Please help and leave an explanation. I am struggling with radicals and exponents.
Answers
The radical form of the given expression [tex](3^\frac{2}{3})^\frac{1}{6}[/tex] is [tex]\sqrt[9]{3}[/tex]. So the option B is correct.
The given expression is [tex](3^\frac{2}{3})^\frac{1}{6}[/tex].
We have to express the given expression with a rational exponent as a radical expression.
As we can see that in the given expression have two power.
We firstly solve their power.
We using the Law of Power of a Power.
In this law, if any variable have a two power as [tex](a^m)^n[/tex] so their have multiplication relation between their power.
So [tex](a^m)^n=a^{mn}[/tex]
Now we solving the given expression using that rule.
The expression is [tex](3^\frac{2}{3})^\frac{1}{6}[/tex].
Simplifying the power first.
[tex](3^\frac{2}{3})^\frac{1}{6}=(3)^{\frac{2}{3}\times\frac{1}{6}}[/tex]
Now simplifying
[tex](3^\frac{2}{3})^\frac{1}{6}=(3)^{\frac{2}{18}}[/tex]
[tex](3^\frac{2}{3})^\frac{1}{6}=(3)^{\frac{1}{9}[/tex]
Since the power is [tex]\frac{1}{9}[/tex] which means variable [tex]3[/tex] have in radical.
Now expressing the simplified variable in the form of radical and the power of radical should be [tex]9[/tex].
[tex](3^\frac{2}{3})^\frac{1}{6}=\sqrt[9]{3}[/tex]
Hence, the radical form of the given expression [tex](3^\frac{2}{3})^\frac{1}{6}[/tex] is [tex]\sqrt[9]{3}[/tex]. So the option B is correct.
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Related Questions
i need help, what is 4x+14≤38
Answers
Answer:
x ≤ 6 I think!
Answer: [tex]x\leq 6[/tex]
Step-by-step explanation: [tex]4x\leq 38-14[/tex]. Move the 14 to the right side first.
Then you would get [tex]4x\leq 24[/tex]
Divide 4 on both side
[tex]x\leq 6[/tex]
Factorise 12x raise to power of 2 and y raise to power of 2 +11xy-5
Answers
According to the solving the factorized value of the given equation is:
(4x-5). (3x+1).
What is factorization?Writing a number or any mathematical object as the sum of several factors—typically smaller or simpler objects that use the same known as factorization or factoring. For instance, 3 5 factors the polynomial x2 - 4 as well as the integer 15.
Why do we factor?Factoring is a crucial procedure that aids in our understanding of our equations. We factorize our polynomials to create a simpler form, and when we factorize equations, we obtain a wealth of important information.
According the given data:Detailed explanation:
12x² - 11x-5
12x²+4x-15x-5
4x(3x+1) - 5(3x+1)
(4x-5). (3x+1)
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how many solutions does the equation 7x+3-8=2(5x-4) have
Answers
The number of solutions in the equation where the equation is given as 7x + 3 - 8 = 2(5x - 4) is one solution
How to determine the number of solutions in the equation?The equation is given as
7x + 3 - 8 = 2(5x - 4)
The above equation is a linear function with one variable
So, we have
7x + 3 - 8 = 2(5x - 4)
Open the brackets
So, we have
7x + 3 - 8 = 10x - 8
Subtract 10x from both sides of the equation
So, we have
-3x + 3 - 8 = - 8
Subtract (3 - 8) from both sides of the equation
So, we have
-3x = - 3
Divide by -3
x = 1
The above equation is true because it has a definite solution
Hence, the number of solutions in the equation is one
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A projectile is fired vertically upward and can be modeled by the function h(t)=−16t2+900t+175. During what time interval will the projectile be more than 9000 feet above the ground? Round your answer to the nearest hundredth.
Answers
Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175. 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.
Given that,
Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.
We have to find how long will the projectile be above the ground at a height more than 9000 feet.
Answers should be rounded to the closest hundredth.
