Given m∠1≅m∠2
Proof m∠3≅m∠4
Complete the flow chart to proof m∠3≅m∠4

In linear equation, Samuel bought 7 bags of popcorn and 10 bags of candies.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                              Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let x represent the number of bags of popcorn and y represent the number of candies that Samuel bought.

She bought $43.75 worth of bags of popcorn and candies. Hence:

5x + 4.75y = 43.75  ...........  (1)

She bought a total of 17 bags of popcorn and candies altogether. Hence:

x + y = 9       (2)

Solving equations 1 and 2 simultaneously gives:

x = 4, y = 5

Therefore Samuel bought 4 bags of popcorn and 5 bags of candies.

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Answer:

Parabolas

A quadratic function is a function that can be written in the form f(x)=ax2+bx+c

where a,b, and c are real numbers and a≠0

. This form is called the standard form of a quadratic function.

The graph of the quadratic function is a U-shaped curve is called a parabola.

The graph of the equation y=x2

, shown below, is a parabola. (Note that this is a quadratic function in standard form with a=1 and b=c=0

.)

In the graph, the highest or lowest point of a parabola is the vertex. The vertex of the graph of y=x2

is (0,0)

.

If a>0

in f(x)=ax2+bx+c, the parabola opens upward. In this case the vertex is the minimum, or lowest point, of the parabola. A large positive value of a makes a narrow parabola; a positive value of a which is close to 0

makes the parabola wide.

If a<0

in f(x)=ax2+bx+c, the parabola opens downward. In this case the vertex is the maximum, or highest point, of the parabola. Again, a large negative value of a

makes the parabola narrow; a value close to zero makes it wide.

For an equation in standard form, the value of c

gives the y

-intercept of the graph.

The line that passes through the vertex and divides the parabola into two symmetric parts is called the axis of symmetry.

The equation of the axis of symmetry for the graph of y=ax2+bx+c

, where a≠0, is x=−b2a

In all the above graphs, the axis of symmetry is the y

-axis, x=0. In the graphs below, the axis of symmetry is different (marked in red.) Note that c still gives the y

-intercept.

If you write a quadratic function like x=f(y)=ay2+by+c

, where x is a function of y (instead of a y as a function of x

), you get a parabola where the axis of symmetry is horizontal.

Note that in this case, c

is the x-intercept. If a is positive, the graph opens to the right; if a

is negative, the graph opens to the left.

Example:

Write the equation of the axis of symmetry, and find the coordinates of the vertex of the parabola y=−3x2−6x+4

.

The equation of the axis of symmetry for the graph of y=ax2+bx+c

.

x=−b2a

Substitute −3

for a and −5 for b

in the equation of the axis of symmetry.

x=−−62(−3)    =−1

So, the equation of the axis of symmetry is x=−1

.

Since the equation of the axis of symmetry is x=−1

and the vertex lies on the axis, the x-coordinate of the vertex is −1

.

To find the y

-coordinate of the vertex, first substitute −1 for x

in the given equation.

y=−3(−1)2−6(−1)+4

Simplify.

y=−3+6+4    =7

Therefore, the coordinates of the vertex of the parabola is (−1,7)

.

Step-by-step explanation:

Really hope this works!

The solution for the given logarithmic expression would be x = 8.

What are the logarithms?

In mathematics, the logarithm is the inverse function of exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

Given:

  [tex]log_2(256)[/tex]

Let

            [tex]x=log_2(256)[/tex]

By using the property of logarithms we can write

          [tex]2^x=256\\\\2^x=2^8\\[/tex]

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

      x = 8.

Hence, the solution for the given logarithmic expression would be x = 8.

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The following statements are true based on the frequency table:

Twice as many students prefer green than purple

And

Two more students prefer blue than purple

What is frequency table ?

The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.

From the frequency table,

Red= 6

yellow = 2

Blue = 5

Purple = 3

Green = 6

We can see that "Twice as many students prefer green than purple"

And

Two more students prefer blue than purple

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A small group communication occurs when three or more people work together interdependently for the purpose of accomplishing a task.

