y = -8x - 21 y = 6x + 7 solve in Equal Values Method

The graph of the linear equation is attached

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

A bowling alley charges $6 for shoe rental and $2 for each game.

This means that

Intial value = 6

Rate = 2

The function is then represented as

f(x) = Initial + Rate * x

So, we have

f(x) = 6 + 2x

See attachment fr the graph

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The numbers have been matched accordingly as below.

Rational numbers are numbers which can be written in the form of a/b, b ≠ 0, and a and b are integers.

Irrational numbers cannot be written in this form.

√30 is not a perfect square. So it is real, irrational root.

-26 is a negative real integer. So it is a real rational integer.

√64 is actually a perfect square root, 8, which is a whole number. So it is a real, rational root, whole number.

1/4 is of the form a/b. So it is also real, rational.

0.363363336.... is a real irrational decimal.

0.424242..... is a real rational decimal, since it is repeating in nature.

[tex]\sqrt{-7}[/tex] or [tex]7i[/tex] is an imaginary number.

Hence the numbers has been matched according to the properties.

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The exponential function is [tex]y = 1505.88(0.85)^x[/tex].

The monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To model the monthly number of defective parts, we can use an exponential equation of the form:

[tex]y=a(b)^x[/tex]

Where y is the number of defective parts, x is the number of months after Jane was hired, a is the initial number of defective parts, and b is the common ratio between consecutive months.

To find the values of a and b, use the two data points given -

In the first month, there were 1,280 defective parts, which means that y = 1280 when x = 1.

In the second month, there were 1,088 defective parts, which means that y = 1088 when x = 2.

Substituting these values into the exponential equation -

1280 = a(b)

1088 = a(b)²

Dividing the second equation by the first equation -

1088/1280 = (a(b)²)/(a(b))

0.85 = b

Substituting b = 0.85 into the first equation -

1280 = a(0.85)

1280 = 0.85a

a = 1505.88 (rounded to two decimal places)

So the exponential equation that models the monthly number of defective parts is -

[tex]y = 1505.88(0.85)^x[/tex]

To find when the monthly number of defective parts will be less than 500, we can set y = 500 and solve for x -

[tex]500 = 1505.88(0.85)^x[/tex]

Dividing both sides by 1505.88 -

[tex]0.332 = (0.85)^x[/tex]

Taking the logarithm of both sides (with any base) -

log(0.332) = x log(0.85)

Dividing both sides by log(0.85) -

x = log(0.332) / log(0.85)

x ≈ 6.87

Therefore,  the monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

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The ribbon needs to be 25.12 inches.

The distance along a circle's perimeter is referred to as its circumference.

Given:

She is putting ribbon around a cake tray that has a diameter of 8 inches.

The diameter = 8 inches.

The circumference = 8 x 3.14

                                = 25.12 inches.

The ribbon needs to be 25.12 inches.

Hence, ribbon should be 25.12 inches.

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Liliana's next step is to find the area of each of the two trapezoids.

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

Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid

This is done using

Area = 1/2 * (sum of parallel sides) * height

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Complete question

Area of Trapezoids and Other Figures quick check

Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?

Answer:

The value of [tex]r[/tex] is 24 cm.

Option C. 24 cm

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the missing side.

Here is the formula for the Pythagorean theorem.

[tex]a^2+b^2=c^2[/tex]

[tex]a[/tex] and [tex]b[/tex] are the legs of the triangle

[tex]c[/tex] is the hypotenuse

In this example we are given the value of 1 leg and the hypotenuse.

Knowing 2 of the 3 sides, we can evaluate the missing leg.

Let [tex]a=r[/tex]

We are given

[tex]b=10\\c=26[/tex]

Inserting our values into the Pythagorean theorem gives us

[tex]r^2+10^2=26^2[/tex]

Lets solve for [tex]r[/tex].

[tex]r^2+10^2=26^2[/tex]

Evaluate [tex]10^2[/tex].

[tex]r^2+100=26^2[/tex]

Evaluate [tex]26^2[/tex].

[tex]r^2+100=676[/tex]

Subtract [tex]100[/tex] from both sides of the equation.

[tex]r^2=576[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]r=\sqrt{576}[/tex]

[tex]r=24[/tex]

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Answer:

On xy axis draw the line x+y=10  (slope -1; y-intercept 10)

Draw a vertical line at x=6

Draw a horizontal line y=7

The area will be all that above or on x+y=10, but on or below x=6 and y=7

The equation of line that passes through (3,2) and has a slope of 1/3 in point-slope form is y - 2 = (1/3)( x - 2 ).

The point-slope formula is expressed as;

y - y₁ = m( x - x₁ )

Where x and y are the coordinates and m is the slope.

Given the data in the question;

Point (3,2)

Plug the values into the point-slope formula.

y - y₁ = m( x - x₁ )

y - 2 = (1/3)( x - 2 )

Therefore, the equation in point slope form is y - 2 = (1/3)( x - 2 ).

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A quadrilateral with two sets of parallel sides and 4 congruent sides is called a parallelogram. A parallelogram is a quadrilateral with two sets of parallel sides and 4 congruent sides.

