If y varies directly as x and x = 33 when y = 22, find x when y = 32.

The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

To divide polynomials by a polynomial, we use the long division method.

When there is no common factor in both the numerator and the denominator, we can use the long division.

It may be used to find reminders and quotients while dividing.

Here we have

Divide 3x² + 6 by 3x – 3    

On dividing 3x² + 6 by 3x – 3 in long division method

we get the remainder as 9 and the quotient as (x - 1)

For more understanding understand the long division in the given picture.

Therefore,    

The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

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35% of the circle would represent the food budget.

The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics

Given are the vacation expenses budgets labeled in a circle graph.

We can write the total budget as equivalent to the Area of the circle as -

${600 + 450 + 270} → πr²

$1320 → πr²

$1 → πr²/1320

$450 →  πr²/1320 x 450 = 0.35 πr²

Therefore, 35% of the circle would represent the food budget.

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Considering the 12-face diagonals of a rectangular block, 30 pairs of these diagonals are skew lines.

In a rectangular block, there are a total of 12 face diagonals. These diagonals are formed by connecting the opposite vertices of each face of the block. To determine the number of pairs of skew lines among these diagonals, we can consider the following:

There are 6 faces in a rectangular block, each with 2 diagonals.

Every diagonal on one face is unique and does not intersect with any other diagonal on the same face.

However, diagonals on opposite faces are parallel to each other and therefore, do not form skew lines.

So, we will be selecting one diagonal from one face, so we have 6 options, then we select another diagonal from another face, which would be 5 options, and we repeat this process until we exhaust all the diagonals. This will give us 6*5 = 30 pairs of skew lines.

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The simplified form of the expression is option C. (3)^5/12 * (4)^2/3.

An exponential expression is one which has the value of the power of one of its terms to be greater than 1 or in a fraction form. Thus some laws are required to simplify a given exponential expression. These laws are sometimes referred to as the law of indices.

Considering the given question;

(3^2/3 * 3^3/2)^5/12  x (4^2/3)

Simplifying this expression requires applying required laws, so that;

(3^2/3 * 3^3/2)^5/12 = (3^6/6)^5/12

                                 = (3^1)^5/12

                                 = 3^5/12

(3^2/3 * 3^3/2)^5/12 = 3^5/12

Therefore, we have;

(3^2/3 * 3^3/2)^5/12  x (4^2/3) = (3)^5/12 x (4)^2/3

Thus the simplified form is option C.

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The height of right circular cylinder is 8.4 cm.

Given that,

The radius = r = 2.4 cm

Volume      =  152 cubic cm

Let height of right circular cylinder = h

We know that,

The right circular cylinder is a cylinder with circular bases that are parallel to each other. It's a three-dimensional form. The axis of the cylinder connects the centres of the cylinder's two bases. This is the most frequent sort of cylinder encountered in daily life. The oblique cylinder, on the other hand, does not have parallel bases and resembles a skewed construction.

And we know that,

Volume of right circular cylinder = πr²h

                                              152  = 3.14 x 2.4 x 2.4 x h

⇒ h = 8.4 cm

Hence, height is 8.4 cm.

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The 9th term of the geometric sequence is 2304.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

9, -18, 36

First term = 9

Common difference = -18/9 = -2

Now,

The nth term of a geometric sequence.

= a[tex]r^{n-1}[/tex]

For n = 9,

= 9 [tex](-2)^{9 - 1}[/tex]

= 9 x [tex](-2)^8[/tex]

= 9 x 256

= 2304

Thus,

The 9th term is 2304.

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The function that represents their household income if they work the same number of hours is 52x + 25.

Therefore the answer is B. (r + s)(x) = 52x + 25

Rhonda's paycheck is modeled by the function r(x) = 22x + 50, where x is the number of hours worked.

Shalene's paycheck is modeled by the function s(x) = 30x – 25, where x is the number of hours worked.

The function that represents their household income if they work the same number of hours can be determined by adding their individual income

(r + s)(x) = 22x + 50 + 30x - 25

(r + s)(x) = 52x + 25

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Answer: To express 40 1/4% as a fraction, we can convert the percentage to a fraction with a denominator of 100: 40 1/4% = 40.25/100.

To simplify this fraction we can divide both the numerator and denominator by the greatest common factor (GCF) which is 25.

So, (40.25/100) = (4025/10000) = (161/400)

To express 65 5/8% as a fraction, we can convert the percentage to a fraction with a denominator of 100: 65 5/8% = 65.625/100.

To simplify this fraction we can divide both the numerator and denominator by the greatest common factor (GCF) which is 625.

So, (65.625/100) = (65625/10000) = (261/400)

Therefore, the simplest form of 40 1/4% as a fraction is 161/400, and 65 5/8% as a fraction is 261/400

Step-by-step explanation:

Answer:

Given that RS bisects MO at N, we know that:

RN = RO (by definition of a bisector)

MN + NO = MO (by the angle bisector theorem)

Given that MN = 5x + 8 and NO = 10 + 3x, we can substitute these values into the second equation to find the value of x.

MN + NO = MO

(5x + 8) + (10 + 3x) = MO

8x + 18 = MO

Now we can use the first equation to find the value of x.

RN = RO

5x + 8 = 10 + 3x

3x = 2

x = 2/3

Therefore, the value of x is 2/3.

Answer:

A=24+9t

B=40+5t

Step-by-step explanation:

see attached

So, Amy used 30 stamps of 41-cent stamps and 17 stamps of 7-cent stamps.

This is a system of equations problem. We can call the number of 41-cent stamps x and the number of 7-cent stamps y.

The two equations are:

x + y = total number of stamps used

0.41x + 0.07y = 1.79 (the total cost of the postage in dollars)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:

y = total number of stamps used - x

Then we can substitute this into the second equation:

0.41x + 0.07(total number of stamps used - x) = 1.79

Solving for x,

x = (1.79 - 0.07*total number of stamps used) / 0.41

We can substitute this into the first equation to solve for total number of stamps used.

x + y = total number of stamps used

x + (total number of stamps used - x) = total number of stamps used

2x = 1.79/0.41 + 0.07/0.41

x = (1.79/0.41 + 0.07/0.41)/2

x = (1.79 + 0.07)/(0.41*2)

So, x = 30 stamps of 41-cent stamps

and y = (total number of stamps used - x) = (total number of stamps used - 30) = (1.79/0.48 - 30) = 17 stamps of 7-cent stamps

So, Amy used 30 stamps of 41-cent stamps and 17 stamps of 7-cent stamps.

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The summation notation of the sum is:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

The total amount is $84.

Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.

Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.

Let n represent the number of weeks

Thus, this can be written using summation notation as:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

Thus, the total amount = 4¹ + 4² + 4³ = $84

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Answer:

176/3

Step-by-step explanation:

58 2/3 = 58 + 2/3 = 58/1 + 2/3 = 174/3 + 2/3 = 176/3

The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using set builder notation, the domain of this function shown in the graph above can be written as follows;

Domain = {-4, ∞}

Domain = {x|x ≥ -4}

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If the baseball player went up to bat 250 times in a season and hits the ball 100 times then the rate of balls hits to times at bat is 2/5 .

the number of times the player went up to bat is = 250 times ;

the number of times he hits the ball is = 100 times ;

So , the rate of balls hit to times at bat is calculated as :

= (number of times he hits the bat)/(number of times player went to bat)

substituting the required values in formula ,

we get ;

= 100/250 ;

writing the fraction in the simplified form ,

we have ⇒ 2/5 .

Therefore , the rate of balls hit to times at bat in simplified fraction is 2/5 .

The given question is incomplete , the complete question is

A baseball player went up to bat 250 times in a season. he hit the ball 100 times. find the rate of balls hit to times at bat. express as a simplified fraction.

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Grams are the ideal unit for calculating the quantity of spices in a batch of cookies (g).

A system of measurements is called the metric system. It is employed in calculations and research across the globe. Here are some instances of measurements made with the metric system:

The unit used to measure lengths and distances is the meter. In daily life, we use this unit to measure things like the length of a piece of clothing, the distance from school to home, etc.

You may have noticed that the bag of your favorite food has a weight listed on it. 250 grams of potato chips, as an illustration. The unit of weight used here is the gram.

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Answer:

To solve a system of equations by substitution, we can use one equation to solve for one variable in terms of the other variable, and then substitute that expression into the other equation.

Given the system of equations:

10x + 2y = 4

.-9x + 3y = 18

We can start by isolating y in one of the equations. For example, we can use the first equation:

10x + 2y = 4

To solve for y, we can divide both sides by 2:

y = -5x + 2

Now we can substitute this expression for y into the second equation:

-9x + 3(-5x + 2) = 18

-9x - 15x + 6 = 18

-24x + 6 = 18

-24x = 12

x = -0.5

Now that we know x = -0.5, we can substitute this value back into the original expression we found for y:

y = -5(-0.5) + 2

y = 2.5

So the solution of the system of equations is (x, y) = (-0.5, 2.5).

It will take approximately 197.36 minutes for the sample to reach 100,000 bacteria.

Calculate the growth rate of bacteria in each 40 minute interval by dividing 3 (the amount of growth) by 40 (the time interval):
Growth rate = 3/40 = 0.075
Calculate the number of growth periods necessary to get from 38 to 100,000 bacteria. To do this, divide the desired number of bacteria (100,000) by the initial number of bacteria (38):
Growth Periods = 100,000/38 = 2,631.57
Calculate the total time required for the sample to reach 100,000 bacteria by multiplying the growth rate (0.075) by the number of growth periods (2,631.57):
Total Time = 0.075 x 2,631.57 = 197.36 minutes
Therefore, it will take approximately 197.36 minutes for the sample to reach 100,000 bacteria.

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Answer: To find the equation of the tangent line to a function at a specific point, we can use the following steps:

Find the derivative of the function f(x) = 3x3 − x2 + 2

f'(x) = 9x^2 - 2x

Substitute the point a = 0 into the derivative to find the slope of the tangent line at that point

f'(0) = 9(0)^2 - 2(0) = 0

Use the point-slope form of a linear equation, y - y1 = m(x - x1) to find the equation of the tangent line, where m is the slope and (x1, y1) is the point at which the tangent line touches the function.

y - f(a) = m(x - a)

y - (3*0^3 - 0^2 + 2) = 0(x - 0)

y - 2 = 0

So the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0 is:

y = 2

Therefore, the correct answer is A. y = 2

Step-by-step explanation:

The Dimension of parallelogram is 7.57 inches . A special type of quadrilateral known as a parallelogram has opposite sides that are parallel and equal.

A parallelogram is a two-dimensional shape with four sides. The sides of this particular example of a quadrilateral are parallel and equal. The area of a parallelogram is the space enclosed by its four sides. The area of a parallelogram is calculated by multiplying its height by its length.

Area of Parallelogram = b × h

area is 63.9 in x in.

Area of Parallelogram = b × h 63.9

               = x+6.5 × x 63.9-6.5

                       = 57.4 x

                    = 7.57 inches x

height = dimension = 7.57 inches

Because it can be rearranged into a rectangle with the same area, the area of a parallelogram is the base times the height. A particular kind of parallelogram is a rectangle.

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The value to write in the blank so the equation would be true is -4. Option A. no values of x

It is important to note that an algebraic expression is an expression comprising of coefficients, terms, factors, constants and variables.

These algebraic expression also consist of mathematical operations, such as;

From the information given, we have the equation;

4x - 4 = 4x + _

To make the equation true, then, the values must be the same on both sides, the value to add is (-4) because expanding the bracket would give the same value. We have;

4x - 4 = 4x + (-4)

expand the bracket

4x - 4 = 4x - 4

0 = 0

Hence, the value is -4

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Answer:189/2

Step-by-step explanation:

Answer: Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.

Step-by-step explanation:

Speed = Distance/Time

The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours. Then the number of miles he can drive in 4.5 hours will be. This meas that x will be the number of miles covered in 4.5 hours.

x / 4.5 = 171 / 3

x = 256.5 miles

I hope this helps!

Answer:

Step-by-step explanation: Whats you answer? cant see it.

Answer24

Step-by-step explanation:

The required number of baskets made in 90 minutes are 27 baskets.

It is given that Juwan makes 12 baskets in 40 minutes and continues to make the baskets for 90 minutes.

Number of baskets made in 90 minutes = ?

So, let us calculate the number of baskets made in 1 minute.

40 min - 12 baskets

1 min - 12/40 baskets

Now, we need to find out the number of baskets made in 90 minutes.

90 min - ?

1 × 90 min - 90 × 12/40 = 27 baskets

Thus, the required number of baskets made in 90 minutes are 27 baskets.

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The arithmetic sequence is x+4n -55.

Given that,

20th term is = x + 25

a20 = a +19d = x + 25,

40th term is = x + 105

a40 = a +39d = x + 105,

now subtract a20 by a40,

a40 - a20

a + 19d - (a + 39d) =  x + 25 - (x + 105)

20d =  x + 25 -x - 105

20d = 80

d= 4.

a1 = a20 - 19d

a1 = x+ 25 - 19 x 4

a1 = x -51

so,

an = a1 + (n-1)d

an = x- 51 + (n-1)4

an = x- 51 + 4n - 4

an = x + 4n -55.

so, The arithmetic sequence is x+4n -55.

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The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast is 4 / 5 hour.

The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast can be calculated by adding the fractions of time she spends on each activity:

1/10 hour + 1/5 hour + 1/2 hour

= (2 + 1 + 5) / 10 hour

= 8 / 10 hour

= 4 / 5 hour

The addition of two or more fractions with the same denominator is straightforward.

Simply add the numerators and keep the same denominator. For example:

(1/5) + (2/5) = (1 + 2) / 5 = 3/5

If the fractions have different denominators, you will need to find a common denominator before adding the numerators. The common denominator is the least common multiple of the denominators. Once you have found the common denominator, convert each fraction to an equivalent fraction with the common denominator and then add the numerators.

For example:

(1/5) + (2/3) = (3/15) + (10/15) = (3 + 10) / 15 = 13/15

So the addition of two or more fractions is performed by finding a common denominator, converting the fractions to equivalent fractions with the common denominator, and then adding the numerators.

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A person who purchases his/her own policy can exclude the benefits from gross income. It's also good to note that statutory limitations exist for the following amounts:

Benefits that have been collected under the employer's plan

Premiums that have been paid by the employer

benefits that have been collected from the individuals' policy. Therefore the amount Valentino may exclude will be calculated as follows;

Daily statutory amount in 2020 (380 * 61)  

= $23180.

Actual cost of care                                    $27816         $23180

Less: Amount received from Medicare                           ($16690)

Equal amount of exclusion                                              ($6490)

Thus:

Valentino must include (30598 - 6490)=$6800 of the long-term care benefits received in his gross income.

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