The function is
h(t)=-16t²+900t+175
-16t²+900t+175>9000
-16t²+900t+175-9000>0
-16t²+900t-8825>0
The simplest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula.
Gives the roots of a quadratic equation ax² + bx + c = 0.
x = [-b ± √(b² - 4ac)]/2a.
Now, We get
t= [-900 ± √((900)² - 4(-16)(-8825))]/2(-16)
t=[-900 ± √(810000-564800)]/-32
t=[-900 ± √(245200)]/-32
t=[-900 ± 495.17]/-32
First,
t=[-900 + 495.17]/-32
t=[-404.83]/-32
t=12.65
Second,
t=[-900 - 495.17]/-32
t=[-1395.17]/-32
t=43.59
Therefore, 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.
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Solve for x 6 + 2x = 2(x - 3)
Answers
Answer:
No solution
Step-by-step explanation:
6 + 2x = 2(x - 3)
6 + 2x = 2x-6
No solution
Find the distance between the two points rounding to the nearest tenth (if necessary).
(4, -4) \text{ and } (9, -2)
(4,−4) and (9,−2)
Answers
The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.
As per the question statement, two points having coordinates (4, -4) and
(9, -2) plotted on the cartesian plane.
We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.
To solve this question, we need to know the Distance-formula which goes as,
"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"
Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,
√[(9 - 4)² + {(-2) - (-4)}²]
= √[(9 - 4)² + {(-2) + 4}²]
= √[(9 - 4)² + (4 - 2)²]
=√[(5)² + (2)²]
=√(25 + 4)
=√29
= 5.38 units.
Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.
That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.
Distance: In Mathematics, physics or daily life, distance is a numerical or occasionally qualitative measurement of how far objects or points are from each other.Coordinates: In geometry, coordinates are a pair of numbers that can uniquely determine the position of points or other geometric elements on a Euclidean or Cartesian Plane.To learn more about Distances and Coordinates, click on the link below.
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an executive in an engineering firm earns a monthly salary plus a christmas bonus of 5700 dollars. if she earns a total of 83500 dollars per year, what is her monthly salary in dollars?
Answers
The monthly salary of an executive is $6483.
What is monthly salary?
A salary is the amount of money that an employee receives from their employer each month, particularly when they work in a profession like education, law, or medical.
Given: An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 5700 dollars. She earns a total of 83500 dollars per year.
To find the salary for each month.
First to subtract the Christmas bonus from the total amount.
83500 - 5700 = 77800.
So, the salary from each month is, 77800/12 = 6483
Therefore, the salary for each month is, $6483.
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if you finish these both ill give u a cookie
Answers
1. 135, 205, 330, 275, and 365 are divisible by 5.
2. 1, 4, and 7 can be filled in the blank space to make it divisible by 3.
3. 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.
4. 81 is the only composite number all the other nos. are prime.
What is the divisibility rule?Divisibility rules are methods for determining whether a number is divisible by a certain number or not without actually dividing.
We know numbers that are divisible by 5 are those numbers
having 5 or 0 in their unit place.
∴ 135, 205, 330, 275, and 365 are divisible by 5.
A number is divisible by 3 if the sum of all the digits is divisible by 3.
∴ 3,71_ has a digit sum of 11, so 1, 4, 7 can be filled in the blank space to make it divisible by 3.
A list of all the factors of 30 is those numbers that divide 30 completely.
∴ 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.
We know composite numbers are those numbers that are not prime.
∴ 81 is the only composite number all the other nos. are prime and they have only two factors 1 and the number itself.
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paula invited some friends to dinner, and she plans to make fajitas. at the grocery store, she spends $2.56 on red bell peppers and $1.92 on green bell peppers. if both types of bell peppers cost $1.60 per pound, how many total pounds of bell peppers does she buy?write your answer as a whole number or decimal. pounds
Answers
Answer:
2.8 pounds
Step-by-step explanation:
she spends on both types of bell peppers =
$2.56+$1.92=$4.48
$1.60 = 1 pound
$4.48 = ?
