Remember what we know about vertical angles and solve for x.
Then tell me the measure of Angle R.

The equation of the given line is [tex]y= \frac{1}{3}x+2[/tex]

What is the slope of a line?

A line's steepness and direction are measured by the line's slope. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

Given a straight line in a graph, we need to find the equation of this line

from the graph, we can see that the line passes through the axes at (0, 2) and (-6, 0)

now, the slope of the line is [tex]\frac{y2 - y1}{x2 - x1}[/tex]

[tex]= \frac{0 - 2}{-6 - 0} \\= \frac{1}{3}[/tex]

The line makes an intercept of 2 on the Y-axis, as we can see clearly

The slope-intercept form of the line is y = mx + c, where 'c' is the intercept and 'm' is the slope of the line

The equation of the given line is [tex]y = \frac{1}{3}x + 2[/tex]

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A centigram is 100 times larger than a milligram. So, the option b) 100 times is correct for this question.

1 centigram = 100 milligrams. A centigram is a unit of mass in the metric system, equivalent to one hundredth of a gram. A milligram, on the other hand, is a unit of mass in the metric system, equivalent to one thousandth of a gram. Therefore, a centigram is 100 times larger than a milligram. The conversion between the two units can be easily calculated as 1 centigram is equal to 100 milligrams. The use of centigrams is limited in common applications, with milligrams being the preferred unit for expressing very small masses, while grams and kilograms are used for larger masses.

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Answer:

7

Step-by-step explanation:

f(-3)

f(x) = -4x-5

f(-3) = -4(-3) - 5

f(-3) = 12 - 5

f(-3) = 7

The width of the bedroom is approximately 7.32 feet.

A rectangle is a four-sided figure with opposite sides being equal and parallel. The area of a rectangle is given by multiplying the length and width of the rectangle.

Let's assume that the width of the bedroom is 'x' feet. We know that the length of the room is 5 feet longer than its width. Therefore, the length of the room will be (x+5) feet.

Now, we can use the given area of the bedroom to set up an equation:

Area of rectangle = Length x Width

84 = (x+5) x x

Simplifying this equation, we get:

84 = x² + 5x

Rearranging, we get:

x² + 5x - 84 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

In this case, a = 1, b = 5 and c = -84. Substituting these values in the formula, we get:

x = (-5 ± √(5² - 4(1)(-84)))/2(1)

Simplifying this, we get:

x = (-5 ± √721)/2

We can ignore the negative root since the width of the bedroom cannot be negative. Therefore, the width of the bedroom is:

x = (-5 + √721)/2

x ≈ 7.32 feet

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Answer: 28

Step-by-step explanation:

16% = 0.16

Percents are just decimals!

Now you can put this in your calculator, and you will get 28.

However:

It might help you later to know that x% of y = y% of x

In other words, 16% of 175 is the same thing as 175% of 16

This problem is easier, since we can break 175% into 1 and 3/4th. 3/4th of 16 is easy to calculate, (its 12), and so we can add 12 to 16 to find the answer, which is still 28 :)

No calculator needed!

The ratio of employees who work in the office to employees who work in the warehouse is 5: 7

A ratio is a comparison of two quantities, and it is expressed as a fraction.

To find the ratio of employees who work in the office to employees who work in the warehouse, we need to first determine the total number of employees. In this case, we add the number of employees in the office (20) to the number of employees in the warehouse (28), which gives us a total of 48 employees.

Next, we can express the ratio of office employees to warehouse employees as a fraction by using the following formula:

Ratio = Quantity of First Term / Quantity of Second Term

In this case, the first term is the number of employees who work in the office (20) and the second term is the number of employees who work in the warehouse (28). So, the ratio of office employees to warehouse employees is:

Ratio = 20 / 28

Simplifying this fraction, we get:

Ratio = 5 / 7

This means that for every 5 employees who work in the office, there are 7 employees who work in the warehouse.

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The larger container will hold 500 ounces of soup when filled.

We know that the formula for the volume of cylinder is: V = πr²h

Let us assume that for the smaller container, d₁ represents the diameter, r₁ represents the radius, h₁ represents the height of the container and v₁ represents the volume of the container.

