Solve the following and find Q R

Answer:

[tex] \frac{(3x(x - 3))}{(x - 3)(x + 1)} = \frac{3x}{x + 1} [/tex]

A system of equations are 9x+7y=77 and 3x+5y=49. Therefore, cost to rent each chair is $1.75 and cost to rent each table is $8.75.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

a) From the table, first costumer brought 9 chairs and 7 tables per $77

Second costumer brought 3 chairs and 5 tables per $49

Let x be the cost (in dollars) to rent a chair

Let y be the cost (in dollars) to rent a table

Here, 9x+7y=77 --------(I)

3x+5y=49 --------(II)

b) Multiply equation (II) by 3

9x+15y=147 --------(III)

Subtract equation (I) from (III), we get

9x+15y-(9x+7y)=147-77

⇒ 8y=70

⇒ y=8.75

Substitute y=8.75 in (I), we get

9x+7×8.75=77

⇒ 9x+61.25=77

⇒ 9x=77-61.25

⇒ 9x=15.75

⇒ x=1.75

Therefore, the system of linear equations are 9x+7y=77 and 3x+5y=49.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ1

he data in the table appears to be modeled by the function f(x) = -x^2 + 2.

To see this, let's plug in the values for x in the table and see if the resulting values for f(x) match the values in the table:

f(-2) = (-2)^2 + 2 = 4 - 2 = 2

f(-1) = (-1)^2 + 2 = 1 - 1 = 0

f(0) = 0^2 + 2 = 2

f(1) = 1^2 + 2 = 1 + 2 = 3

We can see that the resulting values for f(x) match the values in the table, so f(x) = -x^2 + 2 is a function that could represent the data.

Answer:

36

Step-by-step explanation:

[tex]\frac{1}{4}(12^2)=\frac{1}{4}(144)=36[/tex]

The  quantity of hydrocortisone powder, in g, should be entered on the compounding record as 56.7 g

Generally, To determine the quantity of hydrocortisone powder to be used in the compounding of this prescription, you will need to know the percentage of the final preparation that will be made up of hydrocortisone.

Since the prescription calls for a 1:1 mixture of hydrocortisone cream and Aquaphor, and the final quantity is to be 4 oz, each component will make up half of the final preparation. Therefore, the final preparation will be 50% hydrocortisone.

To determine the quantity of hydrocortisone powder needed, you will need to multiply the final desired quantity of the preparation by the percentage of the preparation that is made up of hydrocortisone. In this case, the desired final quantity is 4 oz, and the preparation is 50% hydrocortisone, so the calculation is:

4 oz * 50% = 2 oz

Since there are 28.35 grams in an ounce, the total quantity of hydrocortisone powder needed in grams is:

2 oz * 28.35 g/oz = 56.7 g

Therefore, you should enter a quantity of 56.7 g of hydrocortisone powder on the compounding record for this prescription.

Read more about prescription

https://brainly.com/question/9537464

#SPJ1

The total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, If Mars travels at 24,126 meters per second in orbit around the Sun and takes 1.88 earth years to complete its orbit,

First, we have to convert the unit from earth year to second obtained as,

1.88 earth year=  59287680 second

As we know that the distance is the multiplication of the speed and the time

Distance = speed × Time

Distance =24,126 m/sec ×  59287680 second

Distance = 1.4 × 10¹² m

If 1 meter consists of 0,000621371 miles, the obtained distance is in miles.

1 metere = 0,000621371 miles

1.4 × 10¹² m=888 × 10⁶ miles

Thus, the total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ1

Answer:

-25

Step-by-step explanation:

The total money was shared = $3304

What are proportion and ratio?

Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

Aaron, Ben, and Charles split a sum of money in the following proportions: 2: 5: 7. What was the initial amount of money shared if Charles' part was 1180 higher than Aaron's portion?

——-

Ben:::: 5x

Charles:7x

Aaron:2x

———-

7x = 2x + 1180 in the equation

5x = 1180

x = 236

————-

2x + 5x + 7x = 14x

14x = 14*236 = $3304

—————————————

Hence the total money was shared = $3304

Learn more about ratio and prportion

https://brainly.com/question/12024093

#SPJ1

Answer:

12 yards

3+4+5=12

3+4=7

7+5=12

Answer:

12, needed to be multiplied ( which I don't think so) 60

Step-by-step explanation:

I really don't have a "step by step explanation" but 4+5=9+3=12

or: 4x5=20x3=60

The required expression for the money spent is given as 25x + 14y.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given problem can be solved as follows,

The price for each yoga mat is $25 and each yoga DVD is $14.

As per the question, the expression for the amount of money spent can be written as,

25x + 14y

The expression can be minimised to reduced the money spent.

Hence, the expression for the money spent by yoga teacher is 25x + 14y and the given expression can be minimised to reduce the total cost.

To know more about algebraic expression click on,

brainly.com/question/953809

#SPJ1

The 7th term of the sequence is 136.6875

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

12, 18, 27....

