Simplify using the laws of exponents. Leave your answer an exponential form. The box is to type in the exponent.

Answer:

57.97 cm²

Step-by-step explanation:

Use the formula for area of a trapezoid

[tex]A = \dfrac{a + b}{2} h\\\\[/tex]

where a and b are the two sides and h is the height

Here a = 7.8, b = 10.8, h = 6.2

Substituting we get
[tex]A = \dfrac{7.9 + 10.8}{2} \times 6.2\\\\A = (7.9 + 10.8) \times \dfrac{6.2}{2}\\\\\\7.9 + 10. 8 = 18.7\\\\\dfrac{6.2}{2} = 3.1\\\\\\A = 18.7 \times 3.1 = 57.97\; cm^2[/tex]

Answer:

55.17

Step-by-step explanation:

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

The common factor of the equation [tex]x^{4}y^{2} -6x^{3}y^{3}[/tex] is [tex]x^{2}y^{2} (x^{2}-6xy)[/tex].

What is a common factor?

A whole number that is a factor of two or more numbers is referred to as a common factor.

The largest factor that will split into two or more integers is known as the highest common factor (HCF).

The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).

The LCM and HCF

when a fraction is added or subtracted.

can be discovered by listing multiple factors. It is more effective to express greater values of a number as the product of prime factors. The Venn diagram is another option.

In finding common factors, the HCF, and LCM need knowledge of how to identify factors, build factor trees, and express integers as the product of their prime factors.

How to locate common factors?

A whole number that is a factor of two or more numbers is referred to as a common factor. Example: The common factors of 30 and 20 are 2, 5, and 10.

A factor that all whole integers share is 1, or 1.

To identify commonalities:

List each number's factors.

To identify the numbers that are the same (or frequent) in both lists, compare the factors.

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Answer

Length of the rectangle = 26 inches

Explanation

Let the length of a rectangle be L

Let the width of the rectangle be W

The length of the rectangle is 3 more than the width.

L = W + 3

But we are provided with the perimeter of the rectangle.

The perimeter of a figure is the sum of the dimensions of its exterior.

For a rectangle,

Perimeter = 2 (L + W)

For this question,

Perimeter = 98 inches

L = W + 3

W = ?

Perimeter = 2 (L + W)

98 = 2 (W + 3 + W)

98 = 2 (2W + 3)

98 = 4W + 6

4W + 6 = 98

4W = 98 - 6

4W = 92

Divide both sides by 4

(4W/4) = (92/4)

W = 23 inches

L = W + 3 = 23 + 3 = 26 inches

Hope this Helps!!!

Answer:

P' = (5, 3)  K'= (3,1) and Y'= (1, 4)

Step-by-step explanation:

We currently have the following coördinates:

P = (-5, -3), K = (-3, -1), Y = (-1, -4)

A rotation of 180 degrees (precesily a half turn!) will give us:

P' = (5, 3)  K'= (3,1) and Y'= (1, 4)

You can draw a line from K to the origin and extend this line precisely the same distance as from K to the origin. This line will end and the point (3,1). The same method can be used for the other two points.

Answer:

A,B,C is the answer

e

You have the following equation:

if you divide by 6 both sides, you obtain:

the slope of the previous line is m = 1/6.

Take into accout that the relation between the slopes of two perpendicular lines is given by:

For the required perpendicular line you have:

Now, use the following general equation for a line:

where (xo,yo) is any point on the line.

Replace (xo,yo) = (3,5) and m' = -6 into the previous formula and solve for y:

Hence, the equation of the perpendicular line is, in intercept slope form:

y = -6x + 23

The domain x with the value of 5 according to the table has a range value of -8.

A. -8

Given data:

The first number is -4.

The second number is 4.

Positive number is always bigger than negative number.

Thus, 4 is bigger than -4.

To make a+b= 0

Since b is positive ( to the right of zero), a must be positive and must be have the same distance from 0.

So:

Answer

Step-by-step explanation

Data is collected from 100 students on whether they walk or bike to school and whether they live more than a mile from school or not is shown in a table.

