How much are you paying in tax on a $95 skateboard if the sales tax is 6%? (Just the tax amount!)

By dividing any number 3 to simplify the expression.

What is simplifying an expression?

To simplify an expression, create a similar expression devoid of any similar terms. Therefore, we will rewrite the expression using the fewest number of terms possible.

When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

One third is one part of three equal parts. When you split an object or number into thirds, you divide it by three.

Thirds are calculated by dividing by 3.

For example: One third of 24 =1/3 of 24 = 24/3 = 8.

Hence, by dividing any number 3 to simplify the expression.

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The prime factorization of 60 from smallest to largest is  2×2×3×5.

Prime factorization is the technique of expressing a number as the product of prime numbers. The only two components in prime numbers are the number itself and the number itself. Prime numbers include, for instance, 2, 3, 5, 7, 11, 13, 17, 19, and so forth. Any number can be represented as a sum of prime numbers using prime factorization.

The prime factorization of the number 60 is,

60 = 6×10.

60 = 2×3×2×5.

60 = 2×2×3×5.

60 = 2²×3×5.

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The value of a base refers to the number that is used as the foundation or foundation number in a mathematical system or system of numbers. A base is typically represented by a number that is used to indicate the power or exponent to which it is raised in order to produce a certain value.

The number of base is the number of different digits or symbols that are used in a particular mathematical system or system of numbers. For example, in the decimal (base 10) system, there are 10 different digits (0–9) that are used to represent different values. In the binary (base 2) system, there are only two different digits (0 and 1) that are used to represent different values. The number of the base can also be referred to as the radix of a number system.

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When y changes directly as x, the variation constant is 5/4.

In a direct variation, the ratio of two variables; in an inverse variation, the product of two variables. The constant of variation k is used in the direct variation equations = k and y = kx, as well as the inverse variation equations xy = k and y =. A constant of variation (k) is a ratio that shows the connection between the independent and dependent variables (x and y) (y). If both variables have known values, it may be determined by dividing y by x. The constant of variation is the number that connects two variables that are either directly or inversely proportional to each other.

Here,

When one thing varies to another there is always a constant of variation. direct variation it is; y = kx

use the x,y values to find k

5 = 4k

5/4 = k

The constant of variation when y varies directly as x is 5/4.

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Answer:

  6 units

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with legs 5 and √11.

The Pythagorean theorem tells you the relation between the legs a, b, and the hypotenuse c of a right triangle is ...

  c² = a² +b²

  c² = 5² +(√11)²

  c² = 25 +11 = 36

  c = √36 = 6

The length of the third side is 6 units.

Answer:

y=x-4

Step-by-step explanation:

y=mx+b

Answer: y=x-4

Step-by-step explanation:

The first step is to see what point runs through the y-axis, so you can get your y-intercept. The line runs through (0, -4), so -4 will be your y-intercept.

To calculate the slope, we can use the formula, y2-y1/x2-x1 to find the slope. We have to take two definite points to solve this. an example of two definite points is (1, -3), and (0,-4). So the change in y would be              -4-(-3), which is -1, and for the change in x, 0-1 is -1 (Think of (1,-3) as point one, and (0,-4) as point 2). SO -1/-1 is 1, making the slope 1, making the equation y=x-4

Answer: 10

Step-by-step explanation:

5x2 = 10

Answer:

10 lol.....................

The cost of Lisa food is 32 dollars.

Lisa ordered food from a delivery service. She tipped the driver $4.80. This was 15% of the total cost of her food. The cost of her food can be calculated as follows:

Therefore,

let

x = cost of her food

Hence,

15% of x = 4.80

15 / 100 × x = 4.80

0.15x = 4.80

divide both sides by 0.15

Hence,

x = 4.80 / 0.15

x = 32 dollars

Therefore,

cost of food = 32 dollars.

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Answer: The expression (p^20)(p^-4)^2 is equivalent to p^n, where n is the power of p in the simplified expression.

To simplify the expression, we need to use the rule of exponents which states that when multiplying two powers of the same base, we can add their exponents.

So, (p^20)(p^-4)^2 = p^20 * (p^(-4))^2 = p^20 * p^(-8) = p^(20+(-8)) = p^12

So the value of n is 12.

Step-by-step explanation:

An isosceles right triangle is a special type of triangle that has two equal sides and one right angle.

It can be described using the Pythagorean Theorem, which states that the sum of the squares of the two legs of a right triangle are equal to the square of the hypotenuse. Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs, and c is the length of the hypotenuse.

In an isosceles right triangle, two of the sides must be equal, so a=b. This means that the Pythagorean Theorem simplifies to 2a^2 = c^2. Solving for a gives a = sqrt(c^2/2). This is the formula for the sides of an isosceles right triangle.

As an example, consider a triangle with a hypotenuse of length 5. Substituting this into the formula gives a = sqrt(25/2), or a = 5/sqrt(2). This means that both of the legs of the triangle have length 5/sqrt(2).

