Convert the rational expression to radical form.m2/3A)m2B)m3C)m2/3D)m3
Answers
To convert the rational expression to the radical form we can remember the exponent property
A good way to memorize that is think about the square root, the square root in rational form is 1/2
In a general way, the number at the numerator will go INSIDE the root, and the number at the denominator will go OUTSIDE the root.
Using this rule, m^(2/3) will be
And we can see that it's letter A.
Therefore, the answer is Letter A!
[tex]m^{\frac{2}{3}}=\sqrt[3]{m^2}[/tex]
Related Questions
=Writing a function rule given a table of ordered pairs: One-step...Below is the table of values of a function. Write the output when the input is n.input267n+ローロ7.Qutput1112ロメロDHХ5?
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The output is n + 5
Explanation:From the table:
when input = 2
output = 7
output = input + difference
7 = 2 + difference
difference in output and input = 7 - 2 = 5
when input = 6
output = 11
output = input + 5
11 = 6 + 5
when input = 7
output = 12
output = input + 5
12 = 7 + 5
when input = n
output = ?
output = input + difference
difference = 5
output = n + 5
The output is n + 5
How would you simplify: 3x(242+ 4%. + 3)
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hi
is this equation correct?
Do you have a picture of this question?
[tex]3x(2x^2+4x+3)=6x^3+12x^2\text{ + 9x}[/tex]I need to know which one has the same volume.
Answers
Answer:
D
Explanation:
The formula for calculating the volume of a prism is expressed as;
Volume of a prism = Base Area * Height
Volume of the given prism = 5 * 4 * 3
Volume of the given prism = 60m^3
We are to find the prism that has the same volume as 60m^3
Checking the volume of the prism in D;
Volume of the prism = 10 * 3 * 2
Volume of the prism = 30 * 2
Volume of the prism = 60m^3
Hence the prism that has the same volume as the one given is prism in option D
ai = 7 + 2(i +1). What is a4, the fourth term of this arithmetic sequence?
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For this question you just have to susbtitute 4 wherever you see an i, doing that we get
[tex]a_4=7+2(4+1)\text{ = 7+2}\cdot5=17[/tex]what's 77,268 rounded to the nearest hundred
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ANSWER
77,300
EXPLANATION
We want to round 77,268 to the nearest hundred.
First, we identify the number after the number in the hundred place value. That is 6.
When rounding up/down, if the number after the required place value is greater than or equal to 5, we round up by adding one to the place value, but if the number is less than 5, we round down by adding 0.
Since 6 is greater than 5, we have that 77,268 rounded to the nearest hundred is:
77,300
Solve the system graphically and check the solution. X+y=8. X-y =4
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we have the system
x+y=8 -----> equation A
x-y=4 ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
so
using a graphing tool
see the attached figure
the solution is the point (6,2)Explanation
To graph, the lines find out the intercepts
x+y=8 -----> equation A
x-intercept (value of x when the value of y=0)
For y=0
x+0=8
x=8
the x-intercept is (8,0)
y-intercept (value of y when the value of x=0)
For x=0
0+y=8
y=8
y-intercept is (0,8)
x-y=4 ----> equation B
x-intercept ---------> (4,0)
y-intercept -------> (0,-4)
To graph, each line, plot the intercepts and join the points to graph the line
see the attached figure
Please help:The graph shows a system consisting of a linear equation and a quadratic equation.What is the solution to the system? A. (3, 4) and (5, 12)B. (5, 12)C. 4 and 12D. (3, 4)3 and 5A line and a parabola are graphed on a coordinate plane. The horizontal x-axis ranges from negative 1 to 6 in increments of 1. The vertical y-axis ranges from negative 1 to 14 in increments of 1. The vertex of the parabola is located at begin ordered pair 2 comma 3 end ordered pair. The parabola opens upward. It passes through begin ordered pair 0 comma 7 end ordered pair and begin ordered pair 4 comma 7 end ordered pair. A straight line passes through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 5 comma 12 end ordered pair.
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To find graphically the solutions to a set of equations, we need to see where the two lines of the graph intersects.
In the graph, we can see that the two lines intersect at (3, 4) and (5, 12)
Thus, the correct answer is the first option, (3, 4) and (5, 12)
Answer: 3, 4 and 5, 12
Step-by-step explanation: k12 test. I got it right.
7/12 ÷ 3/4A 7/9B 7/16C 1 2/7D 21/28
Answers
Answer:
A 7/9
Explanation:
Given the expression:
[tex]\frac{7}{12}\div\frac{3}{4}[/tex]To simplify, the first step is to change the division sign to multiplication sign as follows:
[tex]=\frac{7}{12}\times\frac{4}{3}[/tex]Next, we multiply the numerators and denominators likewise.
