The dimension of the square piece of paper is 6 inches.
How to find the dimension of the square piece?A rectangular piece of paper is twice as long as a square piece and 3 inches wider.
The area of the rectangular piece is 108 in².
A square has all its side equal to each other and a rectangle has two opposite sides equal to each other.
Therefore,
let
x = length of the square
Therefore,
length of rectangular piece = 2x
width of the rectangular piece = 3 + x
Therefore,
area of the rectangular piece = lw
where
l = lengthw = widthTherefore,
area of the rectangular piece = 2x(3 + x)
area of the rectangular piece = 6x + 2x²
108 = 6x + 2x²
2x² + 6x - 108 = 0
divide through by 2
x² + 3x - 54 = 0
x² - 6x + 9x - 54 = 0
x(x - 6) + 9(x - 6) = 0
(x + 9)(x - 6)
Therefore, we can only use positive numbers.
Hence,
x = 6
Therefore,
dimension of the square piece is 6 inches.
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Simplify: 3x^2-9x over x^2-2x-3
Answer:
[tex] \frac{(3x(x - 3))}{(x - 3)(x + 1)} = \frac{3x}{x + 1} [/tex]
stephanie is ordering a pizza for a friends birthday. she wants to offer both meat and vegetarian options. a pepperoni pizza costs $8.00 and the vegetarian pizza costs $13.00. stephanie has $90 to spend on pizza and she wants to have at least 4 pizzas.
Part A: Create a system of inequalities to represent this situation where x represents the number of pepperoni pizzas and y represents the number of vegetarian pizzas she could order.
Part B: Give an example of one solution that would describe how many of each pizza she could buy.
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.
What are inequalities and their types?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.
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1. Which of these numbers can be classified as both real and irrational?
5.858585858
63.4
√21
√36
Answer:
sqrt21 is real and irrational
Step-by-step explanation:
The other answers are a repeating decimal (rational), a terminating decimal (rational) and a perfect square (an integer--so also rational)
They are all real. Numbers that are not real have the imaginary number, i, in them or a square root of a negative number.
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A pharmacy technician receives the following prescription:Hydrocortisone 2.5% cream
and Aquaphor in 1:1 Quantity: 4 oz total. What quantity of hydrocortisone powder, in g.
should be entered on the compounding record?
The quantity of hydrocortisone powder, in g, should be entered on the compounding record as 56.7 g
What quantity of hydrocortisone powder, in g should be entered on the compounding record?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.
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Which box-and-whisker plot represents this data:6,7,9,9,20,22,26,28,29,30
The last boxplot is the one that displays the values of the distribution that is given.
What is the range?The range of a function in mathematics can refer to one of two ideas that are connected in some way: Codomain for the function an illustration of the action If there is precisely one y in Y and there are two sets X and Y, then a binary relation f between X and Y is a function that connects x and y.
Here ,Given information:
6,7,9,9,20,22,26,28,29,30
N = 10 observations were made.
The base number is 6. ( least value)
Quartile lower= n+1(0.25)
term = 0.25(13) = 3.25term = 13
Median equals 0.5 (n + 1)
term = 0.5(13) = 6.5 term = (20 + 24) /2 = 22
Upper quartile: 0.75 (13)
A term equals 9.75 a term equals 26.5
Interquartile Range (IQR) is equal to= Q3 - Q1= (26.5 - 13) = 13.5
The highest value is 30. (highest value in the distribution)
As a result, the Last boxplot is the one that shows the distribution that is given.
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A yoga teacher sells yoga mats for $25 each and yoga DVDs for $14
each. If x represents the number of mats she sells and y represents
the number of DVDs she sells, write an expression that represents
the amount of money she receives from selling mats and DVDs. Tell
whether the expression should be minimized or maximized.
The required expression for the money spent is given as 25x + 14y.
What is an Algebraic expression?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.