A parallelogram is a four-sided polygon with two pairs of opposite sides that are parallel to each other and equal in length. This means that the shape has two sets of parallel sides and all of its sides have the same length.

Parallelograms have several key properties, including opposite sides that are equal in length and parallel, and opposite angles that are equal in measure. Additionally, the diagonals of a parallelogram bisect each other, meaning they split each other in half.

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The solution to the equation cos(x + 2π/3) = √2/2 over the interval

(0, 2π) is [7π/12, 3π/4]

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

The given function is cos(x + 2π/3) = √2/2 over the interval (0, 2π).

(x + 2π/3) = cos⁻1(√2/2).

x + 2π/3 = π/4  or 21π/12   (As cos is +ve on I and IV)

Now,

x + 2π/3 = π/4.

x = π/4 - 2π/3.

x = (3π - 8π)/12.

x = - 5π/12.

x = π - 5π/12.

x = (12π - 5π)/12.

x = 7π/12.

And,

x + 2π/3 = 21π/12.

x = 21π/12 - 2π/2.

x = (21π - 12π)/12.

x = 9π/12.

x = 3π/4.

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The markup is $6.47 and the selling price is $31.87

percentage, a relative value indicating hundredth parts of any quantity.

A markup is the amount added to the cost price of a product to determine the selling price.

Let the cost price of a box of copy paper is $25.4 and the markup is 25.4%

Now let us find the selling price by given formula.

Selling price = Cost price + (Cost price x Markup percentage)

Selling price = $25.4 + ($25.4 x 25.4%)

Selling price = $25.4 + ($25.4 x 0.254)

Selling price = $25.4 + $6.47

Selling price = $31.87

So, the markup is $6.47 and the selling price is $31.87.

Hence,  the markup is $6.47 and the selling price is $31.87

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As a result, the ratio of eighth students to seventh graders is 4:1.

A ratio is a comparison of two or more values, often expressed as a fraction or a colon-separated set of numbers. Ratios can be used to compare quantities of similar items, such as the ratio of the number of apples to the number of bananas in a basket. Ratios can also be used to describe the relationship between different aspects of a system, such as the ratio of length to width of a rectangle, or the ratio of time spent working to time spent sleeping. Ratios are a useful tool for making comparisons and understanding relationships between different values.

Here,

Out of the 15 students in the yearbook club, 3 are in 7th grade, and the rest are in 8th grade, which means there are 15 - 3 = 12 students in 8th grade.

The ratio of 8th graders to 7th graders can be calculated by dividing the number of 8th graders by the number of 7th graders:

12/3 = 4:1

So, the ratio of 8th graders to 7th graders is 4:1.

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Step-by-step explanation:

I can explain what each item is, but I don't know exactly what it's asking

5 is a coefficient. The number attached to the left of the variable/term is always called the coefficient

x is the term/variable. Can always change the outcome, it just depends on the value inputed at that place

3 is a constant, since there's no term attached to it, it will always stay 3

Hope this helps in some way

A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

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The y-intercept will be at (0, 22,995) and the x -intercept at (9, 0).

The y-axis is calibrated in dollars and the x-axis in years.

The graph is a straight line which starts  on the positive y axis and ends on the positive x-axis and has a negative slope .

Y - intercept:

The point of intersection is the point on the Y-axis through which the slope of the straight line passes. This is the y-coordinate of the point where the line or curve intersects the y-axis. This is shown when writing the equation for the y = mx + c straight line. where m is the slope and c is the intersection with the y-axis.

X- Intercept:

The x-intercept is the point at which the graph of the equation intersects the x-axis, and the y-value must be 0 for the point to intersect the x-axis. Consequently, the x segment can always be represented as (x, 0). The x value indicates where the graph intersects the x-axis.

According to the question:

When X = 0, y = 22995

And, X = 9  and Y = 0.

So the intercepts are (0,22995) and (9,0) which are shown on the right.

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The exact area of the circle would be = 36πcm². That is option B.

The area of a circle can be calculated through the use of the formula = πr²

Where,

radius (r) = 6 cm

area = π × 6²

= 36π cm² ( in the terms of π)

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137 is not a term in this sequence due to the fact that  7n +2= 137 gives n = 19.285 which is not a whole number.

We have to use the formula

tn = a + ( n - 1) d

where we have tn = 137

a is the first term = 9

n i unknown

d is the difference = 16 - 9 = 7

We have to put these values in the formula such that

137 = 9 + (n - 1) 7

then we have to expand this

137 = 9 + 7n - 7

take the like terms

137 = 9 - 7 + 7n

137 = 2 + 7n

137 - 2 = 7n

135 = 7n

divide through by 7

135 / 7 = 7n / 7

n = 19.28571...

This is not a whole number, hence 137 is not a term in the sequence that we have here

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The number of possibilities are 20,160. Therefore, the option A is the correct answer.

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.

Factorials is used in mathematics or statistics to denote the possibilities of an event in an outcome.