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You can conclude that it took you less time on Tuesday to run to and from the playground than it did on Monday.

Distance is defined as the product of speed and time.

To compare the times it took to go to and from the playground each day, you need to calculate the total time for each day.

On Monday, it took 22 minutes to run to the playground and 25 minutes to run back home, for a total time of 47 minutes.

On Tuesday, you ran the entire 4 1/2 miles at a constant speed of 6 1/4 miles per hour, so you can use the formula:

distance / speed = time.

In this case, 4.5 miles / 6.25 mph = 0.72 hours or 43.2 minutes.

Therefore, you can see that it took you 47 minutes on Monday, and 43.2 minutes on Tuesday to run to and from the playground.

Hence, you can conclude that running to and from the playground took you less time on Tuesday than it did on Monday.

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We checked the equation of lines are not parallel to each other.

The two lines when located at the same plane and equidistance from each other are called parallel lines. The properties of parallel lines as shown in equation is that both have same slope but different y intercept.

Two parallel lines never intersect.

equation of line passes through the point (- 3, -3) and (3, 9)

is given by the formula [ y - y₁] = [(y₂- y₁) / (x₂- x₁)] [x - x₁}

                                      [ y- (-3)] = [9 - (-3) / 3- (-3)] [x - (-3)]

                                 (y +3) = [(9+3)/ (3+3)] (x+3)

                                  y+ 3 = 12/ 6 (x+3)

                                  y+3 = 2 (x+3)

                                   y+3 = 2x+6

                                   y = 2x+3 this is the first line.

equation of line passes through (-5, 12) and (1, 0)

                          [y - 12] = [(0 - 12) / 1 - (-5)] [x - (-5)]

                       y -12 = -12/ 6 (x+5)

                         y - 12 = -2 x - 10

                        y = - 2x + 2

the above is the equation of second line.

the above two equation have same slope but different sign. Hence, the lines are not parallel to each other.

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The zeros of the function y = 2x²+7x+1 are -0.35 and -3.35

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.The zeros are often called the roots, solutions, or x-intercepts of the function.

Therefore when y = 0

2x²+7x+1 = 0

using formula method

a= 2, b= 7 and c = 1

x = (-b ± √b²-4ac )/2a

x= -7± √ -7²-4×2×1)/2×2

x= (-7± √ 49-8)/4

x= (-7± √41)/4

x= (-7+√41)/4 or (-7-√41)/4

x =( -7+6.4)/4

or (-7-6.4)/4

x = -1.4/4 or -13.4/4

x = -0.35 or -3.35

therefore the zeros of the function are -0.35 and -3.35

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The set of points that represents a relation and a function are given as follows:

A relation represents a function when each input value is mapped to a single output value.

Hence the desired relations are given as follows:

As they both have different inputs, hence each input is mapped to a single output and they are functions.

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The inequality can be simplified into a compound inequality:

x > 2.43

x < -16.7

Here we want to solve the following inequality:

|0.7*x + 5| > 6.7

To solve it, we need to isolate the variable x. The first thing we need to do is "break" the absolute value part, then we will get a compound inequality.

0.7*x + 5 > 6.7

0.7*x + 5 < -6.7

Now we can isolate x in both of these inequalities:

0.7*x > 6.7 - 5

0.7*x < -6.7 - 5

0.7*x > 1.7

0.7*x < -11.7

x > 1.7/0.7

x < -11.7/0.7

x > 2.43

x < -16.7

That is the solution of the inequality.

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The meaning of 2n in mathematics is just a simple series that gives us different values when we put the integral values of n.

Oftentimes we come across a special series in the mathematical problems.

This mathematical series can be simplified into a quite simpler and a shorter form.

The given form 2n is also nothing but just yet another example of the mathematical series.

When we put the values of end to be 1,2,3,4,5,6,7,8...

We get the values of the expression to be 2,4,6,8,10...

This mathematical series makes problem easier for us understand and solve.

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On solving the provided question, we can say that equality of given trapezium we find, y=13/10 and x=21

A convex quadrilateral with exactly one pair of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices.

Since ABCD~PQRS

then, on comparing

5y-3/4 = 7/8

y=13/10

On comparing angle,

3x+24=87°

3x=63°

x=21

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The expression that should be subtracted is 4x² - 3y² - xy.

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

We will be using the concept of addition and subtraction of algebraic expressions to solve the given question.

Let us assume the missing part is X.

Therefore according to the question,

(3x² - 4y² + 5xy + 20) - (X) =  - x² - y² + 6xy + 20

Let us shift the terms to find the value of X

X = 3x² - 4y² + 5xy + 20 - (- x² - y² + 6xy + 20)

X = 3x² - 4y² + 5xy + 20 + x² + y²- 6xy - 20

X = 4x² - 3y² - xy

Thus, the expression that should be subtracted is 4x² - 3y² - xy.

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Answer:

The answer would be 3x/8.

