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By finding a common factor, we can rewrite the expression as:

54 + 72 = 18*(3 + 4)

The distributive property says that we can write:

C*(A + B) = C*A + C*B

In this case, we want to rewrite the expression:

54 + 72

So the first thing we need to find is a common factor between these two numbers.

We can rewrite these as:

54 = 2*3*3*3

72 = 2*2*2*3*3

The maximum common factor between these two nmbers is:

2*3*3 = 18

Then we can rewrite:

54 = 18*3

72 = 18*4

Then we can rewrite the expression as:

54 + 72 = 18*3 + 18*4 = 18*(3 + 4)

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The domain of the given graph is (-∞ < x < ∞)

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

Given is a graph,

For f(x) = x, there is no restriction on x

Both the domain and range are the set of all real numbers.

Hence, The domain will be (-∞ < x < ∞)

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area of n sided polygon  inscribed in a circle is

A = (1/2)nr²sin(360/n)    (r = radius of circle)

A = (1/2)12*8²*sin30

   = 1/2*12*64*1/2

A  = 192  square unit

Answer:

true

Step-by-step explanation:

20 away from nothing is 20

Answer:

Step-by-step explanation:

20-0=20

Example 1: Suppose you have 20 friends and they are given the choice of choosing a sport from cricket or basketball. All of them decide to play cricket and 0 chooses basketball. So, the total number of students who decided cricket is 20 students(20-0=20).

Example 2: Suppose you have 20 chocolates and you give 0 chocolates to your sister then you have a total of 20 chocolates(20-0=20).

Example 3: Suppose there are 20 students in a class and 0 were absent out of them. So, the total number of students that were present are 20 students(20-0=20).

Example 4: Suppose you have 20 clothes in your wardrobe and you gave 0 clothes for washing. So, the total number of clothes in the wardrobe is 20 clothes(20-0=20).

There are 3,024 different ways 1,214 can be shown.

Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given 1,214

since there are 4 places in the digit,

so 4 values less than 10 can be solved by

9, 8, 7, and 6

so by permutation to find ⁹P₄ = 9!/(9 - 4)!

= (9 x 8 x 7 x 6 x5!)/5!

⁹P₄  = 3,024

Hence there are 3,024 different ways.

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Answer:

Step-by-step explanation:

Answer:

I would say (option A)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see that our x-values can be any number. Therefore, we have all real numbers as our domain:

→ A) x < 2.

Hope this helps!

Answer: 70 cm

Step-by-step explanation: perimeter = 2*width + 2*length

408 = 2*width + 2*134

408 = 2*width + 268

Subtract 268 from both sides.

140 = 2*width

DIvide both sides by 2

Width = 70 cm

Answer:

The width of the rectangle is 70 cm

Step-by-step explanation:

Given,

To Find : The width of the rectangle

As we know, the formula to find the Perimeter of the rectangle is

[tex]P = 2(l+b)[/tex]

Now the Perimeter is given and the length

[tex]408 = 2(134 + b)[/tex]

Now using distributive property

[tex]408 = 268 + 2b[/tex]

[tex]408 - 268 = 2b[/tex]

[tex]140 = 2b[/tex]

[tex]\frac{140}{2} = b[/tex]

[tex]70cm = b[/tex]

Hence, the width of the rectangle is 70 cm

Answer:

7 times a number increased by 4 times the number

Let a number and the number be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:

7 times a number: 7x

4 times the number: 4x

The phrase increased by means we add 4x to 7x:

7x + 4x

Simplifying, we get: (7 + 4)x

11x

Step-by-step explanation:

false

it is a decimal not a fraction

According to the Central Angle Theorem, the central angle occupied by two points on a circle will always be twice the inscribed angle occupied by those same two points, therefore ∠ABC = 1/2 × 56 = 28°.

Since subtended and inscribed angles are mentioned in the definition, we must first understand them in order to understand the central angle theorem. An object at a specific outer position forms an angle known as a subtended angle.

If you disagree with that definition, think about this: On Earth, you are standing and gazing up at the sun. A triangle with three sides is created. The sun's height, the sun ray that travels from the bottom of the sun to your eyes, and these three directions are the three sides of the sun.

The Central Angle Theorem states that the central angle occupied by two points on a circle is always twice the inscribed angle occupied by those same two points.

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Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

The expression 6² - 2(5 + 1 + 3) after evaluation gives 18.

BODMAS rule is rule for operation of numbers in a specific order when more than one type of operations is involved.

BODMAS is the abbreviated form for Brackets, Order including powers and exponents, Division, Multiplication, Addition and Subtraction.

Given expression is, 6² - 2(5 + 1 + 3).

First we should do the operation in brackets.

6² - 2(5 + 1 + 3) = 6² - 2 (9)

Now we should do the power operations.

