Answers
First you should reduce the fraction
Subtract the exponent by its common variables;
x^8 - x^2 = x^6
y^9 - y^4 = y^5
Now your equation should be \frac{ \sqrt{6x^{6}y^{5} } }{ \sqrt{5} }
Then you should simplify your radical,
there are 3 groups of 2 in the x variables and 2 groups of 2 in the y variables, as a result, the x and y go outside the square root, and one y variable remains in the root (as there wasn't enough y's to make another group of 2) this should be over 5
Related Questions
ΔABC and ΔXYZ are similar triangles. If BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x, find the value of x.
Answers
Answer:
-3/2 or -1.5
Step-by-step explanation:
-3/2 = -1.5
BC = -1.5 + 7 = 5.5
AC = -1.5 + 6 = 4.5
YZ = 4 - (-1.5) = 5.5
XZ = 3 - (-1.5) = 4.5
Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:
Answers
Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0
We calculate
[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)
Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)
The required value of elasticity at x = 65 is -0.007.
Given that,
The demand equation for a certain item is [tex]1p + 1x^{2} -160 = 0[/tex].
We have to determine,
The value of elasticity at 65.
According to the question,
The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.
Therefore,
Price of elasticity = [tex]\frac{dp}{dx}[/tex]
Calculate change by differentiation with respect to p:
[tex]\dfrac{d(p+x^{2} -160)}{dx}\\\\1 + 2x\frac{dp}{dx} = 0\\[/tex]
Then,
[tex]E(x) = \frac{dp}{dx} = \frac{-1}{2x}[/tex]
Therefore, The elasticity at x = 65 is ,
[tex]E(65) = \frac{-1}{2(65)} = -0.007[/tex]
Hence, The required value of elasticity at x = 65 is -0.007.
For more information about Elasticity click the link given below.
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The probabilities for four different simple events are given. Of the four, which is MOST LIKELY to occur?
A. 0.5
B. 0.9
C. 0.35
D. 0.0100
Answers
100%=1 so the number closes to 1 is the most likely
we can't have a probility of more than 1 so we can say that the greatest number is most likely
if we rank the numbers we get
0.9>0.5>0.35>0.00100
so the answer is B. 0.9 which is equivilent to an 90% chance of the event occuring
A marketing firm conducts a survey to find out how many people use a product. One hundred people are contacted for the study and fifteen confirm that they use the product. Which describes the survey?
The marketing firm is going forward in time and observing groups sharing common factors.
The marketing firm is applying some treatment to the subjects and then proceeding to observe its effect on the subjects.
The marketing firm is observing and measuring specific characteristics of the subjects, but is not attempting to modify the subjects.
The marketing firm is going back in time to collect data over some past period
Answers
The marketing firm is observing and measuring specific characteristics of the subjects, but is not attempting to modify the subjects.
Final answer:
The marketing firm's survey, where a sample of people is asked if they use a product, is an example of survey research aimed at observing and measuring characteristics without attempting modification. This cross-sectional study helps understand consumer behavior. (Option C)
Explanation:
The survey described by the marketing firm where one hundred people are contacted and fifteen confirm that they use the product is an example of survey research, which is a quantitative research method. In this survey, the firm is observing and measuring specific characteristics of the subjects, but not attempting to modify the subjects. This type of survey can help the firm in understanding consumers' preferences, tastes, attitudes, and behaviors regarding the use of the product. They are not applying any treatment to the subjects or observing them over time as would be done in a longitudinal study. Instead, they're conducting a cross-sectional survey at a single point in time. (Option C)
what is the equation for horizontal line through the point (0,3)?
Answers
The y-intercept is three and there is no slope.
Hope this helps!
The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr a cylinder with a circumference of about 63 mm a cylinder with a circumference of about 126 mm a cone with a base circumference of about 63 mm a cone with a base circumference of about 126 mm
Answers
The shape and the circumference of the base created by the rotation is; Cone and Circumference of 63 mm
What shape is created by rotation?We are given;
Each side of equilateral triangle = 20 mm
Now, when the triangle is rotated about the line ‘a’ which passes through the midpoint of any of the 3 sides of the equilateral triangle we will get a conical shape.
The distance from the line a which cuts one side of a triangle to one vertex of the triangle is the radius = 10 mm
We know that;
Circumference of a circle = 2πr
Thus;
C = 2 × 3.14 × 10
C = 6.28 × 10
C = 62.8 mm
C = 63 mm
Thus, the approximate circumference of the base is 63 mm.