Small Group Communication

Small group communication is the term used to describe face-to-face conversation between more than two people. This kind of internal communication exists.

A small group is typically thought of as a collection of three or less people, with a maximum number of twelve to fifteen. A group would not be considered tiny if it had more than fifteen members or if it had just two.

Since almost all businesses and organisations employ people in small squads, there are advantages or even strengths to small group communication. When compared to one individual working alone on a project, it has been found to be more appropriate and produce better results.

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Answer:

Step-by-step explanation:

Reason 2: The box in the corner of the angle indicates that the angle is a right angle, which is 90 degrees.

Statement 3:

m<abd +m<dbc=m<abc

Answer:

x = 10

Step-by-step explanation:

Given equation,

→ -24 - x = -34

Now the value of x will be,

→ -24 - x = -34

→ -x = -34 + 24

→ -x = -10

→ [ x = 10 ]

Hence, the value of x is 10.

Answer: x=10

1. Rearrange the terms

-24 - x= -34

-x - 24= -34

2. Add 24 to both sides

-x - 24= -34

-x - 24= -34

+24 +24

3. Simplify(add the numbers)

-x=-10

4. Divide both sides by the same factor

-x=-10

-x/-1 = -10/-1

Simplify (cancel terms, divide numbers)

X=10

Step-by-step explanation:

The source explains where you found the information that is in your graph. X-Axis  Bar graphs have an x-axis and a y-axis. Y-Axis

Given equation of the line,

If x = 0,

f(x)=-1.5+6

f(x)=-1.5(o)+6=6

Thus, the line intersects the y - axis at (0, 6)

If f(x) = 0,

o=-1.5+6= -1.5*=-6=x=4

Thus, the line intersects the x-axis at (4,0)

Plotting theses points in the given graph,

Then join them,

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The price of reusable tote bags and the interest rate may change over time, which could affect the length of time that Dariya's savings will last.

What is the interest rate?

The proportion of a loan that is charged as interest to the borrower is typically expressed as an annual percentage of the loan outstanding.

If Dariya deposits $4,000 into a savings account with an annual nominal interest rate of 5%, the amount of interest she earns each year will be $4,000 * 5% = $200.

If the price of a reusable tote bag is $10.00 and Dariya wants to buy one every year, the cost of buying one reusable tote bag every year will be $10.00/year.

To determine how long Dariya's savings will last, you can divide the amount of her annual interest earnings by the cost of buying a reusable tote bag each year.

In this case, Dariya's savings will last for 200/10 = 20 years.

Keep in mind that this calculation assumes that the price of reusable tote bags remains constant at $10.00/year and that the nominal interest rate remains fixed at 5% per year.

Hence, the price of reusable tote bags and the interest rate may change over time, which could affect the length of time that Dariya's savings will last.

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Answer:

slope = [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5 ) ← coordinates of y- intercept

and (x₂, y₂ ) = (- 4, 0 ) ← coordinates of x- intercept

m = [tex]\frac{0-5}{-4-0}[/tex] = [tex]\frac{-5}{-4}[/tex] = [tex]\frac{5}{4}[/tex]

Answer:

a.) The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 18.5 (million).

b.) after 8.4 years, so 2008

Step-by-step explanation:

b.) 26.6 = [tex]18.5e^{0.1708t}[/tex]

1.43783784 ≈ [tex]e^{0.1708t}[/tex]

ln 1.43783784= 0.1708t

t=8.4... years

The trigonometric expression (sec x - csc x) / (1 - tan x) is equivalent by trigonometric formulas and algebra properties to - sin x.