[tex]\begin{gathered} =\frac{7\times4}{12\times3}\text{ (We write 12=3 x 4)} \\ =\frac{7\times4}{4\times3\times3}\text{ (Cancel out 4 in the numerator and denominator)} \\ =\frac{7}{3\times3} \\ =\frac{7}{9} \end{gathered}[/tex]The sequence 1/6, -2/7, 3/8, -4/9 is given.Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points)Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points)Part C: Is the sign of f (53) positive or negative? Justify your reasoning mathematically without determining the value of f (53). (2 points)
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a. The next four terms are 5/10, -6/11, 7/12, -8/13.
b. The explicit equation for f (n) is f(n) = (-1)ⁿ × (n+1)/(n+6) , n = 0,1,2,3...
c. If n = 53, then (-1)ⁿ = (-1)⁵³ = -1. so, f(n) is negative.
What is the explicit equation?
Without expressing the other terms of the sequence, explicit formulas are always utilized to represent any term of the sequence. The word "explicit" means something that may be found directly without having to know the other phrases in the sequence. A single formula, known as the explicit formula, can be used to describe each term in a series in an individual way.
Explicit formulas of different sequences:
Arithmetic Sequence: aₙ = a + (n - 1) d,
Geometric Sequence: aₙ = a× r^(n - 1),
Harmonic Sequence: aₙ = 1 / [a + (n - 1) d].
Here. we have
Given sequence 1/6, -2/7, 3/8, -4/9
a. The next four terms are 5/10, -6/11, 7/12, -8/13.
b. The explicit equation for f (n) is f(n) = (-1)ⁿ × (n+1)/(n+6) , n = 0,1,2,3...
c. If n = 53, then (-1)ⁿ = (-1)⁵³ = -1. so, f(n) is negative.
To learn more about explicit equations from the given link
https://brainly.com/question/741967
#SPJ1
Hi I need help with this question I don’t know if the One that I chose is right or wrong
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The given equation is
1/8(2x - 1) = 1/4(x - 1/4)
The first step is to multiply both sides of the equation by 8. We have
8 * 1/8(2x - 1) = 8 * 1/4(x - 1/4)
2x - 1 = 2(x - 1/4)
By expanding the parentheses on the right, it becomes
2x - 1 = 2 * x + 2 * - 1/4
2x - 1 = 2x - 1/2
Subtracting 2x from both sides, we have
2x - 2x - 1 = 2x - 2x - 1/2
- 1 = - 1/2
We knpw that - 1 is not equal to - 1/2
Thus, there is no solution
Suppose that the function h is defined, for all real numbers, as follows.Find h(- 4), h(- 1) , and h(0) .h(x)= -2&if x<=-1\\ (x+1)^ 2 &if-1=2
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The piecewise function is given as shown below:
[tex]h(x)=\begin{cases}{-2,\text{ }if\text{ }x\leq-1} \\ {(x+1)^2,\text{ }if\text{ }-1QUESTION 1: h(-4)-4 satisfies the interval:
[tex]\begin{gathered} x\leq-1 \\ -4\leq-1 \end{gathered}[/tex]Therefore,
[tex]h(-4)=-2[/tex]QUESTION 2: h(-1)
-1 satisfies the interval:
[tex]\begin{gathered} x\leq-1 \\ -1\leq-1 \end{gathered}[/tex]Therefore,
[tex]h(-1)=-2[/tex]QUESTION 3: h(0)
0 satisfies the interval:
[tex]\begin{gathered} -1Therefore,[tex]\begin{gathered} h(0)=(0+1)^2=1^2 \\ h(0)=1 \end{gathered}[/tex]Monica lives in Ohio but she is visiting her grandmother in California. Monica goes shopping with her grandmother. She wants to buy a new bicycle that costs $89.00. The sales tax in California is 7.5%. Monica can buy the same bicycle at the same price when she returns home to Ohio where the sales tax is 7%. If Monica waits until she gets home to buy the bicycle, how much money will she save?
Answers
Answer:
She will save $0.45 if she waits until she get home to buy the bicycle.