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John likes 400 but not 300; he likes 100 but not 99; he likes 3600 but not 3700. Which does he like?
o 900
o 1000
o 1100
o 1200
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which constant term would mean that the expression is completely factored x ^ 2 - 3x +
-10
0
10
Answers
To completely factorize [tex]\(x^2 - 3x + c\),[/tex]the correct constant term is 10. With this, the expression becomes [tex]\((x - 2)(x - 5)\),[/tex] achieving complete factorization.
To find the correct constant term that would allow for complete factorization of the quadratic expression [tex]\(x^2 - 3x + c\),[/tex] let's consider what it means to factorize a quadratic expression:
A quadratic expression can be factored if it can be represented in the form [tex]\((x - a)(x - b)\),[/tex] where a and b are the roots of the expression. Given the original expression [tex]\(x^2 - 3x + c\),[/tex] we can expand [tex]\((x - a)(x - b)\)[/tex] and then compare coefficients to determine the constant term c.
Expanding [tex]\((x - a)(x - b)\)[/tex] :
- [tex]\((x - a)(x - b) = x^2 - (a + b)x + a \cdot b\).[/tex]
Comparing Coefficients :
- By comparing with [tex]\(x^2 - 3x + c\),[/tex] we can identify that [tex]\(a + b = 3\)[/tex] (the coefficient for [tex]\(x\)[/tex] and [tex]\(a \cdot b = c\)[/tex] (the constant term).
- Given \(a + b = 3\), let's find possible values for a and b that would yield a correct factorization:
- Consider [tex]\(a = 1\), \(b = 2\):[/tex] Then [tex]\(a \cdot b = 1 \times 2 = 2\),[/tex] which is different from the given constant \(c\).
- Consider [tex]\(a = -2\), \(b = -5\):[/tex] Then [tex]\(a \cdot b = -2 \times -5 = 10\),[/tex] suggesting that [tex]\(c = 10.[/tex]
- Consider [tex]\(a = 5\), \(b = 2\):[/tex] Then [tex]\(a \cdot b = 5 \times 2 = 10\),[/tex] also suggesting [tex]\(c = 10\).[/tex]
Considering this process, the correct answer that would allow for complete factorization of the given expression [tex]\(x^2 - 3x + c\)[/tex] is 10:
Thus, the factorization of [tex]\(x^2 - 3x + 10\)[/tex] results in [tex]\((x - 2)(x - 5)\),[/tex] suggesting that the constant term in question should be 10.
The complete question is : Which constant term in the expression [tex]\(x^2 - 3x + c\)[/tex] would allow it to be completely factored? Consider the possible values of c and determine which would result in a fully factored form. Options: -10, 0, 10.
The correct constant term that completes the factoring of the expression [tex]\( x^2 - 3x + \ ? \)[/tex] is 10.
To find the constant term that completes the factoring of the quadratic expression [tex]\( x^2 - 3x + \ ? \)[/tex], we can follow these steps:
Understand that when factoring a quadratic expression of the form [tex]\( ax^2 + bx + c \)[/tex], we are looking for two numbers that multiply to ( ac ) and add to ( b ).
In our case, ( a = 1 ), ( b = -3 ), and ( c ) is the constant term we're looking for.
Since ( a ) is 1, we need to find two numbers that multiply to ( c ) and add up to ( -3 ).
These two numbers are the factors of ( c ).
Given that the constant term ( c ) is the term that doesn't include ( x ), it will be the product of these two factors.
To find the constant term, we can factorize the expression ( ac ), where ( a = 1 ) and ( c ) is the constant term.
Once we find the factors of ( c ), we can test different values until we find the correct one that makes the expression factorable.
Let's start by factoring ( ac ):
Since ( a = 1 ), and ( b = -3 ), we have ( ac = c ).
Given that the product of the factors should be ( c ), and the factors should add up to ( -3 ), we can find the factors of ( c ) by trial and error.
Let's try different values of ( c ) and see which one works:
If ( c = 10 ), the factors of ( c ) would be 1 and 10. However, 1 + 10 = 11, not -3.
If ( c = -10 ), the factors of ( c ) would be -1 and 10. However, -1 + 10 = 9, not -3.
If ( c = -10 ), the factors of ( c ) would be 1 and -10. However, 1 + (-10) = -9, not -3.
If ( c = 10 ), the factors of ( c ) would be -1 and -10. However, -1 + (-10) = -11, not -3.
If ( c = 0 ), the factors of ( c ) would be 0 and 0. However, 0 + 0 = 0, not -3.
Based on these trials, we see that none of the values satisfy the condition of adding up to -3.
Therefore, the correct constant term that completes the factoring of the expression [tex]\( x^2 - 3x + \ ? \)[/tex] is 10.