Step-by-step explanation:

Both fractions would need to have a common denominator, so you could multiply x/2 by 4 on both the top and bottom to get 4x/8.

You could then subtract both the numerators from each other.

4x-x=x

The denominator will stay the same.

X/8.

The perimeter of the parallelogram is 16x - 8

The properties of a parallelogram are;

The formula for perimeter of a parallelogram is;

Perimeter = 2(a + b)

substitute the values

Perimeter = 2(6x - 4 + 2x)

collect like terms

Perimeter = 2(8x - 4)

expand the bracket

Perimeter = 16x - 8

Hence, the value is  16x - 8

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Answer:  

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is a variable.

The equations that are quadratic equations are:

(i) x^ 2 + 6 x − 4 = 0

(v) 2 x^ 2 − √ 3 x + 9 = 0

The equations that are not quadratic equations are:

(ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0

(iii) x^ 2 + 1/ x^ 2 = 5

(iv) x − 3/ x = x ^ 2

(vi) x ^ 2 − 2 x − √ x − 5 = 0

(vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3

(viii) x + 1 x = 1

In (ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0 the coefficient of x^2 is not a real number.

In (iii) x^ 2 + 1/ x^ 2 = 5 the equation is not in the form of ax^2 + bx + c = 0

In (iv) x − 3/ x = x ^ 2 the equation is not in the form of ax^2 + bx + c = 0

In (vi) x ^ 2 − 2 x − √ x − 5 = 0 the equation is not in the form of ax^2 + bx + c = 0

In (vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3 both sides are not equal

In (viii) x + 1 x = 1 the equation is not in the form of ax^2 + bx + c = 0

So, the equations that are quadratic equations are (i) and (v).

Step-by-step explanation:

Using division we know that each job site will receive 458 sand bags.

Multiplication is the opposite of division.

If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

So, we know that:

Number of bags: 10992

Bags to be distributed are 24 jobs.

Now, to know the number of bags each job site will receive:

10992/24

458

Therefore, using division we know that each job site will receive 458 sand bags.

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Answer:

[C] 3 3/4 Miles

Step-by-step explanation:

Given:

Zoe jogs 3/4 of a mile every 1/5 of an hour.

How many miles does Zoe jog per hour?

[A] 3/20 Miles

[B] 4/15 Miles

[C] 3 3/4 Miles

[D] 6 2/3 Miles

Solve:

Since, Zoe jogs 3/4 of a mile every 1/5 hour. And 5/5 = 1 hour.(Also known as 60 minutes) Which means 1/5 is 12 minutes. In order to find how much Zoe jogs per hour, we have to multiply.

Knowing that;

1/5 = 12 minutes

2/5 = 24 minutes

3/5 = 36 minutes

4/5 = 48 minutes

5/5 = 60 minutes (1 Hour)

Hence, 3/4 Multiply by 5.

3/4 × 5 = 3.75 = 15/4 = 3 3/4

As a result, Zoe jogs 3 3/4 miles per hour.

RevyBreeze

Answer:

The expression p + 0.08p can be interpreted as "p plus 8% of p". Mathematically, this expression is equal to 1.08p, which is the same as saying "p multiplied by 1.08".

Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.

given

1. percentage

p = base x rate

= 80 x 85%

= 68

2. percentage

= 70 x 45%

= 31.50

3. base

b = percentage ÷ rate

= 7 ÷ 35%

= 20

4. base

= 660 ÷ 110%

= 600

5. base

= 120 ÷ 80%

= 150

6. base

= 125 ÷ 250%

= 50

7. rate

= 64 ÷ 16 x 100

= 400%

8. rate

= 85 ÷ 340 x 100

= 25%

9. base

= 13 ÷ 26%

= 50

10. base

= 2.5 ÷ 0.5%

= 500

Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.

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The total perimeter of fencing that is needed for the entire animal pen is equal to 48 feet.

In order to determine the feet of fencing that is needed for the entire animal pen, we would have to calculate the third side of this right triangle pen by applying Pythagorean's theorem:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right triangle.

16² + b² = 20²

b² = 400 - 256

b = √144

b = 12 feet.

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

Perimeter of a triangle = a + b + c

Where:

a, b, and c represents the length of sides of a triangle.

Perimeter of a triangle = 16 + 20 + 12

Perimeter of a triangle = 48 feet.

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Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: 11

Step-by-step explanation:

Let the number be N.

Let's set up the equation.

2N + 15 = 37

Let's subtract 15 from both sides.

2N = 22

Divide both sides by 2, and you get

N = 11

Final Answer : 11

Answer: Your answer would be 152 cm

Step-by-step explanation:

Outer part of the shape:

Length  =  18 cm  

width  =  12 cm

Area of large rectangle  =  (18 ⋅ 12)

=  216 cm2------(1)

Inner part of shape:

Length  =  6 cm

width  =  3 cm

Area of small rectangle  =  (8 ⋅ 8)

=  64 cm2------(2)

(1) – (2)

=  (216 – 164) cm2

=   154 cm2

I hope this helps!