Identify the error in this statement. ∛x/∛y. ∛y / ∛y =∛x y/y
[tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{x}{y} } }[/tex] is the correct form.
We need to find the error in the statement [tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{xy}{y} } }[/tex]
Starting from LHS of the statement, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}}[/tex],
we can cancel the like terms ∛y from the numerator and denominator.
So we get, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}[/tex]
Since both of the numerator and denominator has the cubic root, we can combine it.
That is, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}[/tex] = ∛(x/y) is the right answer.
So in this expression [tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{xy}{y} } }[/tex], y on the numerator is the error.
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Find the inverse of each function. Is the inverse a function? f(x)=√2 x+1
Inverse of the give function F(x) = √2 x + 1 is F⁻¹(x) = ( x - 1 ) / √2
Given is a function of x, F(x) = √2 x + 1
These question can be solved by following 4 easy steps
Step 1 : Switch the F(x) with the variable y
This implies, F(x) = √2 x + 1 becomes y = √2 x + 1
Step 2 : Interchange the variable x and y in the above obtained equation
This implies, from the equation y = √2 x + 1, we get
x = √2 y + 1
Step 3 : Solve the new obtained equation for y
This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.
x = √2 y + 1
=> x - 1 = √2 y
=> √2 y = x - 1
=> y = ( x - 1 ) / √2
Hence we obtain the required equation.
Step 4 : Switch the variable y with F⁻¹(x)
This implies, y = ( x - 1 ) / √2 becomes F⁻¹(x) = ( x - 1 ) / √2
Therefore, we get the inverse of the given function F(x) = √2 x + 1 as F⁻¹(x) = ( x - 1 ) / √2.
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Nicole has been offered a job at High Tech and a job at Best Computers. Which offer should she pick? Explain.
High Tech: $500 per week plus 5% commission
Best Computers; $400 per week plus 7.5% commission
The best option including the commissions is the Hight tech job.
How to find the offer to pick using the commissions?He was offered a job at high tech and Job at the best computers.
The options are as follows:
High Tech: $500 per week plus 5% commissionBest Computers; $400 per week plus 7.5% commissionThe offer that will be best option can be determined as follows:
High tech:
total salary per week = 500 + 5% of 500
total salary per week = 500 + 5 / 100 × 500
total salary per week = 500 + 25
total salary per week = $525
Best Computer:
total salary per week = 400 + 7.5% of 400
total salary per week = 400 + 7.5 / 100 of 400
total salary per week = 400 + 30
total salary per week = $430
Therefore, the best option including the commissions is the Hight tech job.
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someone plis help me with algebro 3 homeowrrok :((((((
Answer:
Step-by-step explanation:
Company A:
The recursive formula is, aₙ=aₙ₋₁+4,000, where a₁=42,000
Company B:
The recursive formula is, aₙ₊₁=(1+0.09) x aₙ, where a₁= 42,000
I'm sure she should go for company B, in the long run, she would make much more money. This is proven because company a is increasing using an arithmetic sequence; based on this all they're doing is adding 4,000. But company B is increasing at a percentage of 9 after a while that can really amount to a lot.
Hope this helps, if you are still confused don't hesitate to ask :))
Josie's pay [tex]a_n[/tex] from company A in the [tex]n[/tex]-th year is given recursively by
[tex]\begin{cases} a_1 = 42000 \\ a_{n+1} = a_n + 4000 & \text{for } n\ge1 \end{cases}[/tex]
while her pay [tex]b_n[/tex] from company B is
[tex]\begin{cases} b_1 = 42000 \\ b_{n+1} = 1.09 b_n & \text{for } n \ge1 \end{cases}[/tex]
From these recurrences, we have
[tex]a_2 - a_1 = 4000[/tex]
[tex]a_3 - a_2 = 4000[/tex]
[tex]a_4 - a_3 = 4000[/tex]
and so on - this is just confirming that the pay from company A increases at flat rate of $4000 each year.
Similarly,
[tex]b_2 = 1.09 b_1 = 45780 \implies b_2 - b_1 = 3780[/tex]
[tex]b_3 = 1.09 b_2 \approx 49900 \implies b_3 - b_2 \approx 4120[/tex]
[tex]b_4 = 1.09 b_3 \approx 54391 \implies b_4 - b_3 \approx 4491[/tex]
and we see here that [tex]b_n[/tex] increases at a larger rate year. In only 2 years of working at company B, Josie would be making more money, and the amount by which her salary increases each year is also increasing.