So, using above formula, the volume of the smaller container would be,

v₁ = π × r₁² × h₁

10 = π × r₁² × h₁

For the larger container, d₂ represents the diameter, r₂ represents the radius, h₂ represents the height of the container and v₂ represents the volume of the container.

Using above formula, the volume of the larger container would be,

v₂ = π × r₂² × h₂

The larger container’s diameter is 5​ times larger than the small container’s diameter.

so, we get an equation

⇒ d₂ = 5d₁

⇒ r₂ = 5r₁

Also, the lrger container is 2​ times taller than the small container.

⇒ h₂ = 2h₁

Consider the ratio of volume of larger cotainer to the volume of smaller container.

v₁/v₂ =  (π × r₁² × h₁) / ( π × r₂² × h₂)

10/v₂ =  (r₁² × h₁) / ( (5r₁)² × (2h₁))

10/v₂ =  (r₁² × h₁) / ( 50 × r₁² × h₁)

10/v₂ = 1/50

v₂ = 500 ounces

which is 50 times more than the smaller container.

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The complete question is:

At a farmer’s market, a vendor sells soup that comes in two different-sized containers, both shaped like cylinders. When the small container is filled, it holds10​ ounces of soup. The larger container’s diameter is 5​ times larger than the small container’s diameter, and it is 2​ times taller than the small container. How many ounces of soup will the larger container hold when filled?

Answer: are have a raztation speed of 20 rotation a min

Step-by-step explanation:W anwer

Answer:

1- graphing

2- substitution

3- elimination.

If randomly throw two darts at the board and break two balloons, then [tex]\frac{2}{35}[/tex] is the probability that both of the balloons you break are purple.

Considering what is meant by probability,

However, you must be aware that probability refers to the likelihood—greater or lesser—of a given event occurring.

In other words, probability creates a connection between the total number of conceivable events and the number of favorable events.

Then, the ratio between the number of favorable circumstances (cases in which event A may or may not occur) and the total number of possible cases is used to define the likelihood of any event A. Laplace's Law is what governs this.

[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]

If the occurrence of one of them has an impact on the occurrence of the other, then two occurrences A and B are dependent. The likelihood for events that are dependent is:

P(A and B)= P(A)× P(B|A)

The phrase "the probability of B, provided that A has occurred" is denoted by the symbol P(B|A).

In this instance:

[tex]P(A)=\frac{4 balloons}{15 balloons} =\frac{4}{15}[/tex]

If the first balloon is purple, there are still 3 purple balloons available out of the total of 14. P(B|A) then equals [tex]\frac{3}{14}[/tex].

[tex]P(A and B)=\frac{4}{15} *\frac{3}{14}[/tex]

[tex]P(A and B)=\frac{2}{35}[/tex]

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Answer:

Step-by-step explanation:

Mariana's quote: 135

Vicent's quote: 34x+67

Say x=1, 34(1)+67=101

For 1 hour of Vincent's work it would be $101.

Say x=2. 34(2)+67=135

Vincent would have to work for two hours to charge the exact same as Mariana.

The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.

What is error model?

Error modelling is used to describe the variability in how well a parameter describes the data.

The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.

" The model as described shows four small arrows going from 4 to 8, 8 to 12, 12 to 16, and 16 to 20, respectively, and one large arrow going from 0 to 20. Since the expression is 20 divided by 4, the model should show four equal parts from 0 to 20, and each part should have a length of 5.

The arrows should start at the beginning of each part and end at the end of each part, resulting in four equal segments.

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Answer:

Step-by-step explanation:

yes no yes

The missing term in the equation is n = -2

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

Substituting the values in the equation , we get

Let the missing term be represented as n

-2x + 18 = nx + 18

Subtracting 18 on both sides of the equation , we get

-2x = nx

Divide by x on both sides of the equation , we get

n = -2

Therefore , the missing term is n = -2

Hence , the equation is n = -2

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Answer:

8(8+7)

Step-by-step explanation:

64+56
8 is the GCF
8(8+7)

The  two equivalent expressions for the total number of granola bars Tomas buys after 5 months is 5(4x + 2y) and 20x + 10y

In mathematics, an expression is a combination of symbols (such as numbers, variables, and operators) that represent a mathematical object or value.

