Answers
Answer:
Third choice from the top is the one you want
Step-by-step explanation:
This whole concept relies on the fact that if the index of a radical exactly matches the power under the radical, both the radical and the power cancel each other out. For example:
[tex]\sqrt[6]{x^6} =x[/tex] and another example:
[tex]\sqrt[12]{2^{12}}=2[/tex]
Let's take this step by step. First we will rewrite both the numerator and the denominator in rational exponential equivalencies:
[tex]\frac{\sqrt[4]{6} }{\sqrt[3]{2} }=\frac{6^{\frac{1}{4} }}{2^{\frac{1}{3} }}[/tex]
In order to do anything with this, we need to make the index (ie. the denominators of each of those rational exponents) the same number. The LCM of 3 and 4 is 12. So we rewrite as
[tex]\frac{6^{\frac{3}{12} }}{2^{\frac{4}{12} }}[/tex]
Now we will put it back into radical form so we can rationalize the denominator:
[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }[/tex]
In order to rationalize the denominator, we need the power on the 2 to be a 12. Right now it's a 4, so we are "missing" 8. The rule for multiplying like bases is that you add the exponents. Therefore,
[tex]2^4*2^8=2^{12}[/tex]
We will rationalize by multiplying in a unit multiplier equal to 1 in the form of
[tex]\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]
That looks like this:
[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }*\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]
This simplifies down to
[tex]\frac{\sqrt[12]{216*256} }{\sqrt[12]{2^{12}} }[/tex]
Since the index and the power on the 2 are both 12, they cancel each other out leaving us with just a 2! Doing the multiplication of those 2 numbers in the numerator gives us, as a final answer:
[tex]\frac{\sqrt[12]{55296} }{2}[/tex]
Phew!!!
Related Questions
Given the parallelogram ABCD, solve for X when angle A equals (30+ 5x)° and angle D equals (15+10x)° degrees. Also, sides AB and CD opposite each other.
Answers
Answer:
x = 9
Step-by-step explanation:
Adjacent angles A and D are supplementary:
(30 +5x)° +(15 +10x)° = 180°
15x +45 = 180 . . . . . collect terms, divide by °
15x = 135 . . . . . . . . . subtract 45
135/15 = x = 9 . . . . . divide by the coefficient of x
The value of x is 9.
Did I do the first question right? can anyone please help me with the 2nd question? Would really appreciate the Help
Answers
Answer:
8. 1483.33
9. 21 months
Step-by-step explanation:
8. Morgan's income after taxes is 55000/12 = 4583.33 per month. The amount available after expenses is 4583.33 -3100.00 = 1483.33 per month.
Morgan is able to put $1483.33 per month into savings.
__
9. If Morgan is able to save $1483.33 per month, it will take her ...
$30,000/$1483.33 ≈ 20.2
months to save $30,000. After 20 months, she won't have quite enough, so it will take her one more month to save the desired amount.
It will take Morgan about 21 months to save $30,000.
_
If you like, you can write an equation for "m", the number of months it will take Morgan to save 30,000:
1483.33×m = 30,000
m = 30,000/1483.33 ≈ 20.2 . . . . . . divide by the coefficient of m
The corners of a square are cut off two centimeters from each corner to form an octagon. If the octagon is 10 centimeters wide, what is it's area?
Answers
Answer:
92 cm²Explanation:
The area of the octagon may be calculated as the difference of the area of the original square and the area of the four corners cut off.
1) Area of the square.
The original square's side length is the same wide of the formed octagon: 10 cm.
So, the area of such square is: (10 cm)² = 100 cm².
2) Area of the four corners cut off.
Since, the corners were cut off two centimeters from each corner, the form of each piece is an isosceles right triangle with legs of 2 cm.
The area of each right triangle is half the product of the legs (because one leg is the base and the other leg is the height of the triangle).
Then, area of one right triangle: (1/2) × 2cm × 2cm = 2 cm².
Since, they are four pieces, the total cut off area is: 4 × 2 cm² = 8 cm².
