Is the set of rational expressions closed under division

Answer:

Step-by-step explanation:

Midpoint formula is x3 = (x1+x2)/2, y3=(y1+y2)/2

so x3=(9-5)/2=2, y3=(-5/2-3/2)/2=-2.

the coordinates is (2, -2).

Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.

Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either contingent equations or identities are categories for equations. An identity holds true for whatever value of the variables.

given

x+y=7

2x-y=-1

8x=20

x= 5/2

-4y = -8

y = 2

Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.

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Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

So on solving the provided question, we can say that the value of k is 4, in this linear equation question.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.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.

1/2k +6= 4k-8

Multiplying both sides by 2,

k+12= 8k-16

7k=28

Therefore,

       k=4

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I believe it's A

I hope this helps and if I'm wrong I apologize

Answer:

Complementary

x = 15

Step-by-step explanation:

Answer:

X < - 50

Step-by-step explanation:

5 - 1/2 x > 30

Move 5 to the other side of the inequality

- 1/2 x > 25

Multiply both sides by 2, to get rid of the denominator on the left side

-x > 50

Now switch the inequality sign and multiply to get the minus on the other side

x < - 50

[tex]5-\dfrac{1}{2} x > 30[/tex]

Simplify:

[tex]-\dfrac{1}{2} x+5 > 30[/tex]

Subtract 5 from both sides:

[tex]-\dfrac{1}{2} x+5-5 > 30-5[/tex]

[tex]-\dfrac{1}{2} x > 25[/tex]

Multiply both sides by [tex]-\dfrac{2}{1}[/tex]:

[tex]-\dfrac{2}{1} \times(-\dfrac{1}{2} x) > -\dfrac{2}{1} \times(25)[/tex]

[tex]\fbox{x} < \fbox{-50}[/tex]

On solving the provided question, we can say that - the value of the function is = x-5/x + 2 => x= 2  => -3/4

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

x-5/x + 2

x= 2

-3/4

ans also  4x² = 4 *2*2 = 16

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Of the given statements, only the option number {5} and {6} are true.

The perpendicular bisectors of a triangle are lines passing through the midpoint of each side which are perpendicular to the given side. A triangle's three perpendicular bisectors meet at a point. known as the circumcenter, which is also the center of the triangle's circumcircle.

Given is a triangle as shown in the image.

Since PS is the perpendicular bisector of QR, we can write -

QS = SR

6n + 3 = 4n + 11

2n = 8

n = 4

QR = QS + SR

QR = 6n + 3 + 4n + 11

QR = 10n + 14

QR = 10 x 4 + 14

QR = 54

and

SR = 4n + 11

SR = 16 + 11

SR = 27

Therefore, of the given statements, only the option number {5} and {6} are true.

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The nth term of the following sequence is: 5n²

Arithmetic sequence is a sequence where each consequtive term has a common constant difference.

An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.

We are given the sequence are;

5, 20, 45, 80, 125

The quadratic sequence formula : an²+bn+c

2nd difference 2a = 10

a = 5

1st difference 3a+b = 15

Then substitute 5

3(5)+b = 15

b = 0

The nth term rule : a + b + c = 5

Now substitute a and b values into equation

5 + 0 + c = 5

c = 0

The nth term is: 5n²

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Answer:

Answer: £272.51

Step-by-step explanation:

First, we need to determine how much money Selma needs to have in her account in order to pay the bill and still have £10 left over. The bill is for £465.20, so Selma needs to have £475.20 in her account in order to pay it.

Next, we need to determine how much money Selma needs to pay into her account in order to reach this total. She starts with £202.69 on Monday, so she needs to pay £475.20 - £202.69 = £<<475.20-202.69=272.51>>272.51 into her account on Tuesday. Answer: £272.51

The original price of each notebook is $5.5

Trace is purchasing some notebooks

Each notebook is $2 off the original price

He buys 8 notebooks for $28

The first step is to calculate the price of one notebook

8= 28

1= x

Cross multiply both sides

8x= 28

x= 28/8

x= 3.5

1 notebook is $3.5

$2 was removed from the initial price. Therefore the original price is

2 + 3.5

= 5.5

Hence the original price of the notebook is $5.5

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After 3 years, the price of the house would be $2,494,822.48. After 5 years, the price of the house would be $2,830,530.94.

