Write the equation of a line in slope intercept form that has a slope of 1/2
and passes through the point (-2,3).

Answer:

2+7=9 so 9x9=81

Step-by-step explanation:

The equation of the axis of symmetry of y=−3x^2+18 parabola algebraically is x = 0.

we use for that the fact that the x position of the vertex of a parabola of the general form: [tex]y = ax^{2} + bx + c[/tex], is given by:

[tex]x_{vertex}[/tex] = [tex]\frac{-b}{2a}[/tex]

which in our case becomes:

[tex]x_{vertex}[/tex] = [tex]\frac{-0}{-6}[/tex]

[tex]x_{vertex}[/tex] = 0

Parabola:

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The amount of variability between groups quantified is group of answer choices comparing the standard deviations of each group to each other comparing the sample means of each group to each other.

A variability measure is a summary statistic that describes the amount of variation in a dataset. Central tendency measures describe typical values, while variability measures define how far away data points tend to be from the center. We talk about variability in the context of value distribution. A small variance indicates that the data points tend to be clustered near the center. A large spread means they tend to move further apart.

Analysts often use averages to summarize the center of a population or process. Averages are good, but people are often more sensitive to fluctuations. The less variability in the distribution, the more consistent the values ​​within the dataset. However, the higher the variability, the more diverse the data points and the more likely extreme values ​​will occur. Therefore, understanding variability helps us to understand the likelihood of anomalous events.

Meteorologists have seen weather forecasts showing extreme heat and drought in some areas and flooding in others. We often feel more uncomfortable in the extreme than in the middle. Understanding this variability about the mean provides important information.

Variation is everywhere. My commute time varies slightly from day to day. Parts coming off the assembly line look the same, but have slightly different lengths and widths.

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∠A = ∠C  by congruent parts of congruent sides

Corresponding parts of congruent triangles is referred to as CPCT. According to the CPCT theorem, if two or more triangles are taken that are congruent to one another, then the corresponding angles and sides of the triangles are likewise congruent to one another.

According to the given Information

Given

AB = CB

DB bisects ∠ABC

∠ABD = ∠CBD

Proof

In Δ ABD and Δ CBD

         AB = CB ( given )

   ∠ABD = ∠CBD  ( given )

        BD = BD ( Common Side )

So

  Δ ABD ≅ Δ CBD ( SAS congruence )

           ∠A = ∠C ( CPCT )

Congruent Parts of Congruent Sides

Hence

∠A = ∠C  by congruent parts of congruent sides

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The graph of a function can be sketched by plotting points.

First and foremost, it is to be determined if the function is odd/even or periodic. Next, we find the x and y intercepts. To sketch a graph of a function, one can start by plotting a few points that lie on the graph using the coordinates given by the function. For example, if the function is y = x², then points (0, 0), (1, 1), and (2, 4) can be plotted by substituting the values of x into the function to find the corresponding values of y.

Subsequent to this, one can connect the points with a smooth curve to form the graph of function. If the function is a straight line, the graph will be a straight line. If the function is quadratic, the graph will be a parabola. The graph may take on a more complicated shape for more complex functions.

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No, 1 is not a perfect square. A perfect square is a number that is the result of multiplying an integer by itself.

A perfect square is a number that is the result of multiplying an integer by itself. Therefore, 1 does not meet this criteria.A perfect square is a number that is the result of multiplying an integer by itself.

For example, 4 is a perfect square because it can be expressed as 2 x 2. Similarly, 9 is a perfect square because it can be expressed as 3 x 3. However, 1 does not meet this criteria as it is not the result of multiplying an integer by itself.

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Step-by-step explanation:

the middle one has to be the same for both part ratios.

the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there

for that (as a ratio is a fraction) we also have to adapt the A element in the same way.

so, we get

4×2 : 5×2 : 9 =

= 8 : 10 : 9

and that is also shown in the graphic.

Answer:

X:Y:Z= 8:10:9

Step-by-step explanation:

Let x be the number of students in class A

Let y be the number of students in class B

Let z be the number of students in class C

x:y = 4:5

y:z= 10: 9

x:y:z = ?