Assuming Josie hopes to make more money, invest in her future, etc, she should take the offer from company B.
what are the zeros of the function below f(x)= x^2-x-12/x^2+x-12
The function is equal to zero when x = -3 or +4
What are the zeros of a function?We know that a function is a mathematical rule. It is an instruction to perform an operation on a given set of values. In this case, we have the function given as; f(x)= x^2-x-12/x^2+x-12. Recall that the function is equal to zero when the numerator is equal to zero.
Now we have to solve the quadratic equation;
x^2-x-12 =0
x^2 - 4x + 3x - 12 = 0
x(x - 4) + 3(x - 4) = 0
(x - 3) (x - 4) =0
x = -3 or +4
We can now see that the function is equal to zero when x = -3 or +4
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determine what type of solutions the function f(x)=x^2+9 will have
Type of solutions the function f(x)=[tex]x^2[/tex]+9 will have Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}. Range is [-9,[tex]\infty[/tex]),{y|y≥-9}.
Given function [tex]f(x)=x^{2} +9[/tex]
To determine the function's domain and range.
Domain and range is nothing but the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. For instance, if the relation is R ={(1, 2), ( 2, 2), ( 3,3 ), ( 4, 3)}
Domain is the set of all x-coordinates with values of {1, 2, 3, 4}.
The set of all y-coordinates in the range is equal to {2, 3}.
Domain and range for the function is
Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}.
range is [-9,[tex]\infty[/tex]),{y|y≥-9}
Therefore, the function has the domain and range as
Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}.
range is [-9,[tex]\infty[/tex]),{y|y≥-9}.
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Need help , having trouble with this
Answer:
that would 14 jars LoL in of pop tarts
domain of 3 cubed of 1 minus x squared
What property has x (yz)
Answer:
The Distributive Law
Step-by-step explanation:
Here is a list of four fractions. 3/15 2/10 5/20 15/75 One of these fractions is not equivalent to 1/5
Answer:
5/20 is not equivalent to 1/5.
Step-by-step explanation:
We can start by simplifying all of the fractions, by finding numbers we can divide both the numerator and denominator by the same number.
[tex]\frac{3}{15} =\frac{1}{5}[/tex] by dividing by 3.
[tex]\frac{2}{10} =\frac{1}{5}[/tex] by dividing by 2.
[tex]\frac{5}{20} =\frac{1}{4}[/tex] by dividing by 5.
and last but not least
[tex]\frac{15}{75} =\frac{1}{5}[/tex] by dividing by 15.
We can see that 5/20 is the only one that equals to 1/4 when simplified.
Therefore, 5/20 is not equivalent to 1/5.
Hope this helped! Have a great day!
5. Lines and mare perpendicular. A point Q has this
property: rotating Q 180 degrees using center P has the
same effect as reflecting Q over line m.
a. Give two possible locations of Q.
b. Do all points in the plane have this property?
me
Lines and mare perpendicular is The same result is obtained by reflecting Q over the Line M as well as rotating Q 180 degrees using the center P.
As a reminder, perpendicular lines are those that cross at a 90-degree angle. Two non-vertical lines are said to be perpendicular when they are in the same plane and intersect at a right angle.
The axes of the coordinate plane, or the horizontal and vertical lines, are simply perpendicular to one another. Additionally, the slopes of the parallel lines have negative reciprocal slopes.
Since Lines L and M are perpendicular lines, or lines that meet at a right angle (90°), rotating Q 180 degrees using the center P has the same result as reflecting Q across Line M.
Q will therefore be identical to reflecting Q over any of the perpendicular lines when rotated 180 degrees from the center.
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Maintenance: When calculating time zone differences, you should always [answer] and [Answer] an hour for each time zone to the west.
Answer choices, divide, add, subtract or multiply.
When calculating time zone differences, you should always add and subtract an hour for each time zone to the west.
How to illustrate the information?A time zone is a region that adheres to a common standard time for social, commercial, and legal activities. Because it is easy for locations in frequent communication to preserve the same time, time zones typically follow the boundaries between countries and their subdivisions rather than rigidly following longitude.
The definition of every time zone is an offset from Coordinated Universal Time. For nearly half of the year, certain regions at higher latitudes observe daylight saving time, which is commonly accomplished by adding an hour to local time in the spring and summer.
It should be noted that the Time Zone gives an overview of current local times around the world. It should be noted that calculating time zones is simple and involves adding or subtracting an hour for every 15 degrees of longitude.
Therefore, when calculating time zone differences, you should always add and subtract an hour for each time zone to the west.
