What is the slope of a horizontal line? Write the equation of an example of a horizontal line.

Answer:

Step-by-step explanation:

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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Answer:

19

Step-by-step explanation:

Karen and Kate have 50 CDs between them. Karen has 6 less than kate. How many each has?

25&25  

If Karen Has 6 Less Then Kate, Karen Would Have 19 CDS

Hope This Helps

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

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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1. The number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is 4.

2. An expression representing the miles driven on each day of the road trip and a final simplified expression of the total drives in three days are as follows:

a) Day 1: x

b) Day 2: 2x + 10

c) Day 3: x - 100

d) Final simplified expression to represent total miles driven in three days: 4x + 10 - 100.

e) A real-world situation in which order matters when writing the expression x - 100 is that the value of x is supposed to be more than the value of 100.

A mathematical expression is the combination of constants, numbers, mathematical operators, and variables without the equation sign (=).

Literarily, a mathematical expression is like a phrase in the English language because it does not make complete sense without the equation sign.

1) Multiplication:

(20x + 24) ÷ (5x + 6) = 4

Check:

4(5x + 6) = 20x + 24

2) Road Trip Expressions:

Day one driving distance = x miles

Day two driving distance = 2x + 10

Day three driving distance = x - 100

Total distance = x + 2x + 10 + x - 100

= 4x + 10 - 100

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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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On solving the provided question, we can say  that -  the linear equations, is [tex]x =10 / 5 = 2 = > x=2[/tex]

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

Here,

to solve the system of equations given. .

[tex]2x + y = 4 \\+\\3x - y = 6\\= > 5x =10[/tex]

system of equations  2x + y = 4  ,

6=3x-y is 5x =10

The value of x :

[tex]x =10 / 5 = 2\\ x=2[/tex]

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Answer:

x= -4/19

Step-by-step explanation:

19x+4

19x+4=0

19x= - 4

x= -4/19

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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Answer:

30 quarts= 0.8057 bushels

rounded to the nearest hundredths = 0.81

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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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

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%.

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

The representation of the set builder notations are:

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

The set builder notations

Solving: set builder notation 1

This is given as

{y | 22.3 < y ≤ 77.5}

The less than (<) operator means that the smallest value of y is greater than 22.3 and the operator ≤ means that the highest is 77.5

Solving: set builder notation 2

This is given as

{w | w ∈ Z}

The notation Z means integers

This means that the set w is the set of all integers

Solving: set builder notation 3

This is given as

{x | x > -1}

The greater than (>) operator means that the smallest value of y is greater than -1

Solving: set builder notation 4

This is given as

{t | t ∈ Q}

The notation Q means rational numbers

This means that the set t is the set of all rational numbers

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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:

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: To solve this problem, we can use the information provided to set up and solve an equation. Let x be the number of countries that participated in the 1896 Olympic games.

According to the problem, we know that the number of countries in the 2004 Olympic games was more than 14 times the number of countries in the 1896 games. So we can write the following equation:

x * 14 < 202

To solve for x, we can divide both sides of the inequality by 14:

x < 202/14

x < 14.43

x is the number of countries, it must be an integer.

so x = 14

Therefore, 14 countries participated in the 1896 Olympic games.

Step-by-step explanation:

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: t=-20

Step-by-step explanation:

Not necessary when solving this system of equations by graphing is

to determine the shaded area for each line. The correct option is C.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found. The point where the two lines join is (-3, -4), which is where this equation system's solution lies.

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Answer:

P. Sue uses 1/6 of the pitcher to fill 1 glass

Step-by-step explanation:

The image that shows the graph equivalent to the fraction 1/4 is option A, because only one part of the 4 available is shaded.

To identify the correct graph, we must first identify which fraction we must represent. In this case, the fraction is 1 / 4. To understand this fraction, we must take into account that the top number (1) refers to the number of parts that are shaded and the bottom number (4) refers to the number of total parts. into which the figure is divided.

According to the above, we can infer that it is a figure that is divided into 4 parts, and one of them is shaded. So the correct choice would be option A.

Note: This question is incomplete because there is some information missing. Here is the complete information:

image attached

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Answer:Sure! Here are four daily life examples where 20 subtracted by 0 is equal to 20:

1. You have 20 pieces of fruit in a basket, and you take 0 pieces of fruit out of the basket. You are left with 20 pieces of fruit in the basket.

2. You have 20 minutes left on your parking meter, and you add 0 more minutes to the meter. You still have 20 minutes left on the meter.

3. You have 20 dollars in your wallet, and you spend 0 dollars. You still have 20 dollars in your wallet.

4. You have 20 pages left to read in a book, and you haven't read any additional pages. You still have 20 pages left to read.

By using the formula for the perimeter, we will get that the width of the pool is 20 meters.

Remember that for a rectangle of length L and width W, the perimeter is given by the formula:

P = 2*(L + W)

In this case, we know that the perimeter is 90m, and the length is 25m, then we know that:

P = 90m

L = 25m

Replacing that in the formula above we will get:

90m = 2*(25m + W)

now we can solve this for W.

90m/2 = 25m + W

45m - 25m = W

20m = W

The width of the pool is 20 meters.

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