1 mile or not

Ways Yes No Total

Work 10 31 41

Bike 32 27 59

Total 42 58 100

The question then asks us to examine four options, to obtain the one(s) that are correct.

First Option

Of the students who live more than one mile away, about

8[tex]\frac{2}{9}[/tex] as improper fraction is [tex]\frac{74}{9}[/tex]

A fraction that has the numerator higher than or equal to the denominator is said to be improper. A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate. 4/3, 7/3, 11/5, and other incorrect fractions are a few instances. In fact, using improper fractions in mathematics is simpler than using mixed fractions. However, mixed numbers are easier for individuals to understand in daily life. It is crucial that you understand how to change from one form to another.

Given,

Mixed Fraction

8[tex]\frac{2}{9}[/tex]

Improper fraction:

[tex]\frac{8(9) +2}{9}[/tex]

[tex]\frac{72 +2}{9}[/tex]

[tex]\frac{74}{9}[/tex]

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SOLUTION

The standard quantity of water is 2000 liters

The quantity of water in the pool is 10,000

Since 3 chlorine is added to every 2000 liters of water then the number of chlorine added to 10000 liters of water is:

Since 8 tablets is added instead of 15 then:

The park pool has less chlorine than the safety standards require

Answer:

It depends on what the question is.

Step-by-step explanation:

Your question is unclear.

If the question is the fraction 0/03, then that equals 0, but that is not a choice.

If the question is 0.03, then the answer is 3/100.

If the question is 0.03030303... (repeating 03, then the answer is worked out below.

Let x = 0.030303...

    100x = 3.0303030...

-         x = 0.0303030...

---------------------------------

     99x = 3

x = 3/99

x = 1/33

The decimal number is given 16.837

Convert into fractional form by removing the decimal from the given number.

Hence the fractional notation determined is

SOLUTION:

Step 1:

In this question, we are given the following:

Find the equation of the line through the point (10,-6) that is perpendicular to the line with equation

-11x-18y=-2070

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

Answer: 19

Step-by-step explanation:

To find an average, you take each of your values, add them, and then divide by the numbers of values you have. There were 8 students interviewed, so your total numbers of values is 8.

Addition: 16 + 14 + 20 + 18 + 16 + 31 + 13 + 24 = 152

Division: 152 ÷ 8 = 19

Answer:

a=1,b=-3,c=2

Explanation:

The standard form of a quadratic equation is given as:

Comparing with the equation:

We observe that the equation is already in the standard form.

Furthermore:

Given:

Principal P (Initial amount) =$5100

Rate(R)= 2.75

Time(t) = 16 months = 16/12 ( In years)

We can proceed to calculate the interest using the formula below:

The amount he has for the investement = 5100 + 187 = $5287

The median of the given data would be 2.35 meters.

The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.

The given set of data as:

{2.1, 2.5, 2.2, 2.4, 2.2, 2.7, 2.4, 2.3, 1.9, 2.6}

Arrange the data in ascending order.

1.9, 2.1, 2.2, 2.2, 2.3, 2.4, 2.4, 2.5, 2.6, 2.7

Since the number of elements in the data set is 10.

Median = [(n/2)th term + ((n/2) + 1)th term]/2

Median = [(10/2)th term + ((10/2) + 1)th term]/2

Median = [5th term + 6th term]/2

Median = [2.3 + 2.4]/2

Median = 4.7/2

Median = 2.35

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The value of x would be 70° which is the correct answer would be an option (C).

Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.

To determine the measure of an Exterior angle of a polygon:

First, we have to find the measure of the supplemental interior angle

Then write the equation: Int. + ext. = 180

Here take an interior angle = 93°, find its Exterior angle

⇒  93 + ext. = 180 ⇒  ext. = 180 - 93 = 87°

Since the sum of all exterior angles of a convex polygon = 360°

As per the given figure,

⇒ x° + 52° + 87° + (x+3)° + 78° = 360°

Combine the likewise terms to get,

⇒ 2x + 220 = 360

⇒ 2x = 360 - 220

⇒ 2x = 140

⇒ x = 70

Therefore, the value of x would be 70°.