6² - 2 (9) = 36 - 2 × 9

Now we do multiplication.

36 - 2 × 9 = 36 - 18

Now we do subtraction.

36 - 18 = 18

Hence the answer of the expression given is 18.

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A recipe for a mixture that will make the same shade of green but a larger amount is =4 Cups of Yellow + 7 Cups of Blue

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

A shade of green paint is made by mixing `2` cups of yellow with `3.5` cups of blue.

Now,

2 Cups of Yellow + 3.5 Cups of blue

Multiply all by 2

=4 Cups of Yellow + 7 Cups of Blue

Hence,  a recipe for a mixture that will make the same shade of green but a larger amount is =4 Cups of Yellow + 7 Cups of Blue

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The rectangle that has side lengths of 7 units and 8 units is (a) a rectangle that has an area of 56 square units

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

Side lengths of 7 units and 8 units

These parameters can be represented as

Length = 7 units

Width = 8 units

Using the options in the question as a guide, we have the following computations

We start by calculating the area of the rectangle

The area of the rectangle can be calculated using the following area formula

Area = length * width

Substitute the known values in the above equation, so, we have the following representation

Area = 7 * 8

Evaluate

Area = 56

Hence, the rectangle is (a)

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Complete question

Which rectangle has side lengths of 7 units and 8 units?

(a) a rectangle that has an area of 56 square units

(b) a rectangle that has a perimeter of 56 square units

(c) a rectangle that has an area of 65 square units

(b) a rectangle that has a perimeter of 6 units

=======================================================

Explanation:

1 balloon = 0.7 ft^3 of helium

200 balloons = 200*0.7 = 140 ft^3 of helium

Katerina needs 140 cubic feet of helium to fill all 200 balloons.

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

1m^3 = 35ft^3 which is approximate

0.2 m^3 = 0.2*35 = 7 ft^3

Each canister holds approximately 7 cubic feet of helium.

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

To summarize so far.

Let x be the number of canisters. Because of fact 2 mentioned above, 7x represents the total amount of helium from all of the x number of canisters.

Set this equal to the amount she needs (140) and solve for x.

7x = 140

x = 140/7

x = 20

Katerina needs 20 canisters.

The volume of each drinking cup is 7.9 cubic inches.

An office uses paper drinking cups in the shape of a cone, with dimensions as shown.

The formula provides the volume of a cone.

V =  (1/3) * π * r² * h.

We can find the solution by entering the already-known data into the formula.

d = 2.75 m.

Since radius is half of d, we can say

0.5 * 2.75 = 1.375 in.

4 inches is listed as the height.

The result of plugging all of them into the original formula is:

V = (1/3) * π(1.375)² (4) = 7.9

Our final response, rounded to the closest tenth, is:

V = 7.9 cubic inches.

The volume of each drinking cup is 7.9 cubic inches.

The complete question is An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the volume of each drinking cup?

d = 2.75 m.

h = 4

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Answer:

c.

Step-by-step explanation:

First at all you need the half circle area formula:

(Pi*r2)/2 = 18Pi

After resolved this you have: r = 6, then diameter= 12

Then c) Its perimer is 40 because AB + CD + BC + AD = 40

The correct answer in the number line is 2 and 0.888 .

A picture of numbers on a straight line is referred to as a number line in mathematics. Across the length of a number line, the numbers are arranged in a sequential manner at equal intervals. It is frequently seen horizontally and can extend indefinitely in any direction.

The addition, subtraction, division, and times table problems can all be illustrated with a number line. You can better comprehend the idea of negative numbers by using the number line.

The addition, subtraction, division, and times table problems can all be illustrated with a number line. You can better comprehend the idea of negative numbers by using the number line.

1. 9/2 in 2

2.4/9 by 2 is = 4/4.5 = 0.888 .

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After completing the square, the solution of equation are,

⇒ x = (2 + √2i)

And, x = 2 - √2i

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ x² - 4x + 6 = 0

Completing the square as;

⇒ x² - 4x + 6 = 0

⇒ x² - 4x + 4 + 2 = 0

⇒ (x - 2)² + 2 = 0

⇒ (x - 2)² - (√2i)² = 0

⇒ (x - 2 - √2i) (x - 2 + √2i) = 0

This gives two complex solution as;

⇒ x = (2 + √2i)

And, x = 2 - √2i

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Answer:

14

Step-by-step explanation:

5 quarts = 10 pints

10 pints + 4 pints = 14 pints

Using the pythagoras theorem in the given figure, the required length of c is [tex]49\sqrt{6}[/tex].

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean Theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides.

The pythagoras theorem is named after the Greek mathematician-philosopher Pythagoras.