Vicente is watching a movie that last 1 hour and 37 minutes you watch 52 minutes of our how many minutes are left in the movie
Answers
Hope this helps
What is the change in temperature between -8°c and 3°c ?
Answers
help me pls i need to pass
Answers
The surface area (S) of a rectangular prism is given in terms of its length (L), width (W), and height (H) as
... S = 2(LW +WH + LH)
Substitute your numbers and do the arithmetic.
... S = 2(7.2·10 + 10·6.3 + 7.2·6.3)
... = 2(72 + 63 + 45.36)
... = 2·180.36
... = 360.72 . . . . square inches
3^2·3^5·3^-3 Please help.
Answers
Can somebody solve this system equation using addition please?
-4x-5y=7
3x+5y=-14
I can’t solve it and it’s due tomorrow for my math class also please show work on how you’ve solved it
Answers
-4x - 5y = 7
3x + 5y = -14
You can add these two equations together straightaway since the y-terms have opposite coefficients.
-4x - 5y = 7
3x + 5y = -14
+___________
-x - 0 = -7
-x = -7
x = 7
Substitute 7 for x into either of the original equations and solve algebraically to find y.
3x + 5y = -14
3(7) + 5y = -14
21 + 5y = -14
21 = -14 - 5y
35 = -5y
-7 = y
Finally, check work by substituting both x- and y-values into both original equations.
-4x - 5y = 7
-4(7) - 5(-7) = 7
-28 + 35 = 7
7 = 7
3x + 5y = -14
3(7) + 5(-7) = -14
21 - 35 = -14
-14 = -14
Answer:
x = 7 and y = -7; (7, -7).
You own a coffee shop where a cup of coffee costs $2.10. Your cost on the cup of coffee is $0.30. Calculate the margin per cup of coffee.
Answers
Profit margin = 1.8/2.1 x 100 = 85.71%
Answer: 85.71%
If a bank has total deposits of $7,700 and reserves of $2,100: instructions: round to the nearest whole number. (a) what is its current reserve ratio? % (b) how large is its loan portfolio (outstanding loans)? %
Answers
b.What is the total amount of loans? _Loans = $7,500 - $2,000 = $5,500_
Use synthetic division and the Remainder Theorem to find P(a)
P(x)=x^4+3x^3-6x^2-10x+8 ; a=2
28
–16
2
4
Answers
P(2)=16+3(8)-6(4)-20+8
P(2)=16+24-24-20+8
P(2)=4
P(a)=4
Answer: Fourth option. 4
Using synthetic division and the Remainder Theorem, we find that P(a) for P(x) when a=2 is P(2)=4, which is the remainder of the synthetic division.
To find P(a) for the given polynomial P(x)=x⁴+3x³-6x²-10x+8 when a=2, we can use synthetic division. The Remainder Theorem states that the remainder of the division of a polynomial by a linear divisor (x - a) is equal to P(a).
Let's perform the synthetic division:
Write down the coefficients of P(x): 1, 3, -6, -10, 8.Write the value of a below the synthetic division bar: 2.Bring down the leading coefficient: 1.Multiply this coefficient by a and write the result below the next coefficient: 1 * 2 = 2. Add this to the next coefficient: 3 + 2 = 5.Repeat this process for all coefficients.The synthetic division should look like this:
2 | 1 3 -6 -10 8| 2 10 8 -4
|_____________________
1 5 4 -2 4
The final number in the bottom row is the remainder, which is also P(2). So, P(2)=4.
the cost of internet access at a cafe is a function of time the cost for 8, 25, and 40 minutes are shown write the equation in slope-intercept form that represents the function then find the cost of surfing the web at the cafe for one hour
Answers
Answer:
?
Step-by-step explanation:
Where is the graph?
Last year 40 people adopted a manatee through Fia's Foundation.This year 30% more people adopted a manatee. How many more people adopted a manatee this year ?
Answers
[tex]30 / 100 = 0.3[/tex]
The problem can be solved with the following equation:
[tex]0.3(40) = difference[/tex]
Multiply 0.3 by 40.
[tex]0.3 * 40 = 12[/tex]
12 more people adopted a manatee this year.
Q10 Q6.) Find a set of parametric equations for the line that passes through the given points
Answers
See picture below for the answer!
The correct answer is option A
Q10 Q2.) Find the standard form of the equation of the parabola satisfying the given conditions.