[tex]\text{ \$0.45}[/tex]Explanation:
Given that;
At California the sales tax is 7.5%
And at Ohio the sales tax is 7%
The cost of the bicycle in both states is;
[tex]\text{ \$89.00}[/tex]Since the price are the same in both states, the difference is only in the amount paid on the sales tax;
[tex]\begin{gathered} 7.5\text{\% - 7\%} \\ =0.5\text{\%} \end{gathered}[/tex]So, the difference in sales tax which is 0.5% is;
[tex]\begin{gathered} d=0.5\text{\% of \$89.00} \\ d=\frac{0.5}{100}\times89 \\ d=0.445 \\ d=\text{ \$0.45} \end{gathered}[/tex]Therefore, she will save $0.45 if she waits until she get home to buy the bicycle.
[tex]\text{ \$0.45}[/tex]The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X= percent of fat calories.(a) Find the z-score corresponding to 30 percent of fat calories, rounded to 3 decimal places. (b) Find the probability that the percent of fat calories a person consumes is more than 30. (c) Find the maximum number for the lower quarter of percent of fat calories. Round your answer to 3 decimal places.
Answers
SOLUTION
Write out the given parameters
[tex]\begin{gathered} \mu=36 \\ \sigma=10 \\ x=30 \end{gathered}[/tex]a). The Z-score is given by
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{30-36}{10} \\ \end{gathered}[/tex]Then
[tex]z=-\frac{6}{10}=-0.600[/tex]Hence
The Z-score value corresponding to 30 % of fat calories is -0.600
b). The probability that the percent of fat calories a person consumes is more than 30 is given by
[tex]p(x>30)=p(z>-0.6)=0.7257469[/tex]Hence
The probability that the percent of fat calories a person consumes is more than 30 is 0.7257
Triangle STU is dilated by a scale factor of 2/3to form triangle S'T'U'. What is the measure of side US?
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The dilation factor is 2/3. So ratio of sides of triangle is,
[tex]\frac{U^{\prime}S^{\prime}}{US^{}}=\frac{2}{3}[/tex]Determine the length of side US.
[tex]\begin{gathered} \frac{20}{US}=\frac{2}{3} \\ US=20\cdot\frac{3}{2} \\ =30 \end{gathered}[/tex]So measure of side US is 30 units.
Hi, can you help me answer this question please, thank you!
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The correct options are:
1. Option C
2. Option B
Explanation:[tex]H_0[/tex]is the null hypothesis, it is usually the opposite of
[tex]H_a[/tex]which is the alternative hypothesis.
From the given options, we have:
[tex]H_0\colon\mu=53\text{ hours}[/tex]The null hypothesis is usually a statement of equality
And
[tex]H_a\colon\mu\ne53\text{ hours}[/tex]The alternative hypothesis is usually the opposite of the null hypothesis
I need help with this question... the correct answer choice
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Given the point P with the coordinate indicated below
[tex]\begin{gathered} P(a,b) \\ x\Rightarrow a \\ y\Rightarrow b \end{gathered}[/tex]When a point is reflected across the line y=x, the transformation rule is shown below:
[tex](x,y)\rightarrow(y,x)[/tex]From the above transformation rule, we see that the coordinate will be swapped for reflection over the line y = x.
Thus, the coordinate of Q is shown below.
[tex]P(a,b)\rightarrow Q(b,a)[/tex]Hence, the coordinates of point Q is ( b , a )
The second option is the correct option.
I need 6g the volume 8 in 10 in 6 in
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Question 6G.
Given the dimensions of the rectangular prism:
Width, w = 8 in
Length, L = 10 in
Height, h = 6 in
Let's find the volume of the rectangular prism.
To find the volume of the rectangular prism, apply the formula:
Volume = width x length x height
Thus, we have:
Volume = 8 in x 10 in x 6 in = 480 in³
Therefore, the volume of the package is 480 in³
ANSWER:
480 in³
Please help me figure out this solution. I am extremely confused
Answers
Answer:
Predicted enrolment = 15596
Explanation:
In this scenario,
x represent the years
y represents the number of enrolment
We would write equation in the slope intercept form which is expressed as
y = mx + c
where
m represents slope
c represents y intercept
We would calculate the slope by applying the formula,
m = (y2 - y1)/(x2 - x1)
From the information given,
x1 = 1987, y1 = 11800
x2 = 1998, y2 = 13540
m = (13540 - 11800)/(1998 - 1987) = 1740/11
We would find the y intercept by substituting m = 1740/11, x = 1987 and y = 11800 into the slope intercept equation. We have
11800 = 1740/11 * 1987 + c
11800 = 3457380/11 + c
c = 11800 - 3457380/11
c = - 3327580
The equation would be
y = 1740x/11 - 3327580/11
For 2011, we would substitute x = 2011 into the equation. It becomes
y = 1740/11 * 2011 - 3327580/11
y = 15596
Predicted enrolment = 15596
1 1/3 as the sum if three fractions.