Price is the value of a product or service that an individual or business is willing to accept in exchange for a good or service. It is typically determined by the market forces of supply and demand. Prices are usually expressed in monetary terms, but can also be expressed in terms of labor time or other resources. Prices can vary widely depending on the availability of a good or service, the amount of competition, and other factors.

To calculate the price of the house after 3 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 3. Therefore, the price of the house after 3 years is P x (1 + 0.06)^3, which equals to $2,494,822.48.
To calculate the price of the house after 5 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 5. Therefore, the price of the house after 5 years is P x (1 + 0.06)^5, which equals to $2,830,530.94.

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Answer: 1000 times less

Step-by-step explanation: multiply 0.054x1000

Answer:

1000 times

Step-by-step explanation:

To find how many times less 0.054 is than 54,

we can divide 54 by 0.054.

This gives us 54/0.054 = 1000

This means that 0.054 is 1000 times less than 54.

Answer:

109.18

Step-by-step explanation:

Subtract 13.4-7.2 then solve the triangle (base x height) getting 32.86. Next solve the rectangle getting 76.32. Then add all of it concluding in 109.18.

Answer:

[tex]\frac{7}{5}[/tex]

Step-by-step explanation:

I am thinking that you mean 84 minutes compared to an hour?

[tex]\frac{84}{60}[/tex] ÷ [tex]\frac{12}{12}[/tex] = [tex]\frac{7}{5}[/tex]

Answer: 28

Step-by-step explanation:

280/10=28

(/=divide)

If you have 10 baskets and have 280 apples to evenly distribute them in every basket, you would have 28 in each basket. If that makes sense.

Hope this helps!

25 kilograms of fertilizer would be needed to fertilize the lawn.

In essence, percentages are fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage.

given, A certain type of fertilizer contains 8 percent of nitrogen. If 2 kilograms of nitrogen are needed to fertilize a lawn.

Since fertilizer contain 8% nitrogen in it

thus for 80 grams of nitrogen = 1 kg of fertilizer

for 1 gram of nitrogen = 1/80 kg fertilizer

for 2000 gram of nitrogen = (1/80)* 2000 kg fertilizer

for 2 kilograms of nitrogen = 25 kg fertilizer

therefore, To fertilize the yard, 25 kg of fertilizer would be required.

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Solving the provided question, we can say that the quadratic equation is [tex]-16t^2 +vt +s[/tex] so answer is -16+48+3 = 35

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

[tex]-16t^2 +vt +s[/tex]

v = 16

s =3

t =

so answer is -16+48+3 = 35

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The mean absolute deviation of $29, $58, $15, $75, and $22 is $32.67.

The average (mean) distance between each data value and the data set mean is known as the mean absolute deviation, or MAD. The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It provides insight into a dataset's variability.

From tje information, it should be noted that the mean will be:

= (29 + 58 + 15 + 129+ 75 + 22) / 6.

= 54.67

Means absolute deviation = 1/6+25.67 + 3.33 - 39.67 + 74.33 + 20.33 + 32.67)

= 32.67

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Complete question

Find the mean absolute deviation of the fulfilled items on Sherrie's registry: $29, $58, $15, $129, $75 & $22.

Answer:

x=2 y= -1

Step-by-step explanation:

Took me 5 minutes to write steps and unfortunately it disappeared. I am so sorry. But the answer is correct

The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.

A line's slope determines how steep it is. A mathematical expression for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two points. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is used to represent it. The y-intercept is located at a point where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).

given

for parallel their slope will be equal

y1= 1x/2 + 3/8 .... eq1

y2= kx/4 + 5k/4  ..... eq2

y1 = y2

1x/2 + 3/8 = kx/4 + 5k/4

1/2 + 3/8 = k/4 + 5k/4

7/8 = 6k/4

k = 7/12

for perpendicular product of their slope is 1

y1 * y2 = 1

1x/2 + 3/8 * kx/4 + 5k/4 = 1

1/2 + 3/8 * k/4 + 5k/4 = 1

k = 1/21

so The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.