3) Area of the octagon:
Area of the square - area of the cut off triangles = 100 cm² - 8cm² = 92 cm².And that is the answer: 92 cm².
Use the figure to answer the questions
a. Explain why the triangles are similar
Geometry - Shaping Sheet
Triangle ______ and Triangle ______ are similar by the __________ postulate. This postulate works because __ (explain your reasoning here) ________.
*Use this format to appropriately write your answer below this box.
b. Find the value of x
Answers
Answer:
A. EAB and EDC by AAA because congruent corresponding angles lead to similar triangles regardless of side length. This postulate works because the parallel lines cause angle a and angle d to be congruent as well as angle b being congruent to angle c, and vertical angle e is congruent.
Step-by-step explanation:
Since we have computer algebra systems that can solve polynomial division problems for us, why is it necessary to learn how to do these things by hand?
Answers
Answer:
Probably because learning to do polynomials by hand boosts understanding of the topic and improves general algebraic solving ability,both of which are required in further topics like advanced calculus and algebra
Learning polynomial division by hand is crucial for understanding concepts, enhancing problem-solving skills, and fostering critical thinking in mathematics.
Explanation:The importance of learning polynomial division by hand despite the availability of computer algebra systems lies in developing a deep understanding of the underlying concepts, fostering problem-solving skills, and enabling visualization of geometric interpretations.
By manually carrying out mathematical operations, students can better grasp the logic behind the processes, which aids in building a strong foundation for more complex mathematical tasks.
Furthermore, mastering hand calculations equips students with the ability to perform quick mental math, apply critical thinking skills, and comprehend the practical applications of the mathematical concepts.
Adelia drove from her house to Townsville one evening. Her distance was 180 miles. She left home at 6:27 and was at townsville at 6:42 what was her speed
Answers
Answer: 720 mph or 12 miles a minute
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
(I actually have the problem in front of me, and I think you switched the minute and hour hands on the clock)
Adel
left at 5:30 and arrived at 8:30. That’s 3 hours, which is 180 minutes. 180/180 = 1 mile per minute
60 minutes in an hour
60*1 = 60 mph
. Solve the following system of equations: 1. y - 3x + 15 = 10
2. 6 - 4x = y
Answers
The first equation can be further simplified so first do that by subtracting 15 to both sides
y - 3x + (15 - 15) = 10 - 15
y - 3x = -5
We know from the second equation that y is 6 - 4x so in the equation y - 3x = -5 plug in 6 - 4x for y
(6 - 4x) - 3x = -5
6 - 4x - 3x = -5
Combine like terms
6 - 7x = -5
(6 - 6) - 7x = -5 - 6
-7x = -11
Isolate x
-7x/-7 = -11/-7
x = 11/7
To solve for y plug in 11/7 in for x in the equation 6 - 4x = y
6 - 4(11/7) =y
6 - 44/7 = y
y = -2/7
so...
(11/7 , -2/7)
Hope this helped!
~Just a girl in love with Shawn Mendes
1.) Solving for X problem 1#
y-3x+15=10
-3x+15-15=10-15-y
-3x=-y-5
-3x/-3=-y-5/3
x=(-y-5)/3
2.) Solving for Y problem 1#
y-3x+15=10
y-3x+3x+15-15=10-15+3x
y=3x-5
1.) Solving for X problem 2#
6-4x=y
-4x+6-6=y-6
-4x/4=y-6/4
x=(y-6)/4
2.) Solving for Y problem 2#
6-4x=y
y=-4x+6
Help! the file is attached
Answers
Answer:
924/5 ft/s369.6 ftStep-by-step explanation:
126 mi/h = (126 mi)/(1 h)·(5280 ft)/(1 mi)·(1 h)/(3600 s) = (126·5280/3600) ft/s
126 mi/h = 184.8 ft/s = 924/5 ft/s
__
In 2 seconds, the parachutist falls ...