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1 1/3 as the sum if three fractions.
____________________
1 1/3 = 1/2 +1/2 + 1/3
[tex]undefined[/tex]Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. cos 27° = ____
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Given the cosine of an angle of 27 degrees, the numerical value can be given as
[tex]\begin{gathered} \cos 27^0=0.8910 \\ \text{ In the nearest hundreth } \\ \cos 27^0=0.89 \\ \end{gathered}[/tex]Hence, the value of cos27° = 0.89 ( in the nearest hundredth)
Estimate each quotient using compatible numbers 5,391 divided by 77
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Remember that
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally
so
we have
5,391 divided by 77
Find out the compatible numbers
5,391 -------> 5,400
if the denominator is 5,400
then
find the prime factors
prime factors=2,3,5
75=5^3 -----> is compatible
All Factors of 5400: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700 and 5400
you need to find a factor compatible with the number 77
the number is 75
therefore
5,400 /75=72
Port A: Under a dilation of scale factor centered at (7.5). SM becomes HG. Determine the coordinates of HG and sketch HG on the graph. The coordinates for HG (2.5,-1.5),(1.5,-1.5) Port B: Under a dilation of scale factor 2 centered at the origin, SM becomes TP. Determine the coordinates of TP and sketch TP on the graph, Part C: Under a dilation of scale factor-centered at (-4,-6). SM becomes CB. Determine the coordinates of CB and sketch CB on the graph.
Answers
Part B)
S is located at (-8, -2)
M is located at (-4, -6)
After the dilation is applied centered at (0,0) by a scale factor of 2, we get:
S(-8, -2) -> (-8*2, -2*2) -> T(-16, -4)
M(-4, -6) -> (-4*2, -6*2) -> P(-8, -12)
Part C)
If point A(a,b) is dilated centered at (x,y) with scale factor k:
A' = [k(a - x) + x, k(b - y) + y]
Replacing with points S and M, center of dilation (-4, -6), and k = 1/2, we get:
S(-8, -2) -> 1/2[-8 - (-4)] + (-4), 1/2[-2 - (-6)] + (-6) -> C(-6, -4)
M(-4, -6) -> 1/2[-4 - (-4)] + (-4), 1/2[-6 - (-6)] + (-6) -> B(-4, -6)
A complex number 21 is plotted below. Plot its complex conjugate, 21.Im86-4-2A++-8 -61-424+++ Re6 2 8-4-6-8
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Step 1
Given;
[tex]\begin{gathered} A\text{ plotted complex number;} \\ z_1 \\ \end{gathered}[/tex]Required; To find the complex conjugate
[tex]\bar{z}_1[/tex]Step 2
Find the complex conjugate
The complex conjugate of a + bi is a - bi. For example, the conjugate of 3 + 15i is 3 - 15i, and the conjugate of 5 - 6i is 5 + 6i.
Hence, from the plot the complex number is;
[tex]\begin{gathered} 7+0i=7 \\ \text{This is because the plot lies on the x-axis and the corresponding y-axis is }0 \end{gathered}[/tex]The complex conjugate hence will be;
[tex]\begin{gathered} 7-0i=7 \\ \text{Therefore the required complex conjugate = 7} \end{gathered}[/tex]Hence
[tex]\bar{z}_1=_{}7[/tex]f(x)=x2+3x g(x)=-2x+2 Find (f-g)(x)
Answers
Given the following functions:
[tex]\begin{gathered} f\mleft(x\mright)=x^2+3x \\ g\mleft(x\mright)=-2x+2 \end{gathered}[/tex]You need to subtract the functions in order to find
[tex]\mleft(f-g\mright)\mleft(x\mright)[/tex]Then you can set up that:
[tex]\mleft(f-g\mright)\mleft(x\mright)=(x^2+3x)-(-2x+2)[/tex]Therefore, now you distribute the negative sign and add the like terms (remember that like terms are those terms that have the same exponents and the same variables). Then, you get:
[tex]undefined[/tex]Find the midpoint of the segment between the points (−5,13) and (6,4)A. (−11/2,9/2)B. (1/2,17/2)C. (1,17)D. (−1,−17)
Answers
To obtain the midpoint, find the average of the x- and y-coordinates.
Let
[tex]\begin{gathered} (x_1,y_1)=(-5,13) \\ (x_2,y_2)=(6,4) \end{gathered}[/tex]Substitute the coordinates into the midpoint formula and then simplify.