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Alicia ran 6 miles in 21 minutes. At this rate, how long will it take her to run 15
miles? Do not round
Answer:
52.5 minutes
Step-by-step explanation:
[tex]21/6=3.5\\3.5*15=52.5[/tex]
Answer: 52 minutes and 30 seconds
Step-by-step explanation:
You are going to do cross multiplication for this. So 6 miles over 21 minutes is equal to 15 miles over x minutes. When we cross multiply this brings us to 315 over 6. Then we divide 315 by 6 getting us 52.5 minutes and .5 of a minute is 30
The perimeter of a square is 20 centimeters. Find the length of a diagonal. Sketch the figure. Round decimals to the nearest tenth (1 decimal place).
length of a diagonal =
The length of the diagonal is 7.05cm of a square.
The perimeter of the square is 20 cm.
The formula of the perimeter of the square is 4a, where a is the length of the side of the square.
So, 4a = 20
a = 5
Now we have to find the diagonal of the square.
In a square there is two diagonal, each of equal length
Therefore,
diagonal = [tex]\sqrt{2}[/tex]a
= 1.41 × 5
7.05cm
Therefore the diagonal of the square is 7.05cm.
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2. Abby, Chantral, Dougie, Kajan, Minh, and
Zara are all in a race and are considered
to be equally fast. What is the probability
that Abby and Chantral will be the first two
finishers?
1414
Based on the Abby, Chantral, Dougie, Kajan, Minh, and Zara being equally fast, the probability that Abby and Chantral will be the first two finishers is 1/15.
How to find the probability?The probability that Abby and Chantral will be the first two finishers can be found by the formula:
= Number of successful outcomes where Abby and Chantral will be the first two finishers / Total number of outcomes
Solving gives:
= (21! - 4!) / 6!
= 48 / 720
= 1 / 15
In conclusion, the probability that Abby and Chantral will finish first is 1/15.
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Angles of Triangles #1: find the angles below
All the angles of the given triangle are;
∠1 = 41°
∠2 = 85°
∠3 = 95°
∠4 = 85°
∠5 = 36°
∠6 = 49°
∠7 = 106°
How to find Congruent Angles?We are given different angles. Thus;
∠3 will be equal to 95° because of the definition of vertically opposite angles.
∠4 = 180° - 95° because sum of angles on a straight line is equal to 180°. Thus;
∠4 = 85°
∠2 = ∠4 = 85° because they are both vertically opposite angles.
∠5 = 180° - 144° because sum of angles on a straight line is equal to 180°. Thus; ∠5 = 36°
∠7 = 180° - (38° + 36°) because sum of angles in a triangle is equal to 180°. Thus; ∠7 = 106°
Sum of angles in a quadrilateral is 360°. Thus;
∠1 = 360 - (90 + 144 + 85)
∠1 = 41°
∠6 = 180 - (90 + 41)
∠6 = 49°
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Gwendolyn draws a hotdog on graph paper using the scale shown below. The hotdog has a length of 999 units in the drawing. What is the length in c, m, , of the actual hotdog?
The length of the actual hotdog is 15 cm
How to determine the length of the actual hotdog?The graph that completes the question is added as an attachment
The length of the hotdog in the figure is given as
Length = 9 units
The scale is given as
Scale: 6 units = 10 cm
So, we have
6 * 9 units = 10 * 9 cm
Divide both sides by 6
So, we have
9 units = 15 cm
Substitute 9 units = 15 cm in Length = 9 units
Length = 15 cm
Hence, the length of the actual hotdog is 15 cm
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What are common factors of 18 roses and 30 what do they represent
The common factors of the numbers 18 and 30 is 6
How to determine the common factors of the numbers?The numbers are given as
18 and 30
Express 18 and 30 as a product of its factors
So, we have
18 = 2 * 3 * 3
30 = 2 * 3 * 5
Multiply the common factors in the above expression
Common factors = 2 * 3
Evaluate the product
So, we have
Common factors = 6
Hence, the common factors of the numbers 18 and 30 is 6
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answer for x
−8x=−x−28
Answer:
x = 4
Step-by-step explanation:
-8x = -x - 28
Move the -x on the right side to the left
-8x + x = -28
-7x = -28
Cross out the negatives
7x = 28
Divide by 7
x = 4
Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
[tex]-8x = -x - 28 \text{ / Add 8x}\\-8x + 8x = -x - 28 + 8x\\\to 0 = 7x - 28 \text{ / Add 28}\\0 + 28 = 7x - 28 + 28\\\to 28 = 7x \text{ / Divide by 7}\\\frac{28}7 = \frac{7x}7\\4 = x[/tex]
Each face of a cube is a square with a side length of 2 feet. what is the total area of all the faces on the cube?
The side length of each face of a cube is equal to 2 feet.
We know, Total surface area of a cube = 6a², where a is the side length of the cube.
Here, a = 2 feet
∴ Total surface area of the given cube is equal to
⇒ 6(2)²
⇒ 6(4)
⇒ 24 sq. ft.
∴ Total surface area of the given cube is 24 sq. ft.