= 4.48/1.60
= 2.8 pounds
Rory has a handful of Skittles. He has 5 red, 8 yellow, 6 purple, 4 green, and 11 orange.
What is the ratio of red and orange to the other Skittles?
Answers
The most appropriate choice for ratio will be given by-
Ratio of red and orange to the other Skittles = 8 : 9
What is ratio?
Ratio determines how many times one number is bigger than the other number, provided both the numbers has the same unit.
The first part of the ratio is called antecedent and the second part of the ratio is called consequent
Here,
Number of red Skittles Rory has = 5
Number of yellow Skittles Rory has = 8
Number of purple Skittles Rory has = 6
Number of green Skittles Rory has = 4
Number of orange Skittles Rory has = 11
Total number of red and orange skittles = 5 + 11
= 16
Total number of other skittles = 8 + 6 + 4
= 18
Ratio of red and orange to the other Skittles = 16 : 18
= 8 : 9
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over the set of integers factor the expression 4x^3 - x^2+16x-4 completely
Answers
The factorized expression of the equation of the function given as lf(x) = 4x³ - x² + 16x - 4 is f(x) = (x² + 4)(4x - 1)
How to determine the factor of the expression?The equation of the function is given as
f(x) = 4x³ - x² + 16x - 4
Factor out x from the equation of the function
So, we have
f(x) = 4x³ - x² + 16x - 4
Group the terms in 2's
f(x) = (4x³ - x²) + (16x - 4)
Factorize the expression in the bracket
So, we have
f(x) = x²(4x - 1) + 4(4x - 1)
Factor out 4x - 1
So, we have
f(x) = (x² + 4)(4x - 1)
Hence, the factorized expression is f(x) = (x² + 4)(4x - 1)
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11.04 = 1/2 (a + 0) 1.5
Answers
Answer: the value of a = 14.72 and if you evaluate it.
Have a good day
Make g the subjest of a=g+h/2
Answers
g = a - [tex]\frac{h}{2}[/tex]
2. A car is going 65 miles per hour down the highway.
a. How far does it travel in 1.5 hours?
b. How long does it take the car to travel 130 miles?
c. Mai wrote the equation y = 65x, with a representing
the time traveled, in hours, and y representing the
distance traveled, in miles. Explain why Mai's equation
matches the story.
C
t
a
m
e
th
d
d
Answers
a. A car travels 97.5 miles in 1.5 hours.
b. A car takes 2 hours to travel 130 miles.
c. Mai's equation matches the story because it is algebraic form of the formula of speed.
In this question, we have been given a car is going 65 miles per hour down the highway.
Part a.
A car is going 65 miles per hour.
This means, in 1 hour car traveled 65 miles.
Let car travels 'm' miles in 1.5 hours.
So, m = 1.5 × 65
m = 97.5 miles
Thus, a car travels 97.5 miles in 1.5 hours
Part b.
Suppose that it will take t hours to travel 130 miles.
We have been given 1 hour = 65 miles
So, we get an equation,
t = 130 / 65
t = 2 hours
This means, a car takes 2 hours to travel 130 miles.
Part c.
Mai wrote the equation y = 65x, with x representing the time traveled, in hours, and y representing the distance traveled, in miles.
We know that the formula of speed.
speed = distance / time
⇒ distance = speed × time
here, speed = 65 miles per hour
⇒ distance = 65 × time
Assuming distance = y and time = x
y = 65x
This means, Mai's equation matches the story.
Therefore, a. A car travels 97.5 miles in 1.5 hours.
b. A car takes 2 hours to travel 130 miles.
c. Mai's equation matches the story because it is algebraic form of the formula of speed.
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I need help with this question. Please help
Answers
A linear function which has the same y-intercept of 5 as the one that is represented by the graph is: table 1.
How to calculate the slope of a linear function?Mathematically, the slope of any linear function can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
At points (-3, -4) and (-1, 2), the slope of the line is given by:
Slope, m = (2 + 4)/(-1 + 3)
Slope, m = 6/2
Slope, m = 3.
