To simplify a complex fraction, we use the following steps:
1- Use various rules of fractions to simplify both the numerator and denominator into a simple fraction. Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator.
2- Use the following rule to evaluate the result.
3- If needed, simplify the rational expression.
A complex fraction in mathematics is one that has another fraction in either the numerator, the denominator, or both. Simplifying difficult fractions is frequently helpful when working with them. This may be accomplished by utilizing a few straightforward procedures and different fractional rules.
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Is 0 Infinity a real number?.
No, 0 Infinity is not a real number. It is an undefined mathematical expression.
No, 0 Infinity is not a real number. It is an expression that is undefined in mathematics. This means that it has no numerical value or meaning, and cannot be accurately represented or calculated. In other words, 0 Infinity is not a valid mathematical expression, and so it is not considered a real number.
This means that it has no numerical value or meaning, and cannot be accurately represented or calculated. In other words, 0 Infinity is not a valid mathematical expression, and so it is not considered a real number.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 8 cubic feet and the volume of each large box is 21 cubic feet. A total of 20 boxes of paper were shipped with a combined volume of 264 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
Answer:14
Step-by-step explanation: so if you add 21 and 264 and 20 u would get 14 hehehehhehehe im da best your not :)
Is √ 64 real or imaginary?.
64 is a real number. It is not a imaginary number. Real numbers have real square roots and imaginary numbers do not have real square roots.
Square of a number is expressed as when a number is squared it is multiplied by itself. 64 is a perfect square of a number. It is a perfect square of the 8. The perfect square of a numbers explains the properties of Real numbers. It includes integers, natural numbers. The real numbers can be of positive and can be of negative numbers. It can be both a rational number or a irrational numbers. The difference between the real number and imaginary number is the square of a real number is non negative but the square of an imaginary number is negative.
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what is the x coordinate of the solution to the following system of equations
x-2y=2
3x+y=6
Answer:
(2,0)
Step-by-step explanation:
I think that the answer
How do you use the zero product property to solve a quadratic equation in factored form?.
Quadratic equations in factored form can be solved by using the Zero Product Property, which states that if the product of two numbers equals zero, then at least one of the values must also equal zero.
The Zero Product Property can be used to resolve any factored quadratic equation, such as (a + b)(a b) = 0. In accordance with the zero product property, if a+b=0, then either an or b must also be equal to zero. This essential characteristic allows us to solve equations like (x+2)(x-5)=0.
The zero product property states that if two quantities are added together and the result is zero, then one or both of the individual quantities must also be zero. You can solve this problem by rewriting it as (x + 3) (2 x 1) = 0.
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Is the square root of a negative number a real number?.
A negative number's square root is not a real number. Since a square is either positive or zero, negative numbers don't have real square roots.
Is the number sqrt (- 3) real?Yes, the number three is real. We are aware that both rational and irrational numbers can make up a real number. We can also say that 3 is a real number because it is an irrational number.
Is it unclear what the square root of a negative number is?On the GED math test, the square root of negative numbers is also marked as UNDEFINED. There is no number in the set of real numbers that is a negative product when multiplied by itself. As a result, there is no known definition for it.
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The second term of a G.P is 6, and the fifth term is 48, find the common ratio and the 3rd term of the G.P.
Answer:
Common ratio = 2, Third term = 12
Step-by-step explanation:
ar⁴ = 48........ equation 1
ar = 6.......... equation 2
divide equation 1 by equation 2
r³ = 8
r = ³√8
r = 2
To get the third term we must first get the first term
Since ar = 6 and r = 2, then 2a = 6 and a = 3
3rd term = ar²
3 × 2² = 3 × 4 = 12
Answer:
r = 2 and a₃ = 12
Step-by-step explanation:
the nth term of a GP is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
given a₂ = 6 and a₅ = 48 , then
a₁r = 6 → (1)
a₁[tex]r^{4}[/tex] = 48 → (2)
divide both sides of (2) by (1) to eliminate a₁
[tex]\frac{a_{1}r^{4} }{a_{1}r }[/tex] = [tex]\frac{48}{6}[/tex] ( cancel r and [tex]r^{4}[/tex] by r )
r³ = 8 ( take cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2
substitute r = 2 into (1) and solve for a₁
a₁ × 2 = 6 ( divide both sides by 2 )
a₁ = 3
a₂ = a₁ × r = 3 × 2 = 6
a₃ = a₂ × 3 = 12
Solve for x. Leave your answer in simplest radical form.
The value of x = [tex]\sqrt{30}[/tex], i.e., 5.478.
What is value?Value is the value of each digit, depending on where it is in the number.
It is calculated by multiplying the digit value of the number by the denomination value.
Value = Location Value x Face Value.
The tens place value 2 in the number 24 is because there are two complete sets of tens.
The value 4 for 24 units is due to 4 units not in the full set of 10.
A value can be defined as something that is valued by someone.
In other words, values are what a person or organization considers “important”.
Examples include courage, honesty, freedom, and innovation.
By Pythagoras theorem,
(Hypotenuse)[tex]^2[/tex] = (Perpendicular)[tex]^2[/tex] + (Base)[tex]^2[/tex]
In the given figure, in first triangle
[tex](8)^2 = (5)^2 + (y)^2\\y^2 = 39[/tex]
In second triangle,
[tex]39 = (3)^2 + (x)^2[/tex]
x = [tex]\sqrt{30}[/tex]
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Mario walked at rate of 5 miles every 3/7 of hour. What was his walking rate in miles per hour?
Answer:
11 2/3 mph about
Step-by-step explanation:
The figure shows the dimensions of a rectangular box Naomi has cubes with edges of
2 1/4 inches long what is the maximum number of Cubes that Naomi can fit in the Box?
Answer:
22x15x5=1650 divided by 3.18= 519
Step-by-step explanation:
The variable x and y are proportional. Ue the value to find the contant of proportionality. Then write an equation that relate x and y. Write any fraction in implet form. When $y=20$ , $x=12$
The constant of proportionally with the equation
[tex]$k = \frac{y}{x}$[/tex] with [tex]$y = \frac{5}{3}x$[/tex]
Proportional constant and equationThe constant of proportionality, also known as the coefficient of proportionality, can be found by using the equation:
[tex]$k = \frac{y}{x}$[/tex]
Plugging in the given values of x and y:
[tex]$k = \frac{20}{12}$[/tex]
Which can be simplified to:
[tex]$k = \frac{5}{3}$[/tex]
The equation that relates x and y is:
[tex]$y = kx$[/tex]
Using the equation [tex]$y = kx$[/tex] to find the constant of proportionality, also known as the coefficient of proportionality, and then substituting that value into the equation to relate x and y is one way to solve the problem.
It is the most common way to express a proportionality between two variables and it is the basic form of all proportional relationships.
So, substituting the value of k found earlier:
[tex]$y = \frac{5}{3}x$[/tex]
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Maya spent 40% of her savings to pay for a bicycle that cost her $85. How much money was in her savings to begin with? How much money does she have left in her savings after buying the bicycle?
A $212.50/$127.50
B $175/$90
C $225/$140
D $302.50/$217.50
Maya have $212.50 money in her savings to begin with, and she have left $127.50 in her savings after buying the bicycle.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Maya spent 40% of her savings to pay for a bicycle that cost her $85.
Now, Let the amount of money in her savings to begin with = x
So, We can formulate;
⇒ 40% of x = $85
Solve for x;
⇒ 40/100 × x = $85
⇒ 2/5x = $85
⇒ 2x = $85 × 5
⇒ 2x = $425
⇒ x = $425/2
⇒ x = $212.50
Thus, She have left in her savings after buying the bicycle is,
⇒ $212.50 - $85
⇒ $127.50
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Mary is making 5 necklaces for her friends, and she needs 11/12 of a foot of string for each necklace. How many feet of string does she need?
A. 3 7/12 feet
B. 5 11/12 feet
C. 7 4/12 feet
D. 4 7/12 feet
Answer:
D.
Step-by-step explanation:
The mass is 500
grams and the
volume is 40 cubic
centimeters
The mass is 125
grams and the
volume is v cubic
centimeters
The volume is 1.4
cubic centimeters
and the density is 80
grams per cubic
centimeter (et m
equal mass in
grams)
The mass is m
grams and the
volume is v cubic
centimeters.