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Solve for X
6y = 2x + 10
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
if a sloth is traveling at its top speed of 0.067 m/s how long does it take the sloth to travel a 11.5 meter tree
The time required for the sloth to travel an 11.5-meter tree is
171.64 seconds.
What is a unitary method?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.
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What is 8.7% of $1,541
Answer:
137.067
Step-by-step explanation:
1 percent = 15.41
0.1 percent = 1.541
8 x 15.41 = 123.28
7 x 1.541 = 10.787
123.28 + 10.787 = 137.067
Find the standard error of the mean for each sampling situation (assuming a normal population).
Standard Error
a. σ = 28, n = 4
b. σ = 28, n = 16
c. σ = 28, n = 64
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.
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How to subtract fractions with different denominators?
Please explain step by step!
Help!
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Slope = -8, passing through (-4,-9)
Answer:
-25
Step-by-step explanation:
The midpoint of GH is M(-6,-3). One endpoint is H (-4,4). Find the coordinates of endpoint G
When the midpoint of GH is M at (-6,-3) and one endpoint is H at (-8,-10), the coordinates of endpoint G are (-8,-10) (-4,4).
What is coordinates?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). a group of variables that accurately depict a stance. The first number on a graph represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is located 12 units down and 5 units up.
Here,
let the points of G be (a,b)
mid point of GH =(-6,-3)
point of H =(-4,4)
for x coordinate,
-6=(a-4)/2
a-4 =-12
a=-8
for y coordinate,
-3=(b+4)/2
-6=b+4
b=-10
The coordinates of endpoint G is (-8,-10) when the midpoint of GH is M at (-6,-3) and one endpoint is H at (-4,4).
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Consider the sets below. Find B^c ∩ C
Answer:
{red, orange , yellow}
Step-by-step explanation:
pls rate as brainliest I need to move to the next rank
You receive a call from a taxpayer who has concerns with her account. The taxpayer has been explaining her concerns for over five minutes. As she is talking, you notice that your lunch break was supposed to begin two minutes ago. In your department, there are strict guidelines on taking lunch breaks during the allotted times. These guidelines are in place to ensure that the taxpayer hotlines are staffed appropriately.
Email your manager to notify her that you are running over on a call and ask her what should you do.
As my manager now knows that I am running over on a call, she could allow me to have a lunch break of whatever time I invested in the taxpayer's call. By doing this, both the taxpayer and I can be stress free.
What Is a Taxpayer?
A taxpayer is anybody who owes taxes to the federal, state, or municipal governments, whether they are an individual or a corporation. Governments primarily obtain their funding through taxes, which are levied on both citizens and companies.
According to the rules of the Income Tax Act, a taxpayer is a person or a business that pays taxes on its income each year. It becomes lawful after you file income tax returns and reveal your revenues.
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There are 11 books stacked on a shelf. The red books are 1 inch high and the blue books are 2 inches high. The height of the books is 14 inches. Use a graph to estimate the number of red books and the number of blue books on the shelf.
Red books are 8 and blue books are 6.
What is inches?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.
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Question 12
Solve -3 + m2 9 or 1+ 2m 19. Write the solution using set-builder notation.
The solution to the linear inequality written in set-builder notation is {m | m ∈ R and m ≥ 12 or m ≤ 9}
Solving Linear inequalitiesFrom 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}
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1/4(2x + 1.2) = 3(0.7x + 3) - 5 1/2
what is the solution?
show your work please!!
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:
How do I find x?
Please help me, I tried everything :(
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 :(
Which number should come next ➔ 7, 13, 13, 14, 19, 15 ?
(a) 15
(b) 25
(c) 19
(d) None of the
a party rental company has chairs and tables to rent. there were two customers who rented both chairs and tables last week
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.
What is a linear system of equations?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.
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A local ice cream shop sold a scoop for $2 the first year they opened and had 1000 customers each day. The price for ice cream increases by 10 cents each year because times are tough. However, 10 fewer people buy ice cream each year. Create a revenue equation. What price should they sell the ice cream to maximize the daily profit?