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Answer:

Step-by-step explanation:
Step 1: Subtract 8cx from both sides of the equation to get

10ax + 9b - 8cx = d

Step 2: Subtract 9b from both sides of the equation to get

10ax - 8cx = d - 9b

Step 3: Multiply both sides of the equation by (-1/10) to get

-8cx/10 = -(d - 9b)/10

Step 4: Add (d - 9b)/10 to both sides of the equation to get

-8cx/10 + (d - 9b)/10 = 0

Step 5: Simplify the left side of the equation to get

x = (9b - d)/80

Therefore, x = (9b - d)/80 is the solution to the equation 10ax + 9b = 8cx + d.

Answer:

17/5

It is already simplified to lowest terms.

This number, as a mixed fraction, would look like this:

3 2/5.

Answer: x = -5, y = 4

Step-by-step explanation:

Align the two equations according to their terms:

[tex]\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.[/tex]

Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:

[tex]3y = 12\\y = 4[/tex]

Plug in y = 4 into the first equation:

[tex]-3x - 3(4) = 3\\[/tex]

Solve for x:

[tex]-3x-12 = 3\\-3x = 15\\x = -5[/tex]

Check by plugging in both x and y:

[tex]-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3[/tex]

So, x = -5 and y = 4

The numeric value of the expression ((2.1)² + 5.2 - 7.2) x 7.1 is given as follows:

17.1.

The expression for this problem is defined as follows:

((2.1)² + 5.2 - 7.2) x 7.1

The precedence of operators follows the PEMDAS acronym, as follows:

Hence the parenthesis takes precedence, thus:

(2.1)² + 5.2 - 7.2.

Then the power takes precedence, thus:

(2.1)² + 5.2 - 7.2 = 4.41 + 5.2 - 7.2

Addition and subtraction can be done in any order, hence:

4.41 + 5.2 - 7.2 = 2.41.

Then the multiplication is given as follows:

2.41 x 7.1 = 17.1.

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The angle at the center of the circle will be;

⇒ θ = 0.5 radian

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A sector of a circle of radius 10 cm and has an area of 25 cm².

Now,

Since, We know that;

⇒ A = 1/2 r²θ

Where, A is area of circle , r is radius of circle and θ is the angle at the center of the circle.

Here, A sector of a circle of radius 10 cm and has an area of 25 cm².

Substitute all the given values, we get;

⇒ A = 1/2 r²θ

⇒ 25 = 1/2 × 10² × θ

⇒ 25 = 50 × θ

⇒ θ = 25 / 50

⇒ θ = 0.5 radian

Thus, The angle at the center of the circle = 0.5 radian

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The solution to the equations are

0 ∈ N is False               7/2 ∈ Q is True

√16 ∈ Q' is False          π ∈ Q' is True

3/2 ∈ I is False              -3 ∈  R is True

0 ∈ I is True                  -1 ∈ I⁺ is False

( 1 - 3 ) ∈ N is False       8/2 ∈ I is True

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as A

Now , the equation will be

a)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is not a natural number

So , the equation is False

b)

Let the number be A = √16

The value of A = 4

The number 4 is a natural number , whole number , rational number and an integer

4 is not an irrational number

So , the equation is False

c)

Let the number be A = 3/2

The number 3/2 is a rational number

3/2 is not an integer

So , the equation is False

d)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is an integer

So , the equation is True

e)

Let the number be A =  ( 1 - 3 )

The value of A = -2

The number -2 is a rational number and an integer

-2 is not a natural number

So , the equation is False

f)

Let the number be A = 7/2

The number 7/2 is a rational number

7/2 is a rational number

So , the equation is True

g)

Let the number be A = π

The number π  is an irrational number

π is an irrational number

So , the equation is True

h)

Let the number be A = -3

The number -3 is a real number

7/2 is a real number

So , the equation is True

i)

Let the number be A = -1

The number -1 is an integer and real number

-1 is a negative integer

So , the equation is False

j)

Let the number be A = 8/2

The value of A = 4

The number 4 is a natural , whole , integer and rational number

4 is an integer

So , the equation is True

Hence , the equations are solved

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Answer: y= -3/4x+8

Step-by-step explanation: