The value of the expression [tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex] after rationalizing the denominator is [tex]\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex].
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a cube root or a square root, from the fraction's denominator to its numerator (numerator).
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex]
Now, let [tex]a=\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex]
[tex]a=\frac{(x^{2}y)(y^{3})}{2\sqrt[3]{5} (x^{2}y)(x^{5})}[/tex]
[tex]a=\frac{y^{3}}{2\sqrt[3]{5} {~}x^{5} }[/tex]
To rationalize the denominator we multiply and divide the expression by ( ∛5 )².
[tex]a=\frac{y^{3}}{2\sqrt[3]{5} {~}x^{5} } \times \frac{(\sqrt[3]{5})^{2}}{(\sqrt[3]{5})^{2}}[/tex]
[tex]a=\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex]
The value of the expression when rationalized [tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex] is [tex]\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex].
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I need to find the mean of -2, 20, -200, 2,000
Answer: 454.5
Step-by-step explanation:
-2, 20, -200, 2,000 ==> 4 numbers
Mean: (-2+20+(-200)+2000)/4=
(18-200+2000)/4=
(-182+2000)/4
1818/4=454.5
Please help me with these questions!
Since slopes m₁ and m₂ are equal to 5, it shows that these two lines are parallel.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + b
Given the following equations:
y = 5x + 1
2y - 10x + 3 = 0 ⇒ y = 5x - 3/2
m₁ = m₂ = 5.
In this context, we can reasonably infer and logically deduce that these two lines are parallel.
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Complete Question:
The equation line L₁ is y = 5x + 1
The equation line L₂ is 2y - 10x + 3 = 0
Show that these two lines are parallel.
Let u = (-1,3), v=(2,4) , and w= ( 2,-5) . Find the component forms of the following vectors. 2u
Given u = (-1,3), v=(2,4) , and w= ( 2,-5), then, by applying scalar multiplication on vector, 2u = (–2, 6)
In the two-dimensional coordinate system, vectors can be split into x-component and y-component.
We can write, for example, a vector q = (1,–5), which means:
x-component = 1
y-component = –5
Operations on vectors:
Addition / subtraction of vectors: Just add or subtract the corresponding components.In the given problem:
u = (-1,3), v = ( 2,4) , and w = (2,-5)
Then,
2u = 2 (-1,3)
= (2 . (-1), 2. 3) = (–2, 6)
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I am a 5-digit number between 52,000 and 53,000. The sum of my digits is 21. My ones digit is a multiple of 3. My tens digit is equal to my hundreds digit.
Read the clues. Find the number
Step-by-step explanation:
5 digit number
5abcd
a = 2 or a = 3. but a = 3 means the upper limit of 53,000. and the sum of digits is 8 and not 21.
so, a = 2.
d = 3n
c = b
5 + a + b + c + d = 21
5 + a + 2b + 3n = 21
a + 2b + 3n = 16
2 + 2b + 3n = 16
2b + 3n = 14
so, n must be an even number to allow an even result (14). therefore, n = 0 or n = 2 (any larger even number n like 4 would not create a single digit result)
if n = 0, then 2b = 14, b = 7
if n = 2, then 2b + 6 = 14, 2b = 8, b = 4
so, we have the options
52770
52446
I suspect that 0 as 0×3 is not considered a multiple of 3 by your teacher, so only n = 2 (or d = 6) is a desired solution.
therefore, I would use
52446
as answer.
help me
In your own words explain the vision statement for vision 2030
list the four main goal of vision 2030
The goals of the vision statement for vision 2030 include:
a vibrant society, a thriving economy an ambitious nation.secure environmentWhat is vision 2030 about?The creation of a climate that opens up business opportunities, broadens the economic base, and generates jobs for all Saudis is a primary objective of Vision 2030. By utilizing the country's special position and potential, luring the top talent, and boosting international investment, we will be able to accomplish this.
It should be noted that the vision is to bring about an economy that's prosperous. Therefore, goals of the vision statement for vision 2030 include:
a vibrant society,
a thriving economy
an ambitious nation.
secure environment
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There are approximately 9.3 x 106 dairy cows in the United States, with each cow producing approximately 2.5 x 10 gallons
of milk each year. How much milk do United States dairy cows produce each year? Write the answer in scientific notation
2.4645×10⁴ gallons of milk do United States dairy cows produce each year.
Why we need scientific notation ?We need scientific notation reason is large number can be written in compact form.
According to the given question There are approximately 9.3 x 106 dairy cows in the United States.
Which is 985.8 cows in the united states.
Also given each cow produces 2.5×10 = 25 gallons of milk per year.
∴ United state cows will produce (985.8×25) gallons of milk each year which is = 24645 gallons of milk per year.
Now 24645 can be represented as 2.4645×10⁴ gallons of milk.
We have raised it to the 4th power of 10 because we have moved the decimal 4 digits before to balance the number and we know that in scientific notation base should be greater than 1 and less than 4 so moving the decimal to some other place is not valid.
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Use the diagram to answer the questions below
The measure of ∠B is 60°
The measure of ∠H is 135°
The length of AB is 2cm
From the question, we are to determine the measure of the angles and the length of line AB.
From the given information, we have that
Quad ABCD. is similar to Quad, EFGH
In the diagram,
Measure of ∠F = 60°
But, ∠B ≅ ∠F
∴ The measure of ∠B = 60°
Measure of ∠H
∠E + ∠F + ∠G + ∠H = 360° (Sum of angles in a quadrilateral)
From the diagram,
m ∠E = 90°
m ∠F = 60°
∠G ≅ ∠C
m ∠C = 75°
∴ m ∠G = 75°
Thus,
90° + 60° + 75° + ∠H = 360°
225° + ∠H = 360°
∠H = 360° - 225°
∠H = 135°
Hence, the measure of ∠H is 135°
Length of AB
The length of HE is twice the length of DA,
Thus,
The length of EF will be twice the length of AB
From the diagram,
EF = 4cm
∴ AB = 4/2 cm
AB = 2 cm
Hence, the length of AB is 2cm
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Which of the following is the slope-intercept form of 9x + 3y – 15 = 0?
Answer:
y = -3x + 5
Step-by-step explanation:
slope-intercept form means it should look like
y = mx + b
9x + 3y – 15 = 0
3y = -9x + 15
y = -3x + 5
Simplify (-6b)(-18b) please!!!
Answer:
108b^2
Step-by-step explanation:
(-6)(-18)=108
(b)(b)=b^2
108b^2
Use the properties of logarithms to write log 18 in four different ways. Name each property you use.
The logarithmic properties used are Quotient property, Product property, Power property and Product and Power Property.
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
log 18
now, log 18 can be written in following four ways :
1. Using Quotient Property of logarithms
[tex]log 18 = log \frac{36}{2} = log 36 - log 2[/tex]
2. Using Product Property of logarithms
[tex]log 18 = log (9.2) = log 9+ log2[/tex]
3. Using Power Property of logarithms
[tex]log 18 = log (324)^\frac{1}{2} = \frac{1}{2} log (324 )[/tex]
4. Using Product and Power Property of logarithms
[tex]log 18 =l og 2.3^2 = log 2 +2log3[/tex]
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If z=30 when x=3 and y=2 , write the function that models the relationship.
z varies inversely with the product of x and y .
The required function following the given conditions is z = 180 / (x × y).
What is a function?
A function is defined as an expression or rule that specifies the relationship between two variables or objects, out of which one is dependent and the other is an independent variable. The image of each and every element is unique.
Writing the function satisfying the given conditions
Given, x = 3, y = 2, z = 30
Let the function satisfying the given conditions be z = k / (x.y) —--- 1
Putting all the values, we get,
k = 3 × 2 × 30
= 180
Using the value of k in equation 1, we have,
z = 180 / (x × y)
Hence, the required function is z = 180 / (x × y).
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Can someone please help me with this i been working so long with this
Answer:
12
Step-by-step explanation:
since both are square it is 12
a train can travel 50% faster than a car.both start from point A at the same time and reach point B 75kms away from A at the same time . on the way ,however, the train lost about 12.5 minutes while stopping at the stations . the speed of car is? a.100kmph b.110kmph c.120kmph d.130kmph
what is the distance (2,-2) and (-3,-1) points
The distance between two points (2,-2) and (-3,-1) is √26 units.
Given points are (2,-2) and (-3,-1)
Let A(2,-2), B(-3,-1)
We need to calculate the distance between two points.
We know that distance between two points means the length of the line segment that connects two points in the 2D plane.
The formula for finding the distance between the two points A(x₁, y₁),
B(x₂, y₂) in a plane is given by
D = √((x₂ - x₁)² + (y₂ - y₁)²)
Now we have two points A(2,-2), B(-3,-1)
By using the above formula we get the distance as
D = √((-3 - 2)² + (-1 - (-2))²)
D = √((-5)² + (-1+2)²)
D = √(25 + (1)²
D = √(25+1)
D = √26 units
∴ The distance between two points (2,-2) and (-3,-1) is √26 units.
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(please help) a couple with 32 children want to save for college. They invest 50,000 in two different corporate bonds for 1 year One bond pays 5% simple interest while the other pays 6.5% simple interest. The total interest they received from the bonds was $3000. Find the amount they invested in each bond
The amount invested in the bond with 5% simple interest is $16,666.67
The amount invested in the bond with 6.5% simple interest is $33,333.33
What is simple interest?
The interest earned under a simple interest arrangement is determined as the amount invested multiplied by the interest rate and the time the investment lasts
I=PRT
let us assume that x was invested in the bond with 5%
interest on x=5%*x=0.05x
amount invested in other bond=50000-x
interest earned on 6.5%=(50000-x)*6.5%
interest earned on 6.5%=3250-0.065x
total interest=0.05x+3250-0.065x
total interest=3250-0.015x
total interest=3000
3000=3250-0.015x
0.015x=3250-3000
0.015x=250
x=250/0.015
x=$16,666.67
amount invested at 6.5%=$50,000-$16,666.67
amount invested at 6.5%=$33,333.33
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Four different linear functions are represented below.
HELP!
Answer:
Step-by-step explanation:
A: Function 2 only; at the point where x = 0, the value of the function is 5, which is greater than 3.
B: Function 3; the coefficient of x is the greatest out of all of them.
C: Function 4; the y-intercept of -1 only deviates from 0 by 1.
can anyone help fast please
The rate at which Riya is applying mulch in m³/m² is 0.25m³/m²
From the question, we are to determine the rate at which Riya is applying mulch in m³/m²
From the given information, we have that
Riya is applying mulch to her garden at a rate of 250,000 cm³ of mulch for every m² of the garden space
That is,
The rate at which she is applying mulch is 250,000 cm³/m²
Now, to determine the rate in m³/m², we will convert 250,000 cm³ to m³
Converting 250,000 cm³ to m³
250,000 cm³ = 250000 × (10⁻²)³ m³
= 250000 × 10⁻⁶ m³
= 0.25 m³
Hence, the rate at which Riya is applying mulch in m³/m² is 0.25m³/m²
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Henry and emma want to buy a total of 0.5 yds of fabric. the fabric costs $8.72 per yard. how much will each pay if they want to split the cost evenly? $1.09 $2.18 $2.36 $4.36
If Henry and Emma want to buy a total of 0.5 yds of fabric and the fabric costs $8.72 per yard then the amount each will pay if they want to split the cost evenly is equal to $2.18.
The amount Henry and Emma will have to pay if they want to split the cost can be calculated by using division.
First, we calculate the cost of 0.5 yards of fabric.
1 yard of fabric cost = $8.72
0.5 yards of fabric cost = x
Here x is the cost of 0.5 yards of fabric
8.72 × 0.5 = x
x = $4.36
As the cost of 0.5 yards of fabric is calculated to be $4.36, the amount each will pay if they want to split the cost evenly can be found by dividing the cost of 0.5 yards by 2.
cost of 0.5 yards of fabric / 2 = 4.36 / 2 = $2.18.
Hence each one of them will pay $2.18 if they want to split the cost evenly.
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Which Of the expressions below means same as w/5
The expression that means the same as the given expression is w ÷ 5
Evaluating an expressionFrom the question, we are to determine which of the given expressions means the same as w/5
To do this, we will simplify each of the given expressions if possible
w + 5This expression cannot be simplified further
w -5This expression cannot be simplified further
w ÷ 5This expression can be written as w/5
5 × wThis expression can be written as 5w
5 - wThis expression cannot be simplified further
5 ÷ wThis expression can be written as 5/w
Hence, the expression is w ÷ 5
Here is the complete question:
Which Of the expressions below means same as w/5
w + 5
w - 5
w ÷ 5
5 × w
5 - w
5 ÷ w
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Write the function that models each variation. Find z when x=4 and y=9 . z varies inversely with the product of x and y . When x=2 and y=4, z=0.5 .
The value of z in the given inverse variation is, z= 1 / 9
What is Inversely variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.
In the question given,
first of all find the value of K in the model by putting in the values of x, y, and z so that to find the function model.
z = k / (x) (y)
0.5 = k / (2) (4)
k = 4
now write the function equation again by putting value of k,
⇒ z = 4 / (x) (y)
put x = 4 and y = 9 to find the value of z.
z = 4 / 36
z = 1 /9
Thus, z = 1/9
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Which is an equivalent expression for this please
Suppose that a function pairs elements from set A with elements from set B . Recall that a function is called onto if every element in B is paired with at least one element in A .
c. For the domain, is the function onto the set of nonnegative real numbers? Explain.
If a function is onto, then its domain can be a set of all non negative real numbers if the function is defined as y = √ x.
It is not necessary that function that is onto should have the domain as non negative real numbers only.
It can also have negative real numbers in its domain.
If the function is of the form:
y = √ x
Then the function will have a domain that is non negative real numbers.