Find the LCM of the y terms (5 and 10 ) which is 10

Divide 10 by the first y term (5) = 2

Divide 10 by the second y term(10) = 1

X: y = (4 x 2) :(5 x 2)= 8:10

y:z =(10 x 1) : (9:1)= 10:9

x:y:z= 8:10:9

To test the given hypothesis : average time to deliver goods, once the order is placed over phone, is more than 30 minutes in the population, the T-test or T statistical test should be performed.

A parametric statistical test makes assumptions about the population parameters and data distributions. T-tests, z-tests, linear regression, and anova tests are examples of these tests, which assume data from a normal distribution.

As we all know, a statistical test known as a t-test is used to compare the means of two groups. It is frequently used in hypothesis testing to determine whether a procedure or treatment truly affects the population of interest or whether two groups differ.

Thus,The T-test or T statistical test should be performed to test the given hypothesis.

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when two non-vertical lines are in the same plane and have the same slope,  they are said to be parallel lines. whereas the non-vertical lines are in the same plane and intersect at an angle of 90, they are said to be perpendicular.

A parallel lines is when two lines have the same slope, meaning they will never intersect. This is represented by the same "rise over run" ratio in the equation of the line. The perpendicular lines  is when two lines have a slope that is the opposite reciprocal of each other. This means that the lines will intersect at a 90-degree angle and can be represented by the equation y = -1/m * x + b, where m is the slope of one of the lines. Both of these concepts are important for understanding the basics of linear equations, as well as for determining the lines of best fit in graphs.

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a) The tree diagram is given by the image shown at the end of the answer.

b) The probability that you will get a head and a number greater than 4 when you flip a coin and toss a die is: 1/6.

A probability in the context of an experiment is calculated as the division of the number of desired outcomes by the number of total outcomes.

The possible outcomes in this problem are given as follows:

The tree diagram at the end of the answer gives these 12 outcomes.

There are two outcomes in which you get a head and a number greater than 4, which are:

(Heads, 5) and (Heads, 6).

Hence the probability is calculated as follows:

p = 2/12 = 1/6.

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Answer:

Step-by-step explanation:

lim x -> +oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

+oo³ (-2 - 13/+oo + 8/+oo² + 52/oo³)

+oo(-2 + 0 + 0 + 0)

-oo

lim x -> -oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

-oo³ (-2 - 13/-oo + 8/-oo² + 52/-oo³)

-oo(-2 + 0 + 0 + 0)

+oo

Answer:

y = -2x+2

Find slope

find x intercept

y=mx+b

Answer:

[tex]\left(\frac{1}{2}, 0 \right)[/tex]

Step-by-step explanation:

Using the midpoint formula,

[tex]\left(\frac{-3+4}{2}, \frac{-5+5}{2} \right)=\left(\frac{1}{2}, 0 \right)[/tex]

The slope of the line that passes through the points (-2,5) and (1,4) is -1/3.

The slope of a line can be defined as the measure of the steepness of that particular line. If we were to define it mathematically, we would define it as the change in y-intercepts divided by the change in x-intercepts.

We know that the formula for finding the slope of a line is -

= m =  y₂-y₁/x₂-x₁ (i)

The given values are = x₁ = -2 ; x₂= 1 ; y₁= 5 ; y₂= 4

We use the given values and (i) to find -

= m = 4-5 / 1-(-2)

= m = -1/3

Hence, the slope of this line is -1/3.

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The slope of the line through − 7 − 2 and − 6 7 is 9. A line's steepness can be determined by looking at its slope.

Where y and x denote the first and second values, respectively, and y and x2 denote the third and fourth values, respectively, and m is the slope

I by itself would result in m in our scenario.

m= y2 - y/x2 - x

Since x and y are random positions, I will state that the first point, X, is at (-7, -2) and the second point, Y, is at (-6, 7). Therefore, we will enter the values below in their place:

m= [7 -(-2)]/ (-6) -( -7)]

m= 9/1

m = 9

The slope of the equation would be nine.