Equation
The density of an object can be found by taking its mass
and dividing by its volume.
Write an equation to represent the relationship between
the three quantities (density, mass, and volume) in each
situation.
Let the density, D, be measured in grams/cubic
centimeters (or g/cm3).
The term "density" refers to the amount of volume (or physical space) occupied by an object or substance in relation to the amount of matter contained therein (its mass).
What is density ?
The quantity of things—which could include humans, animals, plants, or objects—in a given space is referred to as density. To determine density, divide the number of objects by the area's measurement. The number of people in a country divided by its area in square kilometers or miles is known as its population density.
The term "density" refers to the ratio between the volume (the amount of space taken up by an object or substance) and the amount of matter contained therein (its mass). The amount of mass per unit of volume is another method to define density. An object has a high density if it is both heavy and small.
By dividing the mass of an object by its volume, one may determine its density.
This means that if density is D, mass is M, and volume is V.
a)
M = 500 gms
40 cubic cm V
$D=$500/40
$D=12.5$
b)
M = 125 gms
= 1.4 cubic cm
$D = $ 125/1.4
$D=89.28$
D =89.28 gm per cc.
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The term "density" refers to the amount of volume (or physical space) occupied by an object or substance in relation to the amount of matter contained therein (its mass).
What is density ?The quantity of things—which could include humans, animals, plants, or objects—in a given space is referred to as density. To determine density, divide the number of objects by the area's measurement. The number of people in a country divided by its area in square kilometers or miles is known as its population density.
The term "density" refers to the ratio between the volume (the amount of space taken up by an object or substance) and the amount of matter contained therein (its mass). The amount of mass per unit of volume is another method to define density. An object has a high density if it is both heavy and small.
By dividing the mass of an object by its volume, one may determine its density.
This means that if density is D, mass is M, and volume is V.
a)
M = 500 gms
40 cubic cm V
$D=$500/40
$D=12.5$
b)
M = 125 gms
= 1.4 cubic cm
$D = $ 125/1.4
$D=89.28$
D =89.28 gm per cc.
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Carmen swam 8 kilometers against the current in the same amount of time it took her to swim 16 kilometers with the current. The rate of the current was 1 kilometer per hour. How fast would Carmen swim if there were no current?
Answer:
3 kph
Step-by-step explanation:
speed = x kph
(x-1)*t=8; 8/(x-1)= t units are km
(x+1)t=16; 16/(x+1)=t
Set them equal to each other
8/(x-1)=16/(x+1)
cross multiply
8x+8=16x-16
-8x=-24
x=3 kph
Kate has a Major Medical Plan with a 75/25 coinsurance and a deductible of $25. How much will she have to pay if she, not having met any of her deductible, visits the doctor and receives a bill for $125?
Kate will have to pay $56.25 out of pocket for her doctor visit.
The formula for calculating coinsurance is Coinsurance = (Cost of Service x Coinsurance Percent) / 100.If Kate has not met her deductible yet, she will need to pay the full $25 deductible plus 25% of the remaining bill.
The formula for calculating the amount Kate needs to pay is as follows:
Cost to Patient (C) = Deductible (D) + Coinsurance (C) * (Bill – Deductible) In this case, Kate would need to pay (125 x 25) / 100 = $31.25. The extra $25 is the deductible, which is the amount she must pay before her insurance kicks in.This amount is due immediately upon the visit, regardless of whether or not she has met her deductible So in total, Kate would have to pay $25 + $31.25 = $56.25. In summary, Kate will have to pay $56.25 out of pocket for her doctor visit.
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Please help and show work only do the left side
Writing linear equations given two points can be a useful skill when graphing linear equations.
Write a linear equation that passes through the given two points?To write a linear equation given two points, you need to first find the slope of the line. You can do this by finding the change in the y-value and dividing it by the change in the x-value. From there, you can use the slope to solve for the y-intercept and write the equation.For example, if the two points are (3, 4) and (0,5), you would find the slope by calculating the change in the y-value (5-4 = 1) and dividing it by the change in the x-value (0-3 = -3).The slope would then be 1/-3, which can be simplified to -1/3. To solve for the y-intercept, you can plug in one of the points and solve for b. In this case, you would plug in (3, 4) and solve for b, giving you b = 5. Now that you have the slope and y-intercept, you can write the equation as y = -1/3x + 5.y = -1/2xy = 5/3x + 5/3y = 3/5x + 1y = -1/2x - 2y = 6/5x + 5y = -4/4x - 8y = -3/5x - 7/5y = -2x - 4y = 5/6x + 7y = -1/2x + 4To learn more about linear equation refer to:
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A bicycle wheel is centimeters from top to bottom. When the wheel goes all the way around one time, the bicycle travels 198 centimeters. How can this information be used to estimate the value of π?
The height of the wheel is 63 centimeters that is the diameter of the circular wheel.
How do you explain distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.The International System of Units defines a metre as the distance unit. It's interesting to note that many other derived units or quantities, such as volume, area, acceleration, and speed, may be constructed using this as the basic unit and a few formulae.Given data :
A bicycle wheel is 63 centimeters from top to bottom.When the wheel goes all the way around one time, the bicycle travels 198 centimeters.a) The height of the wheel is 63 centimeters that is the diameter of the circular wheel.
b) The distance traveled by the wheel when it goes all the way around one time is 198 centimeters that is the perimeter of the circular wheel.
c) The distance traveled by the wheel when it goes all the way around one time is the perimeter of the circle. To estimate the value of t, divide the distance traveled by the wheel when it goes all the way around by its height.
Completed question :
A bicycle wheel is 63 centimeters from top to bottom. When the wheel goes all the way
around one time, the bicycle travels 198 centimeters. How can this information be used to
estimate the value of ?
63 cm
Click the arrows to choose an answer from each menu.
Because the wheel is circular, the height of the wheel is the Choose...
of
the circle. The distance traveled by the wheel when it goes all the way around one time is the
Choose...
of the circle. To estimate the value of t, Choose... the distance
traveled by the wheel when it goes all the way around by Choose...
y
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a) Work out the minimum number of dogs that could have a mass of more than 24 kg
. b) Work out the maximum number of dogs that could have a mass of more than 24 kg. Mass, z (kg)
Answer:
......................
Evaluate the expression for the given value of the variable. 1/3x+5 x= −6
The value of the expression (1/3)x + 5x, at x = - 6 is - 32.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
We know Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.
Given, An expression (1/3)x + 5x, when x = - 6.
Replacing - 6 with x we have,
(1/3)(-6) + 5(-6).
= - 2 - 30.
= - 32.
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what is the solution for x^2 - 18x < -77
Answer:
7 < x < 11
Step-by-step explanation:
Radius ; 8,7 feet; height: 16 feet
Therefore , the solution of the given problem of volume comes out to be
the volume of cylinder is 3801.6 cubic feet.
Define volume.The amount of space a three-dimensional item occupies is measured by its volume, which is measured in cubic units. Two examples of cubic units are cm3 and in3. Mass, in contrast hand, is a metric of how much matter is present in an object. It is common to use the weight of an object to calculate mass in quantities like pounds or kilograms.
Here,
Given :
Radius = 8.7 feet
and height = 16 feet
To find the volume of cylinder :
=> πr²h
=> 22/7 * 8.7 * 8.7 * 16
=> 237.6 * 16
=> 3801.6 cubic feet.
Therefore , the solution of the given problem of volume comes out to be
the volume of cylinder is 3801.6 cubic feet.
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The complete question is: "Find the volume of cylinder which hase Radius ; 8.7 feet; height: 16 feet ."
Kate wants to buy a new bicycle from a sporting goods store. The bicycle she wants normally sells for $720. The store has a sale where all bicycles cost 3 4 of the regular price. What is the sale price of the bicycle?
$540 is the sale price of the bicycle.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
Given that Kate wants to buy a new bicycle from a sporting goods store.
The bicycle she wants normally sells for $720
The store has a sale where all bicycles cost 3/4 of the regular price.