Note: The y-intercept of the line shown on the graph is 5.
At points (-3, -4), the y-intercept of this line can be calculated by using the slope-intercept form:
y = mx + c
Where:
x and y represents the points.m represents the slope.c represents the y-intercept.Making y-intercept (c) the subject of formula, we have:
y-intercept, c = y - mx
y-intercept, c = -4 - 3(-3)
y-intercept, c = -4 + 9
y-intercept, c = 5.
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Complete Question:
Which linear function has the same y-intercept as the one that is represented by the graph?
Sonia takes a 4/5-mile walk every day. What part of her walk has she completed once she has walked 3/5 mile?
Answers
3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.
As given in the question,
Sonia takes a walk everyday which is equal to
= 4/5 mile
Moreover, she has completed a part of her daily targeted distance = 3/5 mile
We need to find, what part of the total distance which Sonia covers daily, has she covered just now by covering 3/5 mile of distance.
Part of the total distance which Sonia covers daily, from the distance she has covered just now by covering 3/5 mile of distance
= (Distance covered by Sonia)/ (Total distance covered by Sonia)
= (3/5) / (4/5)
= (3/5) × (5/4)
= 3/4 mile
Therefore,, 3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Please use a picture to show where they are plotted if you can.
Answers
The slope of the line in the given diagram = rise/run = 1/2.
How to Determine the Rise and Run of a Line to Determine its Slope?The slope of a line is determined as the ratio of the rise of the line to the run of the line.
The rise of a line = change in y
The run of a line = change in x.
The red line in the image attached below shows the rise of the line which is, 1 units.
The blue line represents the run, which is, 2 units.
The slope of the line = 1 units/2 units = 1/2.
Therefore, we can state that the slope of the line = 1/2.
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Which statement is true
A)Only graph A is a function
B)Only graph B is a function
C)Both graphs are functions
D)Neither graph is function
Answers
Answer:wish i could help
Step-by-step explanation:......
Determine the range of f(x) = |x + 5|.
Answers
Answer:
f(x) ≥ 0
In interval notation Range: [0, ∞]
Step-by-step explanation:
Regardless of the value of x, |x+5| ≥ 0 and there is no upper bound on f(x)
Answer: C
Step-by-step explanation: Got it right for my test
Armand plans to save money every month for the next six months. The function f(x)=2x−1 represents the amount of money, in dollars, Armand will deposit into his savings account at the end of x months since the time he started saving. Which of the following represents the amount of money, in dollars, Armand deposits into his savings account at the end of 3 months since the time he started saving? Select all that apply. Responses f⋅3f times 3 f(3)f of 3 3f(x)3 f x 23−12 cubed minus 1 3(2x−1)3 times open paren 2 to the x th power minus 1 close paren
Answers
AAnswer:
Step-by-step explanation:
Algebra Question, please provide a step-by-step explanation.
Answers
Answer:
4 seconds
Step-by-step explanation:
First I substitute the Y with 0 and then I move the 16x^2 to the left side of the equation and then I divide both sides with 16 leaving me with x^2 then I get the square root of both sides and then I evaluate it and then I got the answer x = 4
Answer:
4 seconds
Step-by-step explanation:
We have a quadtratic equation, that is, we have a function to the highest degree of x^2.
When solving this, we can either solve using the quadratic equation, or by solving for X which would be the easiest and quickest way to do it.
256 -16x^2=0
-16x^2=-256
x^2=16 (divide both sides by -16)
[tex]\sqrt{x} =\sqrt{16}[/tex]
Which leaves x=4 as your answer.
To check this, we can simply input 4 back into the equation, and we will find that it does indeed equal 0.
To further visualize this, when we solve the equation for x, we are finding where the x value that intersects the x axis. We are finding where x=0, or when it touches the ground.
pls help it's very urgent !!
Answers
For given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]
In this question, we have been given a function f(x) = 3x² - 4
We need to write the rule obtained when finding f^(-1)
Le f(x) = y ........(1)
y = 3x² - 4
We find the value of x.