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The correct option for the area of the figure formed by a triangle and a parallelogram is 32 square millimeters.

To get the area of the figure, we solve for the area of the triangle and that of the parallelogram, and then add our results together.

area of a triangle is half the product of its base and height

area of parallelogram is the base multiplied by its height

the triangle has base = 8mm and height = 3mm

so

area of the triangle = (8mm × 3mm)/2

area of the triangle = 24mm²/2

area of the triangle = 12mm²

the parallelogram has base = 5mm and height = 4mm

so

area of the parallelogram = 5mm × 4mm

area of the parallelogram = 20mm²

Therefore, the area of the figure which is the sum of the area of the triangle and the area of the parallelogram is;

12mm + 20mm² = 32mm² or 32 square millimeters

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The last box 2/37.5 = 4/75 = 0.8/15 have same proportional relationship.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

9/8 ≠ 12/8

16/28 = 4/7 ≠6/10.5

12/32= 3/8 ≠8/20

1.5/8 = 3/16 ≠4/18

2/37.5 = 4/75 = 0.8/15

Hence the last box have same proportional relationship.

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The equation of a line that passes through (1/3, 2) is y = 6x – 4 with slope.

1. To solve for the equation of the line, we need to use the point-slope form.

2. The point-slope form is y-y1=m(x-x1).

3. We are given the point (1/3, 2). We can plug this into the equation as x1=1/3 and y1=2.

4. To find the slope (m), we need to calculate the rise over run. We can use the point (1/3, 2) and another point to calculate the slope.

5. Let's choose the point (0,0). The rise is 2 and the run is 1/3. So the slope (m) is 6.

6. Now we can plug our values into the point-slope form and solve for y.

7. y-2=6(x-1/3).

8. We can simplify this equation by subtracting 2 from both sides.

9. y=6x-4.

10. This is the equation of the line that passes through (1/3, 2).

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The values of a and b are 6.83 and 1.17 respectively rounded to the nearest hundredth.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let the numbers be a and b.

Given, (a + b) = 8..(i) and ab = 8.

Now,

(a + b)² = a² + 2ab + b².

64 = a² + b² + 16.

a² + b² = 48.

Now,

(a - b)² = a² + b² - 2ab.

(a - b)² = 48 - 16.

(a - b)² = 32.

(a - b) = 5.66...(ii)

Adding (i) and (ii) we get 2a = 13.66 ⇒ a = 6.83 and b = 8 - 6.83 ⇒ b = 1.17.

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The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph indicates the available expected output, or range of graph.

In the given question, we have to explain how we can find the domain and range of a graph equation and table.

The domain and range are typically listed in a table's left and right columns, respectively. In a relation or function, the domain can alternatively be thought of as the input values (x), and the range as the output values (y).

Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph indicates the available expected output, or range.

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A system of a linear equation is said tk be consistent if it had at least one solution is true

In a linear equation, the largest power of the variable is always equal to 1. It's also known as a one-degree equation. Typically, Ax + B = 0 is used to represent a linear equation with one variable. The variables x, A, and B in this case serve as constants and coefficients, respectively. The typical form of a linear equation with two variables is Ax + By = C. Here, x and y are the variables, A and B are the coefficients, and C is the constant. If there is at least one solution, a set of linear equations is considered to be consistent. This means that when all equations in the system are solved, at least one set of values for the variables can be found which satisfy all equations simultaneously. So, the statement is true.

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The length of the diagonal is 11.7 feet in the rectangular garden.

The two shorter sides of the rectangle have lengths of 10 feet and 6 feet, and the hypotenuse is the diagonal of the rectangle.

So, we can use the Pythagorean theorem to find the length of the diagonal as follows:

a² + b² = c²

where a and b are the lengths of the shorter sides of the rectangle (10 feet and 6 feet), and c is the length of the diagonal.

Substituting the values for a, b, and c, we get:

10² + 6² = c²

100 + 36 = c²

136 = c²

c = √136

c = 11.7

Therefore, the length of the diagonal is 11.7 feet in the rectangular garden.

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the graph will contain all the plane which is less than or equal to 7

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

The given inequality is k−7≤0

k ≤ 7

Hence the graph will contain all the plane which is less than or equal to 7.

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Answer:

6: H

3: A

Step-by-step explanation:

6: We only want a pound of fertilizer, if we have 7.8 pounds then we would have to divide by the cost in order to get only the cost of one. 67.86 ÷ 7.8 = 8.70

3: 3/4 is less than one hour. We only want one hour. We divide the 18 miles by 3, which is 6 but since it's a little less than an hour, it must be lower. The only option less than 6 is 4.5

The machine discharge more than 7.0 oz or does the difference represent chance variation is 0.0274

What is meant by variation?

In math, variance refers any difference between the individuals in a species or groups of organisms of any species.

Here we have given that a coin-operated soft drink machine was designed to discharge, on average, 7 oz of beverage per cup. in a test of the machine, 10 cupful's of beverage were drawn from the machine and measured. the average and SD of the ten measurements were 7.1 oz and 0.12 oz, respectively. assume that the histogram of beverage discharge from this machine roughly follows a normal curve.

And we need to find machine discharge more than 7.0 oz or does the difference represent chance variation.

By using the Applet, to find the exact p-value we first need to find P(Z≥2.63) where Z is a t9​ random variable.

=> P(Z≥2.63)=0.0137

=> 2×P(Z≥2.63)=0.0274

=> P-value=0.0274

So, the p-value associated with the test is 0.0274

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Answer: b.5.32

Step-by-step explanation:

A system of two-variable linear equations can be solved using one of five strategies. Here is a description of those techniques:

Given,

Linear equation in two variables;

The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables since each of the variables has an exponent order of one. A linear equation with two variables has the conventional form axe + by + c = 0, where x and y are the variables.

The answers can also be expressed as ordered pairs, such as (x, y). Two straight lines, which could be intersecting, parallel, or coincident, are included in the graphic representation of the system of linear equations in two variables.

Here,

A system of linear equations in two variables can be solved using one of five techniques. These techniques are described below:

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The center of the dilation from the quadrilateral WXYZ to quadrilateral W'X'Y'Z' is point A.

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

Given that, quadrilateral L' is the image of quadrilateral L under a dilation.

The origin is often used as the center of dilation.

Connect all the points from quadrilateral WXYZ and quadrilateral W'X'Y'Z' to point A.

Therefore, the center of the dilation is point A.

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The values that make the inequality -w<-8 true are 8.1, 9, 13.

The  equivalent inequality is w > 8.

What is the order from least to greatest?

There are two ways to arrange a set of integers in mathematics. It implies that there are two possible orderings for the numbers: ascending and descending. Ascending order refers to the arrangement of numbers in which the smallest number comes before the largest. The numbers are listed in this fashion in ascending order. It is ideal for the first number to be less than the second.

Descending order refers to arranging the integers from largest to least value. The numbers are in decreasing order in this manner. It is ideal for the first number to be higher than the second.

Given inequality is -w < -8.

Now putting w = -13, -8, -3, 07, 8.1, O-9, -7.9, O, 7.9, 9, -8.1, 0 -7, 03, 8, 13 in the given inequality.

-(-13) < -8 → 13 < -8 (false)

-(-8) < -8 → 8< -8 (false)

-(-3) < -8 → 3 < -8 (false)

-7 < -8  (false)

-(8.1) < -8  (true)

-(0-9) < -8 → 9 < -8 (false)

-(-7.9) < -8 → 7.9 < -8 (false)

-9 < -8 (true)

-(0-7) < -8 → 7 < -8 (false)

-(03) < -8 → 3 < -8 (false)

-8 < -8 (false)

-13 < -8 (true)

Rewrite the given inequality:

Multiply -1 on both sides:

(-1) × (-w) > (-1) × (-8)

w > 8

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