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Answer:

Explanation:

Given the equation:

The percent of increase between the average low and high temperatures

in July would be = 26°F

Temperature range is defined as the difference between the degree of hotness and coldness of two different places.

The average daily high temperature of the month = 90°F

The average daily low temperature of the month = 69°F

The temperature difference between the two ranges = 90 -69 = 21°F

When both temperature are compared = 90+69/2 = 159/2 = 79.5°F

The percent increase of daily low temperature;

= 21/79.5 × 100/1

= 2100/79.5

= 26.4

= 26°F ( nearest to the tenth place)

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Let's begin by listing out the information given to us:

In transversal lines, All angles are equal and parallel, so  TV ║ WY  are    parallel lines .                                      

What are transversal lines?

∠TUX  ≅  ∠UXY               ( Alternate angle)

∠SUV ≅  ∠TUX                 ( Vertically angle)

∠UXY ≅  ∠SUV                  ( Interior angle )

 TV ║ WY                          ( All angles are equal and parallel, so  TV ║ WY                                        

                                              are    parallel lines .

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It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. The  answer will be 4.4.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

At a fundamental level, the process of counting how many times one number is included within another is referred to as the division of two natural numbers. This number of times need not be integer. For instance, if 20 apples are distributed equally among 4 persons, each person will get 5 apples.

When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.

It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. In these expanded number systems, division operates in the opposite direction as multiplication, i.e., a = c / b implies that, if b is not zero, a b = c. This is a division by zero, which is not defined, if b = 0. In the case of the twenty-one apples, there would be no leftovers because each person would get five apples and a quarter of an apple.

Different algebraic structures, or ways of defining mathematical structure, use both modes of division. These are known as Euclidean domains and contain polynomial rings in one indeterminate space where a Euclidean division (with remainder) is defined (which define multiplication and addition over single-variabled formulas). Fields and division rings are those where a division (with a single result) by all nonzero elements is defined. The elements in a ring by which division is always feasible are known as the units; in the ring of integers, this would be 1 and 1. The quotient group is another way to apply division to algebraic structures; in this case, the outcome of "division" is a group rather than a number.

Just divide 3.96 by 0.9

[tex]\frac{3.96}{0.9}[/tex]= 4.4

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Using a system of inequalities, it is found that:

The variables to the system of inequalities are given as follows:

At least 6 units of protein are needed, hence, considering the amount of protein or each snack, the inequality is:

3y ≥ 6

y ≥ 2.

At least 10 units of carbohydrates are needed, hence, considering the amount of carbohydrates of each snack, the inequality is:

3x + 2y ≥ 10.

At least 16 units of fat are needed, hence, considering the amount of fats of each snack, the inequality is:

2x + 4y ≥ 16

x + 2y ≥ 8.

Hence the system is:

Each ounce of fruit contains 40 calories, and each ounce of nuts contains 50 calories, hence the calories function is:

Calories function = 40x + 50y.

Possible solutions to the system, containing only integers, as units is an integer amount, and their calorie consumption are:

Hence the quantities with the least calories are: 2 ounces of fruit and 3 ounces of nuts, with a calorie load of 230 calories.

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Step 1:

Concept

To find out if Miles has enough shoeboxes to fit all 327 of his action figures, we first need to find the amount of action figures his current amount of shoeboxes can store. We can do this by multiplying the amount of shoeboxes Miles has by the amount of action figures each shoebox can hold.

Step 2:

Shoe boxes can contain 80

Total = 4 x 80 = 320

Step 3

There will be 7 left

Left over = 7

Base salary = $200 per week

Commission = 10% of total sales for that week

In a certain week, he makes sale of = $750

So, commission for that week = 10% of $750 = 10/100 x $750 = $75

In that particular week, Marques earned = base salary + commission = $200 + $75 = $275

For a week, in which he makes x dollars in sales,

Commission = 10% of x = 10/100 x (x) = $x/10

Total earning for that week = base salary + commission = $200 + $x/10

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