Herein we find a trigonometric expression that must be rewritten in terms of sin x by means of trigonometric formulas and algebra properties. The original expression is shown below:

(sec x - csc x) / (1 - tan x)

First, the original expression is written:

(sec x - csc x) / (1 - tan x)

Second, use the definitions of secant, cosecant and tangent:

[(1 / cos x) - (1 / sin x)] / [1 - (sin x / cos x)]

Third, use algebraic properties to simplify the expression:

[(sin x - cos x) / (sin x · cos x)] / [(cos x - sin x) / cos x]

[(sin x - cos x) · cos x] / [sin x · cos x · (cos x - sin x)]

- sin x

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each pound of shimp costs $13.99

Answer: D

Step-by-step explanation:

B = -6.3

F = -5

M = -4.5

A.) -6.3 is not greater than -4.5

B.) -5 is not less than -6.3

C.) -4.5 is not less than -5

D.) -5 is less than -4.5

The most effectively provide the desired primary data is experimentation

Experimentation is the step in the scientific method that helps people decide between two or more competing explanations—or hypotheses. These hypotheses suggest reasons to explain a phenomenon or predict the results of an action.

With an experiment, you run a test and see what the results are. If you don't get good results, you can try another option, and run another test. Then you can see what the outcomes of the choices are (the info you didn't have when first thinking about the decision), and you can make a better-informed decision now.

According to the question,

A research department wants to test the hypothesis that caffeine from organic coffee more safely stimulates mental alertness than caffeine from nonorganic coffee. Experimentation, one form of primary research, can produce data suggesting cause and effect

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The distribution is bimodal. -  this is a correct statement.

According to the question, the following distribution is 5, 5, 8, 9, 10, 10, and 11.

        In the above distribution, there are two modes i,e 5 and 10.

                 Median:  Middle value

                In the above distribution, the median is - 9.

        Mean =  [tex]\frac{5 + 5 + 8 + 9 + 10 + 10 + 11}{7}[/tex]  = [tex]\frac{58}{7}[/tex] = 8.28

Hence,

The distribution is bimodal. -  this is a correct statement.

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Each person got 16 fish equally divided among 7 fishermen.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given, One fisherman and 6 his friends were fishing.

So, The total no. of people is (6 + 1) = 7.

one decided to go home so he took 48 fish which was 3/7 of all fish in the box.  

Let, 'x' be the total no. of fish.

Therefore, (3/7)x = 48.

x = 48×(7/3).

x = 112.

Now, by dividing the total no. of fish by total no. of fishermen

we get, (112/7).

= 16.

So, Each person got 16 fish.

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The values of a such that the linear equation 2 · a - 4 · x = 4 - a² · x have a solution in the interval (- 8, - 2) is a = 2 and - 7 / 4 ≤ a ≤ - 1.

In this problem we find the case of a linear equation whose values of variable a must be determined in terms of an interval of values of variable x. First, write the defined equation:

2 · a - 4 · x = 4 - a² · x

Second, form the standard form of a quadratic equation in terms of a:

x · a² + 2 · a - 4 · (x + 1) = 0

Third, use the quadratic formula:

a = - 2 / (2 · x) ± [1 / (2 · x)] · √[4 - 4 · x · [- 4 · (x + 1)]]

a = - 1 / x ± (1 / x) · √[1 + 4 · x · (x + 1)]

a = - 1 / x ± (1 / x) · √(4 · x² + 4 · x + 1)

There are two cases for the given interval:

Case 1

a = - 1 / x + (1 / x) · √(4 · x² + 4 · x + 1)

x = - 8

a = - 1 / (- 8) + [1 / (- 8)] · √[4 · (- 8)² + 4 · (- 8) + 1]

a = - 7 / 4

a = - 1 / (- 2) + [1 / (- 2)] · √[4 · (- 2)² + 4 · (- 2) + 1]

a = - 1

Case 2

a = - 1 / x - (1 / x) · √(4 · x² + 4 · x + 1)

x = - 8

a = - 1 / (- 8) - [1 / (- 8)] · √[4 · (- 8)² + 4 · (- 8) + 1]

a = 2

a = - 1 / (- 2) - [1 / (- 2)] · √[4 · (- 2)² + 4 · (- 2) + 1]

a = 2

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With the use of regression analysis, you may determine which of the independent factors actually has an effect statistically and learn how the dependent variable changes when one of the independent variables changes.

Regression analysis is used in statistical modeling to determine the associations between two or more variables:

The fundamental element you are attempting to comprehend and anticipate is the dependent variable. The elements that could have an impact on the dependent variable are known as independent variables.