But if function is of the form:
y = x²
Then it can have the domain as all real numbers.
Therefore, we get that, if a function is onto, then its domain can be a set of all non negative real numbers if the function is defined as y = √ x.
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Look at the following conditionals:
If Vivian is eating pizza, then she is at Big Slice Pizza.
If Vivian is at Big Slice Pizza, then she is eating pizza.
Is the second conditional the contrapositive, converse, or inverse of the first cond
contrapositive
converse
inverse of the first conditional
Answer:
inverse I believe because it is the same statement but opposite
The scale on a map is 1:500000
Two towns are 7cm apart on the map
Work out the actual distance between the towns. Give your answer in kilometres
Answer:
Step-by-step explanation:
1: 500,000 cm
500,000cm can also be written as 5000m or 5 km
So it becomes 1:5km
the 1 represents 1cm on the map so every centimeter in the map is 5 kilometers in real life
If we want to get what 7 cm would be in kilometers then we have to multiply both sides by 7.
So it would be 1 x 7 and 5x 7
it would end up being 7 : 35 km
The answer is: 35km
please answer, posted picture
The required solution of the given system of equation is y=2-9x and y=x/2-1.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The is given system of equation
2-9x=x/2-1
According to given question we have
The equation is
2-9x=x/2-1
We have to split into different system of equation to find the solution of the problem we have
So,
y=2-9x
and
y=x/2-1
Therefore, the required solution of the given system of equation is y=2-9x and y=x/2-1.
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Triangle JOY is transformed to produce triangle PEP.
Select all of the transformations that would guarantee triangles JOY and PEP are congruent.
(A) a dilation, then a translation
(B) a translation, then a reflection
(C) a reflection, then a rotation
(D) a reflection, then a dilation
(E) a rotation, then a translation
The transformations that would guarantee triangles JOY and PEP are congruent are
(B) a translation, then a reflection(C) a reflection, then a rotation(E) a rotation, then a translationHow to select all of the transformations that would guarantee triangles JOY and PEP are congruent?The given parameters are:
Triangles JOY and PEP
From the question, we understand that:
The triangles are congruent after being transformed
The transformations that ensure congruency are rigid transformation
The rigid transformations are:
TranslationReflectionRotationUsing the above as a guide, we have the true options to be:
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E is the midpoint of segment DF. if DE = 3x and EF = 18, find the value of x.
The value of x is 6 if E is the midpoint of the segment.
Given,
E is the midpoint, so DE = EF
DE = 3x
EF = 18
Since DE = EF,
3x = 18
x =18/3
x = 6
If x = 6 , then
DE = 3x
DE = 3(6)
DE = 18
therefore, DE = EF since E is the mid point.
EF = 18
hence we get the value of x as 6.
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O...
photo.
Write in standard notation.
1. 2.3 x 102
2. 4.67 x 107
3. 9.1 x 10-5
4. 1.2 x 10⁰
5. 5x10
The standard notation for the given terms is (1). 234.6; (2). 499.69; (3). 86; (4). 1.2; (5). 50.
What is standard notation?A standard notation is a set of rules for writing a given number, equation, or expression.To represent large or small numbers, a standard form of a number is used. In standard notation, exponents are used to represent such numbers.As a result, to represent very large or very small numbers in a concise manner, we use standard notation.Depending on the mathematical concept, the standard notation will differ.Conversion of the different notation into standard notations is given below:
1. 2.3 x 102 = 234.6
2. 4.67 x 107 = 499.69
3. 9.1 x 10-5 = 86
4. 1.2 x 10⁰ = 1.2
5. 5x10 = 50
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8. Find y
7yº
(5y+36)
Answer:
35ºy^2+252yº
Step-by-step explanation:
Ann and Ben translate documents from German into English. A set of documents that would take Ann 10 days would take Ben 12 days. Ann starts to translate the documents. After 2 days Ann and Ben both work on translating the documents. How many more days will it take to complete the work? You must show your working. Answer:
Using the together rate, it will take more 3.45 days to complete the work.
What is the together rate?The together rate is given by the sum of each separate rate.
For this problem, the rates are given as follows:
Ann: 1/10 = 0.1.Ben: 1/12 = 0.0833.Together: 1/x.Hence the amount completed in 2 days is:
2 x (0.1 + 0.0833) = 0.3666.
The amount it would take them to complete 100% of the project working together is found by the together rate as follows:
[tex]\frac{1}{x} = \frac{1}{10} + \frac{1}{12}[/tex]
[tex]\frac{1}{x} = \frac{6 + 5}{60}[/tex]
x = 60/11
x = 5.45 days.
The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is:
0.6334 x 5.45 = 3.45 days.
It will take more 3.45 days to complete the work.
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