression is the difference. This is the answer you get when subtracting two or more numbers. For example, if you have the numbers 8 and 5, the difference would be 3. Differences can also be used to find the difference between two amounts.

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False; we only remove outliers if we have a very good justification that suggests that removing the outlier is appropriate.

You should discard the outlier if it is clear that it resulted from inaccurately measured or recorded data. You may discard the outlier if it has no effect on the results but has an impact on the assumptions. Outliers might occasionally point to a data-gathering error. However, there are situations when they might have an impact on data collection, making them crucial to keep in mind in order to fully comprehend the information. Eliminating outliers gives some of my variables a normal distribution and improves the effectiveness of modifications for the other variables. As a result, it would appear that eliminating outliers before transformation is the best course of action.

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The side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.

Therefore, the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

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the slope  is 5/-2 so this line "cuts" the y axis at y=-2.50000

y-intercept = 5/-2  = -2.5

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                   -2*y-(-4*x+5)=0

Pulling out like terms

Pull out like factors :

 -2y + 4x - 5  =   -1 • (2y - 4x + 5)

Equation at the end

Equation of a Straight Line

  Solve   -2y+4x-5  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  -2y+4x-5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/-2 so this line "cuts" the y axis at y=-2.50000

y-intercept = 5/-2  = -2.5

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The probability that the selected student was the youngest student from Section B is 2/6.

The total number of  students is 18 which include

Section A: 5 students

Section B: 6 students

Section C: 7 students

Given that the selected student was from Section B

Calculate the probability of selecting a student from Section B

P(Section B) = 6/18 = 1/3

Calculate the probability of selecting the youngest student from Section B

Since there are 6 students in Section B, the probability of selecting the youngest student is 1/6.

Calculate the probability of selecting the youngest student from Section B given that the selected student was from Section B

P(Youngest student from Section B|Section B) = P(Youngest student from Section B ∩ Section B) / P(Section B)

= (1/6) / (1/3)

= 2/6

Therefore, the probability that the selected student was the youngest student from Section B is 2/6.

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One over seventeen raised to the second power is (1/17)².One over seventeen raised to the power of negative two is (1/17)⁻².

In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied. Let's learn more about power and exponent. A power is a phrase that depicts the same component being multiplied repeatedly. For instance, in the number 52, the base is the number 5, and the exponent is the number 2. The base is multiplied by the exponent, which is 2, to get the total number of factors.

Given,

one over seventeen raised to the second power

(1/17)²

one over seventeen raised to the power of negative two

(1/17)⁻²

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Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.

A real number is a quantity that may be represented mathematically by an endless decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. Rational and irrational numbers are both included in real numbers. Real numbers include both irrational and rational numbers such as 3, 22/7, and integers such as (-2, 0, 1), fractions such as (1/2), and decimal numbers such as (1/2).

whole = 0,1,2,3,4,5,6,7,8,9,10,11........….

rational = 12/23,3,3/4,5/6,...…

irrational =  [tex]\sqrt{8}[/tex], [tex]\sqrt{-56}[/tex]etc

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