Regression analysis enables you to statistically ascertain which of the independent variables actually has an impact and explains how the dependent variable changes when one of the independent variables changes. There is a difference between a simple and multiple linear regression in statistics. A dependent variable and one independent variable are modeled using a linear function in simple linear regression. Multiple linear regression is used when there are two or more explanatory variables used to predict the dependent variable.

Here,

estimate a simple regression in excel:

On the Data tab, in the Analysis group, click the Data Analysis button.

Select Regression and click OK.

In the Regression dialog box, configure the following settings: Select the Input Y Range, which is your dependent variable.

Click OK and observe the regression analysis output created by Excel.

Regression analysis illustrates how the dependent variable changes when one of the independent factors changes and allows you to statistically determine which of the independent variables actually has an impact.

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a) The minimum number of dogs that could have a mass of more than 24 kg is 6.

b) The maximum number of dogs that could have a mass of more than 18 kg is 20.

We will first of all have to rearrange the function with the aid of fundamental algebraic concepts that makes us calculate the value of x in the event that the derivative is equal to 0.

Now, the response above will give us the x-coordinate of the function's vertex. This vertex x-coordinate is the point at which  the maximum or minimum will occur. To find the minimum or maximum, we will start by rewriting the solution into the original function.

From the given figures in the question, it is clear that the minimum of the values present in the interval 20 to 40 is 6

From the given figures in the question, it is clear that the maximum of the values present in the interval 20 to 40 is;

(12 + 6) = 18

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well, since we know there are 180° in π/2 radians, then, what's 5π/7 radians?

[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\frac{\pi }{2}\\[1em] d&\frac{5\pi }{7} \end{array}\implies \cfrac{180}{d}~~ = ~~\cfrac{\frac{\pi }{2}}{ ~~ \frac{5\pi }{7} ~~ }\implies \cfrac{180}{d}=\cfrac{\pi }{2}\cdot \cfrac{7}{5\pi } \\\\\\ \cfrac{180}{d}=\cfrac{7}{10}\implies 1800=7d\implies \cfrac{1800}{7}=d\implies 257.14^o\approx d[/tex]

2 * V is equal to 2 v you divide 2 from 8 and your answer is 4

Answer:

You need to subtract

Step-by-step explanation:

50 minus 14 will give you 36

Answer:

k = 44

Step-by-step explanation:

[tex]\frac{3}{4}[/tex]k = 12  Multiple both sides by [tex]\frac{4}{3}[/tex]

k = 44

Answer:

k = 44

Explanation:

You can write this into an equation, where k x 3/11 = 12. If you multiply both sides of the equation by 11 and divide by 3, you get k by itself.

k x 3/11 = 12

3k/11 = 12

3k = 132

k = 44

Answer:1400

Step-by-step explanation:

A master's degree earner's typical weekly salary is $3,092.94.

What is the meaning of percentage?

A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.

Considering that the median gross weekly wage for a bachelor's degree holder was $2,117.00.

If any one had mater degree, then an increase in the median weekly income of about 46.1%.

To find the increment multiply $2,117.00 with increase rate:

The increment is $2,117.00 × 46.1% = 2,117.00 × 46.1/100= $975.937

The total the median weekly income is

$975.937 + $2,117.00

= $3,092.937

≈ $3,092.94

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[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-8,8)\qquad B(-2,-10)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-8,8)=1(-2,-10)[/tex]

[tex](\stackrel{x}{-16}~~,~~ \stackrel{y}{16})=(\stackrel{x}{-2}~~,~~ \stackrel{y}{-10}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-16 -2}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{16 -10}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -18 }{ 3 }~~,~~\cfrac{ 6}{ 3 } \right)\implies {\Large \begin{array}{llll} C=(-6~~,~~2) \end{array}}[/tex]

If the scale factor is less than 1, the dilated figure is smaller than the original, if it is greater than 1 the dilated figure is larger than the original.

The given vertex of the line are;

R(-2, 6), T(-6, -2), S(6, -4)

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