We have to find the sale price of the bicycle.
To find this we have to multiply 3/4 with 720
3/4×720
540
Hence, $540 is the sale price of the bicycle.
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What is the slope and y-intercept of the function y =- 5x 4?.
Due to the absence of an x in the issue, the y-intercept is -4. At the conclusion, it stands on its own and directs you to begin at (0,-4). The slope is -5/1 because the slope of the equation is toward the value of x in the equation.
How steep a slope does Y = - 5x 4 have?y = 5x - 4 has a 5 slope. The line's equation, y = 5x - 4, is expressed in the form y = mx + b, as you can see. It is therefore in slope-intercept form. When a line's equation is written in slope-intercept form, we may determine that the slope of the line equals m, the x-coefficient.
How do you calculate a function's slope and y-intercept?Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
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Which of the following rules describes the function graphed below? On a coordinate plane, points are at (negative 1, 1), (1, 2), (3, 3), (5, 4). a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3 Please select the best answer from the choices provided A B C D
Answer:
B. Output = (2)(Input) – 3.
Step-by-step explanation:
The correct answer is B. Output = (2)(Input) – 3.
This is because the function is a linear function, and the slope is 2 and the y-intercept is -3.
You can see this by considering the difference in y for each pair of points and the difference in x for each pair of points.
For example, from (negative 1, 1) to (1, 2) the difference in y is 1 and the difference in x is 2.
This means the slope is 1/2 which is the same as 2, and the y-intercept is -3
The ratio of consonants to vowels in a word is 7:5. Are there more vowels or consonants in the word?
Answer:
There are more consonants.
Step-by-step explanation:
The given ratio is
[tex]Consonants : Vowels\\& \\7:5[/tex]
To read the ratio given, simply understand which numbers refer to which term. In this case, it reads as:
For every 7 consonants, there are 5 vowels.*
There are 2 parts more consonants in comparison to the amount of vowels in the given word.
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multi step - ricky is saving money to buy a tv listed at 936$, he currently has 40$ , he charges 20$ for every lawn he mows , and he spends about 6 in gas for every three lawns he also has paper route which earns him 45$ per month in how many month will he have enough money is he mows three lawns per week
The number of months it will take Ricky to save enough money to buy the television listed, is 9.05 months
How to find the number of months ?First, find the number of months that it will take Ricky to have enough money to buy the television, first, find the amount he makes per month from lawn mowing :
= ( 3 x 20 ) - 6
= $ 54
When added to the paper route, this is:
= 54 + 45
= $ 99
The number of months he would take is:
= ( Price of television - Amount Ricky currently has ) / Amount earned per month
= ( 936 - 40 ) / 99
= 9.05 months
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Why does the operations subtraction and division Cannot be applied by commutative property and associative property?.
The commutative property and associative property do not hold for subtraction and division, as the end results are completely different after changing the order of numbers.
The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.
For example, 4 + 5 gives 9, and 5 + 4 also gives 9. The order of two numbers being added does not affect the sum. The same concept applies to multiplication too.
Thus, The commutative property and associative property do not hold for subtraction and division, as the end results are completely different after changing the order of numbers.
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The temperature changed at a constant rate between noon and 3:30 p.m. At what rate, in degrees F per hour, did the temperature change between noon and 3:30 p.m.? Show your work or explain your answer.
Answer:
To solve this problem, we need to calculate the change in temperature between noon and 3:30 p.m. and then divide that by the number of hours between noon and 3:30 p.m.
Let's say the temperature at noon was 70 degrees F and the temperature at 3:30 p.m. was 75 degrees F.
The change in temperature between noon and 3:30 p.m. is 75 - 70 = 5 degrees F.
The number of hours between noon and 3:30 p.m. is 3.5 hours.
Therefore, the rate of change in temperature between noon and 3:30 p.m. is 5 degrees F / 3.5 hours = 1.43 degrees F per hour.
How do you find the mean and standard deviation of a population distribution?.
The standard normal distribution (z distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. Any point (x) from a normal distribution can be converted to the standard normal distribution (z) with the formula z = (x-mean) / standard deviation.
In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.
Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.
The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.
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