3x² = y + 4
x² = (y + 4)/3
x = ±√[(y + 4)/3]
From (1),
f^{-1}(y) = ±√[(y + 4)/3]
Since the choice of the variable is arbitrary, we can write this as ,
f^{-1}(x) = ±√[(x + 4)/3]
Therefore, for given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]
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Find the length of WY if WZ=128 ft and WX=YZ
Answers
Answer: 91 ft
Step-by-step explanation:
Since WZ=1287ft .XY=54ft
WX is congruent to YZ
so WX= 1/2 (128-54)
= 1/2 x(<—times) 74
=37ft
WY= WX + XY
=37+54
= 91ft
The population of a village is 6400. The population is decreasing exponentially at a rate of r% per year. After 22 years, the population will be 2607. Find the value of r.
Answers
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$2607\\ P=\textit{initial amount}\dotfill &6400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &22\\ \end{cases} \\\\\\ 2607=6400(1 - \frac{r}{100})^{22} \implies \cfrac{2607}{6400}=\left( \cfrac{100-r}{100} \right)^{22} \implies \sqrt[22]{\cfrac{2607}{6400}}=\cfrac{100-r}{100}[/tex]
[tex]\cfrac{r-100}{100}=-\sqrt[22]{\cfrac{2607}{6400}}\implies r-100=-100\sqrt[22]{\cfrac{2607}{6400}} \\\\\\ r=100-100\sqrt[22]{\cfrac{2607}{6400}}\implies {\Large \begin{array}{llll} r\approx 4 \end{array}}[/tex]
Ashley babysits for 6 hours for $73.50 on Friday and for 3 hours for $36.75 on Sunday. What constant of proportionality relates the number of hours and total pay?
Group of answer choices
$13.50
$12.25
$11.75
$14.25
Answers
Answer:
12.25
Step-by-step explanation:
thanks help bhjjjdjshshshsyshdh
Answers
Answer:
14.90 $ 527.86- 349.11 = 178.75 divided by 12 pta members is 14.89 rounded would be 14.90 the answer depends if u want to round it
Step-by-step explanation:
sub to imaginefn in utube
PLEASE HELP!! PICTURE INCLUDED!!
Please explain how to find angle R!!
Answers
Answer:
∠ R = 75°
Step-by-step explanation:
you are correct with answers to a, b, c
d
the sum of the 3 angles in Δ QRS = 180° , that is
∠ Q +∠ R + ∠ S = 180° , so
55° + ∠ R + 50° = 180°
∠ R + 105° = 180° ( subtract 105° from both sides )
∠ R = 75°
Ryan invests $7,000 for 9 months at a simple interest rate of 8.3%. The amount of interest received is found by
I=PRT
Since R=0.083,
I=0.083 x P x T
What are P and T?
Answers
P, which is the principal invested is $7,000 whereas the T is 0.75
What is simple interest?
The simple interest on an investment such as that of Ryan, can be determined as the principal multiplied by the simple interest rate and the time whose formula is as given below:
I=PRT
I=simple interest amount in dollars=unknown
P=principal investment=actual amount invested on simple interest basis=$7000
R=annual simple interest rate=8.3%
T=period of investment measured in years=9/12=0.75(9months divided by 12months in a year gives 0.75 years)
I=$7000*0.083*0.75
I=$435.75
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23. graph 6x=-90
pls anwser need to turn in asap
Answers
Answer:
Step-by-step explanation:
Step: 1
-Graph the 6x: It will start at (0,0) and will have a rise of 6 and a run of 1
Step: 2
-Graph the 90: From what I understand it should be a horizontal line with its point on 90y
Sorry if this doesn't help very late where I am.
a steamer sails 100 miles east and then 40 miles on a bearing of n60°e. how far is the steamer from its starting point, and at what angle has it traveled from its starting point? round your answer to the nearest thousandth.
Answers
how do i delete an answer?