Answers
1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:
Focus: (-1,4) and Directrix: y=2
2. Therefore you have:
√(x0-(-1))²+(y0-4)²=|y0-2|
(x0+1)²+(y0-4)²=(y0-2)²
3. When you simplify the expression above and clear y0, you obtain:
y0=y
y=1/4(x²+2x+13)
y=(x²/4)+(x/2)+(13/4)
Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)
a band that will be the opening act for a concert charges a $700.00 flat fee as well as 16% of all ticket profits from ticket sales. if the band earned $1,200, how much was made in total ticket sales for the show?
Answers
1. Subtract the flat fee 1,200-700 =500
2. 500 is what just the band made. Divide that by .16 (16%) to get the total ticket amount... 500 divided by .16 = 3,125
The total ticket amount was $3,125.
PLEASE PLEASE HELP ASAP
Answers
BC = m
AC = 18
AD = 11
DC = 7
We will name the some angles as follows:
∠ACB = ∠DCB = β
So the following relations from the triangles are equal to:
(1) [tex]cos( \beta )= \frac{7}{m}[/tex]
(2) [tex]cos( \beta )= \frac{m}{18}[/tex]
So, matching these equations:
[tex] \frac{7}{m}= \frac{m}{18} [/tex]
Solving for m:
[tex]m^{2} = 18x7 = 126[/tex]
∴ [tex] m = \sqrt{126}[/tex]
given that ABCD= PQRS, find AD
A.3
B.5
C.6
D.10
Answers
AD=SP
plugging in the values we obtain:
3m-9=2m-4
solving for m we get:
3m-2m=-4+9
m=5
thus the value of AD will be:
AD=3m-9=3(5)-9=15-9=6
The answer is AD=6
Which of the following is the prime factored form of the lowest common denominator of?
A.2 x 2 x 2 x 3
B.2 x 4 x 2 x 3
C.8 x 6
D.2 x 12
Answers
2 x 2 x 2 x 3 factored form is the prime factored form.
What is a prime number?"A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers."
The given factored forms are:
A. 2 x 2 x 2 x 3
Here, all the numbers are prime numbers.
Therefore, this factored form is the prime factored form.
B. 2 x 4 x 2 x 3
Here, all the numbers are not prime numbers.
Therefore, this factored form is not the prime factored form.
C. 8 x 6
Here, not a single number is prime number.
Therefore, this factored form is not the prime factored form.
D. 2 x 12
Here, all the numbers are not prime numbers.
Therefore, this factored form is not the prime factored form.
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Paisley needs 32 in of ribbon for a hair bow. The ribbon is sold by centimeters. Givin that 1 in = 2.54 centimeters, how many centimeters of ribbon does she need.
Work Pls
Thx
Answers
Multiply 32 inches by 2.54 centimeters to find how many centimeters of ribbon Paisley needs.
(32)(2.54) = 81.28
Paisley needs 81.28 centimeters of ribbon for the hair bow.
A quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. Part B: Solve 3x^2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.
Answers
Question 1:
A quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work.
Answer: The negative value of the radicand means that the equation does not have real solutions.
Explanation:
1) With radicand the statement means the disciminant of the quadratic function.
2) The discriminant is: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation: ax² + bx + c
3) Then, for 3x² - 15x + 20, a = 3, b = - 15, and c = 20
and the discriminant (radicand) is: (-15)² - 4(3)(20) = 225 - 240 = - 15.
4) The negative value of the radicand means that the equation does not have real solutions.
Question 2:
Part B: Solve 3x^2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.
Answer: two solutions x = 1 and x = - 8/3x
Explanation:
1) I choose factoring (you may use the quadratic formula if you prefer)
2) Factoring
Given: 3x² + 5x − 8 = 0
Make 5x = 8x - 3x: 3x² + 8x - 3x - 8 = 0
Group: (3x² - 3x) + (8x - 8) = 0
Common factors for each group: 3x(x -1) + 8(x - 1) = 0
Coomon factor x - 1: (x - 1) (3x + 8) = 0
The two solutions are for each factor equal to zero:
x - 1 = 0 ⇒ x = 1
3x + 8 = 0 ⇒ x = -8/3
Those are the two solutions. x = 1 and x = - 8/3
The quadratic equation 3x² − 15x + 20 = 0 has a radicand of -15, indicating no real solutions. The equation 3x² + 5x − 8 = 0 can be solved using the quadratic formula, yielding solutions of x = 1 and x = -8/3.
For the quadratic equation 3x² − 15x + 20 = 0, the radicand can be found as part of the quadratic formula process, which is b^2 - 4ac. Here, a=3, b= -15, and c=20. Substituting these values in, we get the radicand as (-15)² - 4(3)(20) = 225 - 240 = -15. Since the radicand is negative, this indicates that the equation has no real solutions; the solutions are complex numbers.