The number of specialty pizzas that is being offered by pizza parlor = 8

The number of specialty that Almeida's family wants to order = 2

To calculate the number of possibilities;

= 8!/2!

= 8×7×6×5×4×3×2×1/2×1

= 20,160.

Therefore, the option A is the correct answer.

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Answer: midpoint is 4,5

Step-by-step explanation:

A high standard deviation indicates greater variability in the data set. A low standard deviation indicates lower variability in the data set.

A standard deviation is a measure of how spread out the values in a data set are. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. A high standard deviation indicates that the values in the data set are far from the mean and spread out over a large range of values. This suggests that there is a large amount of variation and diversity in the data. On the other hand, a low standard deviation indicates that the values in the data set are close to the mean and spread out over a smaller range of values. This suggests that there is less variability and diversity in the data. A standard deviation of zero indicates that all values in the data set are the same. This suggests that there is no variation or diversity in the data. No one set of data is more accurate than another; accuracy depends on the context and purpose of the data. For example, if the goal is to identify trends or outliers, a data set with a high standard deviation may be more useful than one with a low standard deviation.

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A mathematical puzzle, where the rational numbers are used is attached with the answer.

A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge.

In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle.

Given is to investigate a mathematical puzzle where rational numbers are used.

Refer to the image attached. It shows a mathematical puzzle attached where the rational numbers are used.

Therefore, a mathematical puzzle, where the rational numbers are used is attached with the answer.

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{Question in english -

Investigate a mathematical puzzle where rational numbers are used.}

An expression which best represents the value of pi include the following: D. C/7.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Making π the subject of formula, we have the following:

π = C/D

Substituting the given parameters into the circumference of a circle formula, we have;

π = C/7.

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Complete Question:

A circular pond has a circumference of about C feet. The diameter of the pond is 7 feet. Which expression best represents the value of pi?

A. C/14

B. 7/C

C. 14/C

D. C/7

The probability that a student is in 4th grade given that they did not choose popular as the most important trait is 0.5 or 50%.

The probability is a concept used in statistics that measures the likelihood of an event occurring.

Let's call the event of a student being in 4th grade as A and the event of a student not choosing popular as the most important trait as B. We can find the probability of A and B happening together by dividing the number of students who are in 4th grade and did not choose popular by the total number of students. This can be represented as

P(A and B) = P(A | B) = (75 / 250) = 0.3.

Next, we can find the probability of B happening by dividing the number of students who did not choose popular by the total number of students. This can be represented as

P(B) = (150 / 250) = 0.6.

Finally, we can use Bayes' theorem to find the probability of A given B. Bayes' theorem states that

=> P(A | B) = P(A and B) / P(B).

Therefore,

=> P(A | B) = (75 / 250) / (150 / 250) = 0.3 / 0.6 = 0.5.

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The elements in (D∩B)' is A,B,D.

A set is defined as collection of well-defined object. It is denoted by capital letters and their elements are denoted by small letters.

Given that ,

In venn diagram, B is the swamp portion and D is the rainforest portion.

C represents the intersection of B and D. i.e., C= (D∩B)

A is the universal set.

(D∩B)' = A - (D∩B)

          = A - C

Hence, (D∩B)' contains  A, B, D.

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a function means that for every input (value of x), there is only one output (value of y)

y can repeat, x cannot (unless it's with the same y value)

eg:

{(1,2), (1,3), (3,2)} is not a function because 1 has two outputs

but if it was

{(1,2), (2,3), (3,2)} it would be a function. It doesn't matter that 2 repeats in the y coordinate

lmk if you still have questions, I'm happy to help!

The least possible number of coins in the treasure chest Jack found is 29.

In Mathematics, the Lowest Common Multiple (LCM) of any two or more natural numbers is the number that is the lowest of their common multiples.

For a minute put 1 coin aside from the collection.

Then, the number of remaining coins is a multiple of both 4 and 7.

So, the smallest such an integer number of coins

= 7 x 4

= 28.

Now, return 1 coins back.

= 28 + 1

= 29 coins.

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Answer:

5.3

Step-by-step explanation:

sin24 = x/13

x = sin24(13) = 5.3

Answer:

Amy is 14 years old and Sam is 10 years old.

Step-by-step explanation:

Let's represent Amy's current age as "A".

Since Sam is four years younger than Amy, his current age can be represented as (A - 4).

Five years ago, Amy's age was A - 5 and Sam's age was (A - 4) - 5 = A - 9.

At that time, Sam was half of Amy's age, so we can write the following equation:

(A - 9) = (A - 5) / 2

Expanding and simplifying the equation, we get:

A - 9 = 2A / 2 - 5 / 2

A - 9 = A - 5 / 2

7 = A / 2

A = 14

So, Amy is 14 years old and Sam is (14 - 4) = 10 years old.

The ratios of vegetarian and meat recipes to all recipes should be in Bradley’s cookbook is 75:50

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Total Recipes= 150

Books have three section: vegetarian dishes, meat dishes, and desserts.

So, vegetarians

= 150 x 1/2

= 75

and, Non vegetarians

= 150 x 1/3

= 50

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