Tomas buys 4 boxes of crunchy granola bars and 2 boxes of chewy granola bars each month. Let's assume that each box of crunchy granola bars contains x bars and each box of chewy granola bars contains y bars.

To express the total number of granola bars that Tomas buys in one month, we can use the following expression:

4x + 2y

This expression shows that Tomas buys 4 boxes of crunchy granola bars, each containing x bars, and 2 boxes of chewy granola bars, each containing y bars.

To find the total number of granola bars that Tomas buys after 5 months, we need to multiply the expression by 5, since he buys granola bars each month for 5 months. This gives us the expression:

5(4x + 2y) = 20x + 10y

Alternatively, we can also express the total number of granola bars that Tomas buys in 5 months using the following expression:

5x(4) + 5y(2) = 20x + 10y

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Answer:

10

Step-by-step explanation:

i love how you look like a dinosaur

Number of ways are there to choose this focus group where all three students do not all come from the same major is 240,000

It is given that a school have three majors i.ie, business, math and psych

Number of students in business majors is 100

Number of students in math majors is 60

Number of students in psych majors is 40

Total number of students (100+60+40) = 200 students

Three different students are chosen to be interviewed for a focus group.

Therefore, number of student in focus group = 3

Now, number of ways are there to choose this focus group where all three students do not all come from the same major

= [tex]^{100}C_{1} \times ^{60}C_{1}\times^{40}C_{1}[/tex]

= 100×60×40

= 240,000 ways

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Answer:

Option B

Step-by-step explanation:

The green graph represents the percentage of calls with the Chicago service center.
For December 1993, the percentage of calls is coming out to at least 95 percent. In addition, the graph is increasing as months go by. Based on these two analysis, the estimate percentage of calls within 10 seconds in January of 1994 is:

Option B: 98

For the graph of given function, At x = 2, the graph crosses x axis At x = - 6, the graph touches x axis, At x = - 12, the graph crosses x axis.

What's an Equation?

The description of an equation in algebra is a fine statement proving the equivalency of two fine expressions.

The two equations 3x 5 and 14 are separated by the" equal" sign in the equation 3x 5 = 14, for illustration.

In mathematics, an equation is a relationship between two expressions that's equal on both sides of the equal to subscribe. An equation is commodity like 3y = 16.

Equation of a function f( x) = ( x − 2) 3( x 6) 2( x 12)

Lets find out the roots and dissect

lets set each factor = 0 and break for x

Exponent in each factor tell us the multifariousness. Using multifariousness we check whether crosses or traces x axis

When multifariousness is odd also graph crosses x axis.

when multifariousness is indeed also graph touches x axis.

f(x) = (x-2)^3(x+6)^6(x+12)

      ⇒(x-2)^3

      ⇒x-2 = 0

      ⇒ x = 2

Root is x = 2 with multifariousness 3. 3 is odd

At x = 2, the graph crosses x axis

⇒ (x+6)^2

⇒ (x+6)=0

⇒ x = -6

At x = - 6, multifariousness is 2 that's indeed.

At x = - 6, the graph touches x axis

x + 12 = 0

x = -12

x = - 12 with multifariousness 1. 1 is odd

At x = - 12, the graph crosses x axis.

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Use identities:

Then apply to the left side of the given equation:

Proved

The amount (present value) that Emma borrowed from Dixons Dynamite Deals (DDD) to repay after 10 years with a one-time payment of $80,000 at 14/6% compounded interest per annum is not more than $20,475.94.

Step-by-step explanation:

To find out how much Emma borrowed from Dixons Dynamite Deals (DDD), we can use the formula for the future value of a loan with compound interest:

Future Value (FV) = Principal Amount (P) * (1 + r)^n

Where:

P = Principal amount (the amount borrowed)

r = Interest rate per period (in decimal form)

n = Number of periods

In this case:

Future Value (FV) = $80,000 (the payment Emma will make after 10 years)

Interest rate (r) = 14.6% per annum = 0.146 (in decimal form)

Number of periods (n) = 10 years

Now, let's calculate the principal amount (P):

$80,000 = P * (1 + 0.146)^10

Now, let's solve for P:

P = $80,000 / (1.146)^10

P ≈ $80,000 / 2.97804

P ≈ $26,874.94

So, Emma borrowed approximately $26,874.94 from Dixons Dynamite Deals (DDD) to start her cupcake business.