To solve the equation 3x² + 5x − 8 = 0, we will use the quadratic formula, x = −b ± √(b^2 - 4ac) / (2a), since we have a quadratic with a, b, and c all non-zero. Substituting a=3, b=5, and c= -8, we find the radicand to be (5)² - 4(3)(-8) = 25 + 96 = 121. Calculating further, x = (-5 ± √121) / 6, which simplifies to x = (-5 ± 11) / 6. Thus, we have two solutions: x = (11 - 5) / 6 = 1 and x = (-5 - 11) / 6 = -16/6 = -8/3.
For a test of upper h 0h0: pequals=0.50, the sample proportion is 0.470.47 based on a sample size of 100. use this information to complete parts (a) through (c) below.
Answers
(a) Calculate the standard error of the sample proportion.
(b) Determine the z-score for the sample proportion.
(c) Find the p-value for the given z-score.
To find the standard error, z-score, and P-value for the given test, follow these steps:
(a) Calculate the standard error using the formula:
[tex]\[ \text{Standard error} = \sqrt{\frac{p \times (1 - p)}{n}} \][/tex]
Given [tex]\( p = 0.50 \) (the population proportion) and \( n = 100 \) (the sample size), substitute these values into the formula:[/tex]
[tex]\[ \text{Standard error} = \sqrt{\frac{0.50 \times (1 - 0.50)}{100}} \]\[ = \sqrt{\frac{0.50 \times 0.50}{100}} \]\[ = \sqrt{\frac{0.25}{100}} \]\[ = \sqrt{0.0025} \]\[ = 0.05 \][/tex]
(b) Calculate the z-score using the formula:
[tex]\[ \text{z-score} = \frac{\text{sample proportion} - \text{population proportion}}{\text{standard error}} \]Given that the sample proportion is \( 0.47 \), substitute this value along with the previously calculated standard error into the formula:\[ \text{z-score} = \frac{0.47 - 0.50}{0.05} \]\[ = \frac{-0.03}{0.05} \]\[ = -0.6 \][/tex]
(c) Finally, find the P-value using a z-table or statistical software corresponding to the calculated z-score. The P-value represents the probability of observing a sample proportion at least as extreme as the one obtained, assuming the null hypothesis is true.
A package of three compact discs cost $24.96. How much does each disc cost?
Answers
24.96/3 =8.32
the circumference of an Oreo is 6.28 inches what is the area of the top cookie?
Answers
The circumference of an Oreo is 6.28 inches what is the area of the top cookie?
Solution:
Circumference= 6.28 inches
The formula of circle =2πr
So, 2πr=6.28
2*3.14*r=6.28
6.28r=6.28
To find the value of r, Let us divide by 6.28 on both sides
6.28 r /6.28 =6.28/6.28
r=1
Area of circle=πr²
=π1²
=π
=3.14 inches²
Area of the top cookie=3.14 inches²
Calculate the taxes based on the following taxable income amounts
I really need help on this fast please!
I need the estimated taxes for each problem at the bottom is the table needed.
1) income of 90,714.00
2) income of 63,036.00
3) income of 220,596.00
4) income of 166,904.00
5) income of 220,770.00
6) income of 97,266.00
7) income of 207,264.00
8) income of 479,956.00
9) income of 511,195.00
10) income of 511,104.00
11) income of 212,817.00
12) income of 435,045.00
13) income of 655,952.00
14) income of 739,334.00
15) income of 322,335.00
Income range Taxes
From To Tax rate. Plus
0.00 8,925.00 10.0%.
8925.00 36,250.00 15.0% 892.50
36,250.00 87,850.00 25.0% 5,437.50
87,850.00 183,250.00 28.0% 21,962.50
183,250.00 398,350.00 33.0% 51,310.00
398,350.00 400,000.00 35.0%. 131,455.50
400,000.000 - 39.6%. 140.000.00
Answers
2.) Taxable income is 12,140.75
3.) Taxable income is 63,634.18
4.) Taxable income is 44,097.62
5.) Taxable income is 63,691.60
6.) Taxable income is 24,598.98
7.) Taxable income is 59,234.62
8.) Taxable income is 171,662.58
9.) Taxable income is 184,033.22
10.) Taxable income is 183,997.18
11.) Taxable income is 61,067.11
12.) Taxable income is 153,877.82
13.) Taxable income is 241,356.99
14.) Taxable income is 274,376.26
15.) Taxable income is 97,208.05
Note: Use the "from" amount as the basis, so if the income is 10,000 then you'll deduct 8,925 (basis) from 10,000 (since 10,000 is more than 8,925 but less than 36,250)