[tex]\text{midpoint}=\mleft(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\mright)[/tex]Thus, we have the following.
[tex]\begin{gathered} midpoint=\mleft(\frac{-5+6}{2},\frac{13+4}{2}\mright) \\ =\mleft(\frac{1}{2},\frac{17}{2}\mright) \end{gathered}[/tex]Therefore, the correct answer is option B.
[tex]{14n}^{3} - {35n}^{2} + 28[/tex]Simplify the following problem
Answers
Simplify
[tex]14n^3-35n^2+28[/tex]First, we take 7 as a common factor of all terms:
[tex]14n^3-35n^2+28=7(2n^3-5n^2+4)[/tex]Now we need to factor the expression in parentheses. There is no direct method to do it, just by guessing or trial and error to find the 'hidden' factor.
[tex]2n^3-5n^2+4=2n^3-4n^2-n^2+2n-2n+4[/tex]The transformations above will help us to find a common factor. We'll factor in pairs:
[tex]2n^3-4n^2-n^2+2n-2n+4=2n^2(n-2)-n(n-2)-2(n-2)[/tex]Factoring n-2:
[tex]2n^3-4n^2-n^2+2n-2n+4=(n-2)(2n^2-n-2)[/tex]Thus, the final simplification is:
[tex]14n^3-35n^2+28=7(n-2)(2n^2-n-2)[/tex]For the equation -3x + 2y = 12, find the following-
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Given equation:
[tex]-3x\text{ + 2y = 12}[/tex]The y-intercept
The y-intercept can be found by substituting 0 for x and then solving for y:
[tex]\begin{gathered} -3(0)\text{ + 2y = 12} \\ 0\text{ + 2y =12} \\ 2y\text{ = 12} \\ Divide\text{ both sides by 2} \\ y\text{ = 6} \end{gathered}[/tex]Answer: (0,6)
The x-intercept
The x-intercept can be found by substituting 0 for y and then solving for x
[tex]\begin{gathered} -3x\text{ + 2(0) = 12} \\ -3x\text{ = 12} \\ \text{Divide both sides by -3} \\ x\text{ = -4} \end{gathered}[/tex]Answer: (-4,0)
the slope
The slope can be found by re-writing the equation in slope-intercept form:
[tex]\begin{gathered} y=\text{ mx + c} \\ \text{Where m is the slope} \end{gathered}[/tex]Hence:
[tex]\begin{gathered} -3x\text{ + 2y = 12} \\ 2y\text{ = 3x + 12} \\ \text{Divide both sides by 2} \\ y\text{ = }\frac{3}{2}x\text{ + 6} \end{gathered}[/tex]Answer:
slope = 3/2
The graph of the line can be obtained by joining two points using a straight line.
We have the points (0,6) and (-4,0)
Hence, the graph of the line is:
Two ratios are shown below:1. There are 4 boys for every 5 girls in the sixth grade.2. Twelve apples are sold at the farmer's market for every 15 pears.Are these ratios equivalent?
Answers
Given:
1) There are 4 boys for every 5 girls in the sixth grade.
[tex]\frac{4}{5}[/tex]2) Twelve apples are sold at the farmer's market for every 15 pears.
[tex]\frac{12}{15}=\frac{4}{5}[/tex]Answer: both the ratios are equivalent.
A mail order company has a 12% success rate. If it mails advertisements to 542 people, find the probability of getting less than 58 sales. Round z-value calculations to 2 decimal places and final answer to at least 4 decimal places.
Answers
P (x < 58 )
n= 542
p = 12%= 0.12
q = 1 - 0.12 = 0.88
542*0.12 = 65.04
Mean= n p = 542 (0.12) = 65.04
Standard Dev= √(n*p* q)= √( 542 * 0.12 * 0.88 )= 7.57
z = 57.5 - M / SD = 57.5 - 65.04 / 7.57 = -0996
Using z score table = 0.15962
probability of getting less than 58 sales = 0.15962
Translate this sentence into an equation.The product of Delia's height and 5 is 85.Use the variable d to represent Delia's height.
Answers
Answer
The equation that represents the statement 'The product of Delia's height and 5 is 85' is
5d = 85
On solving for d, we obtain that
d = 17
Explanation
Delia's height = d
The product of Delia's height and 5 is 85
In mathematical terms,
d × 5 = 85
5d = 85
We can now go ahead to solve for d (Delia's height)
Divide both sides by 5
(5d/5) = (85/5)
d = 17
Hope this Helps!!!