In the above sequence, we can see that the previous term is multiplied by 1.5 to get the current term

Using the above as a guide,

So, we have the following representation

aₙ = 1.5aₙ₋₁

a₄ = 1.5 * 27

Evaluate the products

a₄ = 40.5

Solving further, we have

a₅ = 40.5 * 1.5

Evaluate the products

a₅ = 60.75

Solving further, we have

a₆ = 60.75 * 1.5

Evaluate the products

a₆ = 91.125

Solving further, we have

a₇ = 91.125 * 1.5

Evaluate the products

a₇ = 136.6875

Hence, the 7th term is 136.6875

Read more about sequence at

brainly.com/question/7882626

#SPJ1

The standard error is decreasing on increasing number of Sample.

What is the standard error?

The population mean and sample mean are likely to deviate from one another, and the standard error of the mean, or simply standard error, shows how likely this is.

                    If a study were to be repeated using fresh samples drawn from a single population, it would be possible to calculate how much the sample mean would change.

The standard error is represented by a σ because it is a standard deviation. The subscript (M) indicates that the standard error in question is the standard error of the mean.

Now we will get the standard error for the following situations:

(a) σ_M = 12/√4 = 6

(b) σ_M = 12/√16 = 3

(c) σ_M = 12/√64 = 1.5

Hence from here, we can conclude that the standard error is decreasing on increasing number of Sample.

Learn more about standard error

brainly.com/question/13179711

#SPJ1

Answer:

Step-by-step explanation:

Simplify parentheses : 0.5x+0.3=2.1x+9-5.5

Combine like terms : 0.5x+0.3=2.1x+3.5

Isolate the variable : -1.6x=3.2

Divide by -1.6 on both sides : x=-2

Answer:  the answer is in the picture

have a nice one

Step-by-step explanation:

Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

For a triangle to be Right Angled , It should obey the Pythagoras Theorem

[tex]c^{2} = a^{2}+b^{2}[/tex]

c = hypotenuse

a = perpendicular side

b = base

Hence

if c = 5 , a = 3 and b = 4

Then

[tex]c^{2} = a^{2}+b^{2}[/tex]

[tex]5^{2}= 3^{2}+4^{2}[/tex]

25 = 3 + 16

25 = 25

So

It obeys the Pythagoras Theorem

Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )

To know more about Pythagoras Theorem

https://brainly.com/question/343682

#SPJ1

The solution to the linear inequality written in set-builder notation is {m | m ∈ R and m ≥ 12 or m ≤ 9}

From the question, we are to solve the given linear inequality.

The given linear inequality is

-3 + m ≥ 9 OR 1 + 2m ≤ 19

Solving -3 + m ≥ 9

-3 + m ≥ 9

Add 3 to both sides of the equation

-3 + 3 + m ≥ 9 + 3

m ≥ 12

Solving 1 + 2m ≤ 19

1 + 2m ≤ 19

Subtract 1 from both sides of the equation

1 - 1 + 2m ≤ 19 - 1

2m ≤ 18

Divide both sides by 2

2m/2 ≤ 18/2

m ≤ 9

Thus,

m ≥ 12 OR m ≤ 9

In set-builder notation

{m | m ∈ R and m ≥ 12 or m ≤ 9}

Learn more on Solving linear inequalities here: https://brainly.com/question/24372553

#SPJ1

The values of the angles are m∠ A = 112.5°, m∠ B = 67.5°, m∠ C = 67.5°, and m ∠D = 112.5°

Considering the regular octagon, the sum of angles in an octagon is 1080°. This implies each angle in the octagon will be 1080/8 = 135°

Thus, you can label the angle as shown in the image attached

c + m<A + 135° = 360°  (the sum of angle at a point is 360°)

Since c = m<A (identical sides)

m<A + m<A + 135° = 360°

2 m<A = 360-135

m<A = 225/2 = 112.5°

m<B + m<A = 180°  (Between two parallel lines, consecutive interior angles add up to 180°)

m<B + 112.5° = 180°

m<B = 180-112.5 = 67.5°

m<C = <B    (base angles of isosceles trapezoids are equal)

m<C = 67.5°

m<D = m<A    (base angles of isosceles trapezoids are equal)

m<D = 112.5°

Learn more about angles in a trapezoids on:

https://brainly.com/question/10139767

#SPJ1

Red books are 8 and blue books are 6.

The smallest unit of measurement is the inch (or inches, in plural). A foot is made up of twelve inches. In the metric system, one inch is equivalent to 2.54 cm. When measuring shorter distances, such the breadth of an eraser or the length of a pencil, inches are employed.

Give conditions

Total books = 11

Red book height = 1 inches

Blue book height = 2 inches

Total height = 14 inches

We assume that

8 red books and 3 blue books = 11 books { first condition is satisfied}

In inches case:

8 * 1 = 8 { red book height 1 inches}

3 * 2 = 6 {blue book height 2 inches}

total height = 8 +6 = 14 inches {second condition is satisfied}

since red books are 8 and blue books are 6.

To learn more about to inches refer to:

https://brainly.com/question/876758

#SPJ1

Part A. The system of inequalities to this context is x + y ≥ 4 and

8x + 13y ≤ 90.