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a. The dependent variable for this study is the number of correct answers on the test given.

b. The dependent variable in this study is a discrete variable.

a. The dependent variable for this study is the number of correct answers on the test given to the students after they prepared for the test by either generating and answering questions or reading the passage a second time.

b. The dependent variable in this study is a discrete variable because the number of correct answers can only take on whole numbers (e.g., 0, 1, 2, 3, etc.). It is not possible to have fractional or continuous values of correct answers on the test.

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Circle A is larger.

Circle A's radius is 58 cm and circle B's radius is 57 cm.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

We have,

Area of a circle = πr²

Circumference of a circle = 2πr

Circle A:

Area of a circle = 10562.96

πr² = 10562.96

r² = 3364

r = 58 cm ____(1)

Circle B:

Circumference = 357.96

2πr = 357.96

r = 357.96/6.28

r = 57 cm ______(2)

From (1) and (2)

58 > 57

So,

Circle A is larger.

Thus,

Circle A is larger.

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The solution to the inequality are the region in the shaded area

From the question, we have the following parameters that can be used in our computation:

Y >1/2x-1

Y ≥-3/4x-6

Represent properly

y > 1/2x - 1

y ≥ -3/4x - 6

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (-4, -3)

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n = the numerator of the fraction

[tex]\cfrac{p}{p-2}~~ = ~~\cfrac{n}{4-p^2}\implies \cfrac{p(4-p^2)}{p-2}~~ = ~~n\implies \cfrac{p(-1)(p^2-4)}{p-2}=n \\\\\\ \stackrel{ \textit{difference of squares} }{\cfrac{p(-1)(p^2-2^2)}{p-2}}=n\implies \cfrac{-p(p-2)(p+2)}{p-2}=n \\\\\\ \boxed{-p(p+2)=n}\hspace{5em}\cfrac{-p(p+2)}{4-p^2}[/tex]

5 baskets of tomatoes can make 7 1/2 quarts of tomato sauce.

To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.

Given that, we get 3 quarts of tomato sauce from 2 baskets of tomatoes.

Thus,

2 baskets = 3 quarts

5 baskets = x

Use the method of cross multiplication or butterfly method for multiplication.

x = (3)(5)/2

x = 15/2

x = 7 1/2

Hence, 5 baskets of tomatoes can make 7 1/2 quarts of tomato sauce.

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The solution to the equation 2n + 5 = 6( n² - 5 ) is n = ( 1 - √(211 )) / 6 and n = ( 1 + √(211 )) / 6

Given the quadratic equation in the question;

2n + 5 = 6( n² - 5 )

First we simplify the given equation;

2n + 5 = 6( n² - 5 )

2n + 5 = 6n² - 30

6n² - 2n - 5 - 30 = 0

6n² - 2n - 35 = 0

To solve for n, we use the quadratic formula.

n = (-b±√(b² - 4ac)) / (2a)

Compare 6n² - 2n - 35 = 0 to the quadratic equation in its standard form an² + bn + c = 0.

Plug the values into the quadratic formula

n = (-b±√(b² - 4ac)) / (2a)

n = ( -(-2) ±√( (-2)² - 4 × 6 × -35 )) / (2 × 6 ))

n = ( 2 ±√( 4 + 840 )) / ( 12 )

n = ( 2 ±√( 844 )) / ( 12 )

n = ( 2 ±2√(211 )) / ( 12 )

n = ( 1 ± √(211 )) / 6

n = ( 1 - √(211 )) / 6 or n = ( 1 + √(211 )) / 6

Therefore, the values of n are ( 1 - √(211 )) / 6 and ( 1 + √(211 )) / 6.

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Answer:

if its 50,000k for example it is gonna be Loan term in years is 7 it depends on the price

Step-by-step explanation:

Using arithmetic operation Jude's typing rate is 182 characters per minute, which is option C.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the typing rate in characters per minute, we need use arithmetic operation of division.

Divide the number of characters by the number of minutes -

Typing rate = Number of characters / Number of minutes

In this case, Jude types 1,274 characters in 7 minutes, so her typing rate is -

Typing rate = 1274 / 7 = 182

Therefore, the typing rate is 182 characters/minute.

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