The answer is $6, but I want an explanation as to why
To be profitable and ensure your finances are healthy, look at both your total revenue as well as your net revenue.
What drives our total revenue calculation?A simple way to solve for revenue is by multiplying the number of sales and the sales price or average service price (Revenue = Sales x Average Price of Service or Sales Price).With that being said, not all revenues are equal.Total Revenue = Number of Units Sold X Cost Per UnitTotal Sales X Cost Per Unit equals Total RevenueThe total revenue equation can be used to determine revenue for both goods and services.Think "quantity times price" to help yourself remember.To learn more about total revenue calculation refer to:
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Determine the value of b in the equation b3 = −27.
b = −3
b = 3
b = −9
b = 9
angles x and y are supplementary angle x measures 116.89 and angle y measures (m-10) find m Y
If the measure of the angle x is 116.89 degrees. Then the measure of the angle y will be 63.11 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
It is given that the angles x and y are supplementary angles. Then the equation is given as,
x + y = 180
If the measure of the angle x is 116.89 degrees. Then the measure of the angle y is calculated as,
x + y = 180
116.89 + y = 180
y = 180 - 116.89
y = 63.11 degrees
If the measure of the angle x is 116.89 degrees. Then the measure of the angle y will be 63.11 degrees.
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A sum of money was given to Arin, Greg, and James, the ratio is 2:5:7. James received $1180 more than Arin. How much total money was shared?
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
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Assume that you want to have $ 1900 saved in a sinking fund in 1 year. The account pays 3.5% compounded monthly. What should be your monthly payments?
Monthly Payment =
The monthly payment would be an amount of $163.875.
What exactly is a monthly payment?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.
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If Mars travels at 24,126 meters per second in orbit around the Sun and takes 1.88 earth years to complete its orbit, what is the total distance in miles Mars travels throughout its complete orbit? (Round your answer to the nearest whole number and do not include units or commas in your answer.) Note: There are 1,609 meters in a mile.
The total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.
What is an arithmetic operation?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.
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Here are four equations of absolute value functions and three coordinate pairs.
A. p(x)=[x-9] B. q(x)= [x]+9
Match the equation of each function with the coordinates of the vertex of its graph 1. (-9, 0 2. (9, 0) 3.(0, -9)
A) The vertex (h, k)=(9, 0) if p(x)=[x-9]
B) The vertex (h, k)=(0, 9) if q(x)= [x]+9
What is meant by a function?The earliest known treatment of the idea of function can be found in the writings of the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally merely a simplified illustration of the relationship between two varying quantities. The position of a planet is just one example of how time is used. The concept was historically developed towards the end of the 17th century with infinitesimal calculus, and the functions that were taken into consideration up until the 19th century. The concept of a function was formalised in terms of set theory at the end of the 19th century, greatly extending its range of applications.
Given,
A) p(x)=[x-9]
We have to compare with f(x)=a|x-h|+k
Therefore, the vertex (h, k)=(9, 0)
B) Given,
q(x)= [x]+9
We have to compare with the above equation we get,
The vertex (h, k)=(0, 9)
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Explain how to translate the phrase into an algebraic expression. The difference between four times a number and 10
Translating the phrase into an algebraic expression for the difference between four times a number and 10 is 4x - 10.
What is an expression?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
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Mathamathics for 9th
The equation of the line is y=3÷5x+4.
How to find the slope of a curve at a given point?A straight line that meets a curve only once and does not pass entirely through it is said to be tangential. The point of tangency is the intersection of the curve and the tangent. We are aware that the slope at any point on the line y=mx+cy=mx+c equals mm. The same is true for curves. When we refer to a curve's slope, we actually mean its point-to-point tangent slope.We employ the subsequent steps to calculate slope:In order to get dy/dx of an equation, we must first differentiate the provided equation.After differentiating, we will have the slope equation.To find the slope, enter the value of x into the equation.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.
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