(184.8 ft/s)·(2 s) = 369.6 ft
By what factor does the area change if one diagonal is doubled? Explain.
Answers
The area of deltoid is defined by formula:
[tex]A=\dfrac{e\cdot f}{2}[/tex]
Where e and f are diagonals.
If you were to double the size of either one. Let's say f. You would result with:
[tex]A=\dfrac{e\cdot2f}{2}=e\cdot f[/tex]
Which means if either of diagonals double in length the area of deltoid will be twice as big as it was before.
Hope this helps.
r3t40
the kite, which looks more like a rhombus but being called a kite, will look like the one in the picture below.
now, as you see in the picture, the kite is really 4 congruent triangles, each with a base of 2.5 and a height of 5, so their area is
[tex]\bf \stackrel{\textit{area of one triangle}}{\cfrac{1}{2}(2.5)(5)}\implies 6.25\qquad \qquad \stackrel{\textit{area of all four triangles}}{4\left[ \cfrac{1}{2}(2.5)(5) \right]}\implies 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doubling the base or height}}{4\left[ \cfrac{1}{2}(2.5)(5)\underline{(2)} \right]}\implies \stackrel{\textit{the area is twice as much as the original}}{\underline{(2)}~~\left[ 4\left[ \cfrac{1}{2}(2.5)(5) \right] \right]}[/tex]
Research scientists need a certain type of bacteria to conduct an experiment. There are 2,500 bacteria in a certain culture. The culture grows at a rate of 25% daily. The scientists needs at least 10,000 bacteria to conduct an experiment. What is the least number of days they need to wait for the bacteria culture to reach a quantity of 10,000? (Hint: use a guess-and-check method to determine the lowest number of days that satisfy the requirement.)
Answers
Answer:
7 days
Step-by-step explanation:
At 25% per day, it will take approximately 3 days to double the population, so approximately 6 days for the population to quadruple. Checking that number, we find it is not quite enough for the experiment, so another day is required.
"Guess and check" as a method of solution works especially well if you have an automated checker to evaluate your guess. A graphing calculator or spreadsheet can work well for this.
_____
We guess 3 days as the doubling time using the "rule of 72" that says the product of percentage and doubling time is about 72. That is, 72/25 ≈ 3. (This is only a very rough approximation of doubling time, best for rates near 8%.)
Given 250 mL of HCl HCI at 65% concentration how many milliliters of pure HCl are in the mixture? Help please
Answers
Multiply the total amount by the percentage.
250 mL x 0.65 = 162.5
The answer is 162.5 mL
A bag contains pieces of paper numbered from 5 to 9. A piece of paper is drawn at random. What is the theoretical probability of drawing a number less than 8?
Answers
Answer: 3/5 probability of choosing a number LESS THAN 8
Solve using elimination PLEASE I NEED HELP!!! IT WOULD REALLY MEAN A LOT IF ANYONE CAN ANSWER THIS! 16 POINTS!!!
2x+4y=1
x-4y=5
Answers
Answer:
(x, y) = (2, -3/4)
Step-by-step explanation:
The point of the "elimination" technique is to combine the equations in a way that eliminates one of the variables. Sometimes this involves multiplying one or both of the equations by constants before you add those results together. In any event, the first step is to look at the coefficients of the variable terms to see if there is a simple combination of them that will result in zero.
The y terms have coefficients that are opposites of each other (4, -4), so you can simply add the two equations to eliminate y as a variable.
(2x +4y) +(x -4y) = (1) +(5)
3x = 6 . . . . . simplify
x = 2 . . . . . . divide by 3
Now, you find y by substituting this value into one of the equations. I would choose the equation with the positive y-coefficient:
2(2) +4y = 1
4y = -3 . . . . . . subtract 4
y = -3/4
Then the solution is ...
(x, y) = (2, -3/4)
_____
A graphing calculator confirms this solution.