To solve for c, first taking the small triangle in the left of the figure,

since one of the angle is 45 degree and another is 90 degree, the unlabelled angle is 45 degree. Which makes this triangle a isosceles triangle, hence the sides a and b are equal in length. i.e a = b

Using pythagoras theorem in this triangle,

[tex](7\sqrt{2} )^{2} = \sqrt{a^{2}+\ a^{2} }[/tex]

Therefore, a = 49[tex]\sqrt{2}[/tex]

Now Taking the small triangle in the right of the given figure,

tan 30 = a/c

or, [tex]\frac{1}{\sqrt{3} }[/tex] *c = 49[tex]\sqrt{2}[/tex]

Therefore , c = 49[tex]\sqrt{6}[/tex]

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Answer:16

Step-by-step explanation: If henry hits 80% of pitches, then the easiest way is to make 80% of 10, which is half of 20, is 8. So if it is 20 times he is up to bat, then 8*2, 2*8 is 16, so he hits the ball 16 times.

Answer:

A.

domestic: 316 / 96 / 412

international: 76 / 51 / 127

total: 392 / 147 / 539

B. 51 its the smallest number

C. I don't know what association means but 76.2% of domestic flights land on time and 63% of international flights land on time so id say its positive

The market research department of a Company recommends that the Company to manufacture and market a new transistor radio after suitable test. The marginal cost of the company is 7000 - 2X  and marginal revenue is 10X - X/250.

Marginal cost is an extra cost per unit incurred when an extra unit of output produced or service rendered. Or in other words it can be said that marginal cost is an element of additional unit cost that incurred due to production of goods or services. Some time it is also considering as relevant cost or variable cost.

So in order to compute the transistor manufacturing company's marginal cost, marginal revenue and marginal profit of the company one shall equated the derivative function between them.

In micro economics technical relationship between the said marginal terms is written through derivative function:

Revenue = Price × Quantity Demanded,

Profit Maximize Point where Marginal cost is equal to marginal revenue;

MR = MC,

The marketing department also presents the following demand equation:

X = 5,000 - 500 P

P = 10 - (X ÷ 500), where P is Price and X is quantity demand.

Furthermore, the financial department provides the following cost equation:​

C(X) = 7, 000 + 2x

So the revenue function by the help of substitution method:

X = 5,000 - 500 P

Revenue = Price × Quantity Demanded,

Revenue =  10 - (X ÷ 500) × X

               =  10X - X^2 ÷ 500

Marginal Revenue! = 10X - !2X/500 = 10X - X/250

Marginal Cost =  7, 000 + 2 (5,000 - 500 P)

= 7000 + 10000 - 1000 P

= 17000 - 1000 ( 10 - (X ÷ 500))

= 17000 - 10000 - 2X

= 7000 - 2X

Therefore marginal revenue is revenue or additional earning made by a seller by selling an extra unit. Revenue is earned when extra unit is being sold.

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The linear function q(x) = -3x + 1 is graphed and attached

The graph of the linear function is a straight line graph and the table of values used in making the plot is calculated as follows

For x = -20,  q(x) = -3 * -20 + 1 = 61

For x = -10,  q(x) = -3 * -10 + 1 = 31

For x = 0,  q(x) = -3 * 0 + 1 = 1

For x = 10,  q(x) = -3 * 10 + 1 = -29

For x = 20,  q(x) = -3 * 20 + 1 = -59

Table of values

x     y

-20  61

-10    31

0      1

10     -29

20    -59

These points are plotted in the cartesian coordinate by tracing the point of intersection of the x and y and marking it. Then the marked points are joined together to form a straight line

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will she have enough time for 12 slides?  we dunno, but we know it takes 1/6 hour to make one hmmm for 12 slides that'd be simply their product

[tex]\stackrel{slides}{12}\cdot \stackrel{\textit{it takes one}}{\cfrac{1}{6}}\implies \cfrac{12}{6}\implies 2~hours\qquad \textit{yeap, she has enough time}[/tex]

she even has an extra 30 minutes to check out what's for dinner.

Tee welding joints are formed when two members intersect at a 90-degree angle that makes the edges come together in the center of a plate or component

Answer: 0.071%

Step-by-step explanation:

To get from $3.50 - $3.75, there was an increase of $0.25.

(Sorry if I'm getting the currency bit wrong, I'm British.)

Divide 0.25 by the original cost of 3.50, and you get:

0.07142857142857142857142857142857

Round this and you get a 0.071% increase

Answer:

The percent change in the price of a gallon of gas is 0.0714%.

Step-by-step explanation:

Here, The price increased from $3.50 to $3.75, a change of $0.25.

So,

$0.25 ÷ $3.50 × 100% = 0.0714%

Thus, The percent change in the price of a gallon of gas is 0.0714%.