Part B. An example of one solution is (x, y) is (4, 4), where she buys 4 pizzas of each type which satisfies x + y ≥ 4.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

From the given information 'x' represents the number of pepperoni pizzas and 'y' represents the number of vegetarian pizzas.

Given, She wants to have at least 4 pizzas which is,

x + y ≥ 4...(1)

Also given that a pepperoni pizza costs $8.00 and a vegetarian pizza costs $13.00 and she has $90 to spend.

Therefore, 8x + 13y ≤ 90...(2)

An example of a solution is (x, y) ⇒ (4, 4) where she buys 4 pepperoni pizzas and 4 vegetarian pizzas.

learn more about inequalities here :

https://brainly.com/question/28823603

#SPJ1

The time required for the sloth to travel an 11.5-meter tree is

171.64 seconds.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A sloth is traveling at its top speed of 0.067 m/s.

∴ The time required for the sloth to travel an 11.5-meter tree is,

= (11.5/0.067) secs.

= 171.64 seconds.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ1

The monthly payment would be an amount of $163.875.

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

As per the given question, we have

Here P = $1900 , r = 3.5%, and T = 1 years

The total payback = P× r/100 × T + P

The total payback = 1900 × 3.5/100 × 1 + 1900

The total payback = 1900 × 0.04 × 4 + 1900

Apply the multiplication operation, and we get

The total payback = $1966.5

The total payback of the borrowings will be $1966.5 over a one-year period. The monthly payment for this will be,

The monthly payment = Total payback / No. of payment

The monthly payment = 1966.5/12

The monthly payment = $163.875

Therefore, the monthly payment would be an amount of $163.875.

Learn more about the monthly payments here:

https://brainly.com/question/20761642

#SPJ1

The equation is [tex]36x-y=145[/tex].

The domain is (∞,-∞), {x,x∈R}.

What is the domain of a function?

The domain of a function is the set of all conceivable values that are acceptable as inputs, or alternatively, it can be interpreted as the full set of potential values for independent variables. The denominator of the fraction is not equal to zero, and the digit under the square root bracket is positive, which is an indicator of the domain.

Let us first take any 2 coordinates of the function, say (-143,-2) and (0,-71).

let us take the slope of these 2 points,

[tex]m=\frac{x_{2}-x_{1} }{y_{2}- y_{1} } \\m=\frac{-71+143}{0+2} \\m=\frac{72}{2} \\m=36[/tex]

Now, using the slope, we can find the required equation:

[tex]y-y_{1} =m (x-x_{1} )\\y+143=36(x+2)\\36x-y=145\\[/tex]

The domain for the function is (∞,-∞), {x,x∈R}.

To learn more about the domain of the functions, visit the link below:

https://brainly.in/question/27845598

#SPJ4

95% of the time confidence intervals like this capture the true average time between a felony.

The average of the true ranges throughout the given period is known as the average true range (ATR). ATR calculates volatility by accounting for any gaps in price movement. 14 periods, which can be intraday, daily, weekly, or monthly, are typically used in the ATR calculation. Utilize a shorter average, such as 2 to 10 periods, to gauge recent volatility. Use 20 to 50 periods for volatility over longer time spans.

To know more about the true average visit: brainly.com/question/11195029

#SPJ$

Answer: D 12.54-10.67

The equation of the line is y=3÷5x+4.

Here, we need to figure out the slope of this curve.

if two lines are perpendicular to each other and both of their slopes exist, the product of their slopes is equal to -1.

k1 = -9-6÷1-(-4)

   = -5÷3

k2-k1  = -1

∴k2= 3÷5

y-1= 3÷5[x-(-5)]

y= 3÷5÷x+4

Hence, The equation of the line is y=3÷5x+4.

To learn more about slope of a curve refer to:

https://brainly.com/question/28789772

#SPJ1

Answer:

70

Step-by-step explanation:

I believe that since these are complementary angles, you are supposed to add two to get 180. In this case, there is a 110, so 70 more would be 180, but i could be wrong. you can delete my answer if it is wrong :(

Translating the phrase into an algebraic expression for the difference between four times a number and 10 is 4x - 10.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Let the number be given as x.

Therefore, 4 times will number will be 4x.

Then, difference between four times a number and 10 will be:

= 4x - 10

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Answer: x=3y−5

Step-by-step explanation: 6y=2x+10

Swap sides so that all variable terms are on the left hand side.

2x+10=6y

Subtract 10 from both sides.

2x=6y−10

Divide both sides by 2.

2

2x

​ =

2

6y−10

​

Dividing by 2 undoes the multiplication by 2.

x=

2

6y−10

​

Divide 6y−10 by 2.

x=3y−5

To be profitable and ensure your finances are healthy, look at both your total revenue as well as your net revenue.

To learn more about total revenue calculation refer to:

https://brainly.com/question/25623677

#SPJ1

Answer:

-4x-12

Step-by-step explanation:

7x-8x-3x = -4x

14-26 = -12

-4x-12