Choose the correct reason for each algebraic statement. A. Subtraction Property of Equality B. Combine like terms C. Distributive Property D. Division Property of Equality 3.__ 4.__ 5.__ 6.__
Answers
Answer:
b
Step-by-step explanation:
hope this helps
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answers
The rise from one point to another is 2, and the run is 3 and since slope is rise/run, the slope is 2/3
Answer: The slope of the line is: [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The slope can be calculated with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
You need to choose two points of the line. You can pick the point (6,2) and the point (-6,-6)
You can identify that:
[tex]y_2=-6\\y_1=2\\x_2=-6\\x_1=6[/tex]
Now, you must substitute these values into the formula:
[tex]m=\frac{-6-2}{-6-6}[/tex]
With this procedure you get that the the slope of the line on the graph is:
[tex]m=\frac{-8}{-12}[/tex]
[tex]m=\frac{2}{3}[/tex]
PLEASE HELP ME
There are two answers!
x=-3
x = -2
x = -1
x = 0
x = 1
x = 2
x = 3
Answers
Answer:
x = 0x = 1Step-by-step explanation:
Find two rows in the table that have the same values in the f(x) and g(x) columns.
The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to –z standard deviations from the mean?
Answers
Answer:
The right answer is B: The probability is equal to p%.
Step-by-step explanation:
Points A and B have coordinates (3,1,2) and (1,-5,4) respectively. Point C lies on line AB such that AC:BC=3:2. Find position vector of Point C.
Final answer is (-3,-17,8)
Answers
Answer:
The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k
Step-by-step explanation:
* Lets revise how to solve the problem
- If the endpoints of a segment are (x1 , y1 , z1) and (x2 , y2 , z2), and
point (x , y , z) divides the segment externally at ratio m1 :m2, then
[tex]x=\frac{m_{1}x_{2}-m_{2}x_{1}}{m_{1} -m_{2}},y=\frac{m_{1}y_{2}-m_{2}y_{1}}{m_{1}-m_{2}},z=\frac{m_{1}z_{2}-m_{2}z_{1}}{m_{1}-m_{2}}[/tex]
* Lets solve the problem
∵ AB is a segment where A = (3 , 1 , 2) and B = (1 , - 5 , 4)
∵ Point C lies on line AB such that AC : BC=3 : 2
∵ From the ratio AC = 3/2 AB
∴ C divides AB externally
- Lets use the rule above to find the coordinates of C
- Let Point A is (x1 , y1 , z1) , point B is (x2 , y2 , z2) and point C is (x , y , z)
and AC : AB is m1 : m2
∴ x1 = 3 , x2 = 1
∴ y1 = 1 , y2 = -5
∴ z1 = 2 , z2 = 4
∴ m1 = 3 , m2 = 2
- By using the rule above
∴ [tex]x=\frac{3(1)-2(3)}{3-2}=\frac{3-6}{1}=\frac{-3}{1}=-3[/tex]
∴ [tex]y=\frac{3(-5)-2(1)}{3-2}=\frac{x=-15-2}{1}=\frac{-17}{1}=-17[/tex]
∴ [tex]z=\frac{3(4)-2(2)}{3-2}=\frac{12-4}{1}=\frac{8}{1}=8[/tex]
∴ The coordinates fo point c are (-3 , -17 , 8)
* The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k
I need help
You find 20 books that you checked out from the library as you are cleaning your room. You need to take 4 books back to the library, and you want to set them aside in a pile on your desk. Â
How many ways can 4Â of the 20Â books be arranged in a pile?
Answers
Answer:
the answer is 20P4 = 4845
Step-by-step explanation:
Answer:
There are 20 ways to pick the first book, 19 ways for the second
Step-by-step explanation:
If order of the 4 books does not matter then
₂₀C₄ = 20! / (20-4)!4! = 20!/(16!*4!) = 4845 ways
A bag contains marbles: 10 2 are green, 3 are red, and 5 are blue. Debra chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is red and the second is blue? Write your answer as a fraction in simplest form.
Answers
Because the first time you can take 3 from 10 marbles, and the second time there are 5 marbles from the 9 marbles left.