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If 30% of my money is $15.00, how much is 75% of my money?
Answer: $1875
Step-by-step explanation:Take x as the amount of money you have. 30%=30/100. So, 30/100*x=15. x= 2500. So, 75% of x is 75/100 * 2500 = 1875$
The apparent brightness of stars is measured on a logarithmic scale called magnitude, in which lower numbers mean brighter stars. The relationship between the ratio of apparent brightness of two objects and the difference in their magnitudes is given by the formula
m₂-m₁=-2.5 log b₂ / b₁, where m is the magnitude and b is the apparent brightness.
The star Rigel has a magnitude of 0.12 . How many times brighter is Capella than Rigel?
Capella is 1.09 times brighter than Rigel.
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 =expression or equation
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations. Some of them are listed below.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)In the question given here to us,
We use the given formula:
[tex]m_2-m_1= -2.5log\frac{b_2}{b_1} \\[/tex]
Here, m1 = magnitude of Rigel = 0.12
m2 = magnitude of Capella =0
put the values in eq.
[tex]= > m_2-m_1= -2.5log\frac{b_2}{b_1} \\\\= > - 0.12 = -2.5log\frac{b_2}{b_1}\\\\= > 0.04 = log \frac{b_2}{b_1}\\ \\= > \frac{b_2}{b_1} = 10^{0.04} = 1.09 approx[/tex]
Hence, Capella is 1.09 times brighter than Rigel.
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I forgot how to do theseeeee!!
Answer:
y=3
Step-by-step explanation:
Step 1: Cross-multiply.
14/3y+5=3/y
14*y=3*(3y+5)
14y=9y+15
Step 2: Subtract 9y from both sides.
14y−9y=9y+15−9y
5y=15
Step 3: Divide both sides by 5.
5y/5=15/5
y=3
how do you compare 6.51326 and square root of 39
Answer:
6.51326 is greater than √38
Step-by-step explanation:
6.51326 compared with √39
6.51326 compared with 6.244998
means 6.51326 is greater than √38
What is 5,780 divided by 240 as a decimal?
A 24.083324
B 24.08324,083
C 24.08324
D 24.083
Answer:
answer is D
how ?
when doing long division it will give 24.0833333333 so to 3dp is 24.083
There are 4 white and 8 red roses in a bouquet. Find the ratios.
the ratio of the number of all roses to the number of red roses
Answer: White rose ratio: 4/12 (simplify) Red rose ratio: 8/12 (simplify)
But you ask for total then red rose so 12/8
Step-by-step explanation: 4+8=12 That is total number of roses. You have 4 white rose so 4 out of 12. Have 8 red rose so 8 out of 12
A fair coin comes up 'heads' 50% of the time. If we toss such a coin eight times in a row, what is the probability, written as a percentage, that exactly five of those tosses are 'heads'?
Answer:
21.875%.
Step-by-step explanation:
This is a Binomial Probability Distribution.
Prob (exactly 5 heads) = 8C5(0.5)^5(0.5)^3
= 56 * 3.90625 * 10^-3
= 0.21875
= 21.875%.
Solve using the Quadratic Formula. 5 x²+x=3
The correct answer of the question is {-1+√61}/ 10 or {-1-√61}/ 10 .
The given quadratic equation is 5 x²+x=3
First, we have to convert the equation in the form
ax² + bx + c = 0, then apply the quadratic formula i.e.
x = {-b±√(b²- 4ac)}/ 2a .
Now,
5 x²+x=3
⇒ 5 x²+ x - 3 = 0
Here, a = 5, b = 1 and c = -3
Now, applying quadratic formula
{-b±√(b²- 4ac)}/ 2a
= {-1±√(1²- 4 × 5 × -3)}/ (2 × 5)
= {-1±√(1 + 60)}/ 10
= {-1±√61}/ 10
= {-1+√61}/ 10 or {-1-√61}/ 10
Therefore the final answer to the given equation is is {-1+√61}/ 10 or {-1-√61}/ 10 .
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Write each expression in exponential form. -√17
The number -√17, expressed as a value or number exponential is -17¹/².
What are exponentials?An exponential number is a mathematical expression and one of the many mathematical operations of reduction, it involves the successive multiplication of a number, it has the form:
aᵇ
Where:
a is the number that is multiplied by itself known as the baseb is the number of times it is multipliedTo convert a root into a exponential we must know the way in which these are related, and it is by means of the following property:
√a = a¹/²
Now in our case we have -√17 which can be expressed as.
(-1)√17, where 17 = a, then
(-1)17¹/²
-17¹/²
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Please help me with this!!! Will give Brainliest!
Answer:
Step-by-step explanation:
Perimeter = 110 in
Area = 490 in²