The LAST QUESTION PLEASE HELP
The position d of a block that is attached to a spring is given by the formula d=6cos(pi/2 t) where t is in seconds. What is the maximum distance of the block from its equilibrium position (the position at which d = 0)? Find the period of the motion.
Answers
Step-by-step explanation:
Waves have the form:
y = A sin (2π/T x + φ) + B
where A is the amplitude (the distance from the center of the wave to the max or min),
T is the period (time it takes for one cycle),
φ is the phase shift (moves the wave left or right),
and B is the offset (moves the wave up or down).
This can also be written with cosine.
Here, we have d = 6 cos(π/2 t).
The amplitude is A = 6, so the maximum distance from the equilibrium position is 6 units.
The period is:
2π / T = π/2
T = 4
So the period is 4 seconds.
Hamad made a cuboid of size 2cm X 3cm X 4cm. How many such cuboids will be required to make a cube?
Answers
Answer:
576 cuboids
Step-by-step explanation:
Let
x -----> the length side of the cube
n -----> number of cuboids that are needed
we know that
The volume of the cuboid is equal to
[tex]V=(2)(3)(4)=24\ cm^{3}[/tex]
The volume of the cube is equal to
[tex]V=x^{3}[/tex]
Find the number of cuboids that are needed
[tex](n)24=x^{3}}[/tex]
n*24 must be a perfect cube
so
The minimum value that satisfied n to make n*24 a perfect cube is n=576
[tex]576*24=13,824=24^{3}[/tex]
Answer:
576 Cuboids
Step-by-step explanation:
Help !!!!! GEOMETRY PEOPLE HELP ME LOVES
Answers
The new triangle produced is an exact remake of the first one. The angles or size does not change between the two. Thus, this transformation is an Isometry.
PLEASE HELP ME!!!
Find p(–5) and p(3) for the function p(x) = 2x5 – 9x4 – 2x2 + 12x – 2. Question 8 options: –11,915; –251 –4,487; –551 –11,985; –225 –11,987; –227
Answers
Answer:
p(-5)=-11,987
p(3)=-227
Step-by-step explanation:
To find the value of the function p(-5) just substitute x=-5 into the function expression instead of x:
[tex]p(-5)=2\cdot (-5)^5-9\cdot (-5)^4-2\cdot (-5)^2+12\cdot (-5)-2=\\ \\=-6,250-5,625-50-60-2=-11,987[/tex]
To find the value of the function p(3) just substitute x=3 into the function expression instead of x:
[tex]p(3)=2\cdot 3^5-9\cdot 3^4-2\cdot 3^2+12\cdot 3-2=\\ \\=486-729-18+36-2=-227[/tex]
Answer with Step-by-step explanation:
We are given a function:
[tex]p(x) = 2x^5-9x^4-2x^2+12x-2[/tex]
We have to find the value of p(-5) and p(3)
[tex]p(-5) = 2\times (-5)^5-9\times (-5)^4-2\times (-5)^2+12\times (-5)-2\\\\=-6250-5625-50-60-2\\\\=-11987[/tex]
[tex]p(3) = 2\times 3^5-9\times 3^4-2\times 3^2+12\times 3-2\\\\=486-729-18+36-2\\\\=-227[/tex]
Hence, p(-5)= -11987
and p(3)= -227
How many combinations of 7 candidates can fill 3 vacancies on a city council?
Answers
Answer:
35 combinations
Step-by-step explanation:
You have to use the formula for finding combinations in probability. It looks like this:
₇C₃ = [tex]\frac{7!}{3!(7-3)!}[/tex]
so that gives you
₇C₃ = [tex]\frac{7*6*5*4!}{3*2*1*4!}[/tex]
The 4 factorials cancel each other out, and when you do the math, you get 210/6. That divides evenly into 35. So there are 35 combinations.
what is 12.25 as a fraction
Answers
Answer:
[tex]\large\boxed{12.25=\dfrac{49}{4}}[/tex]
Step-by-step explanation:
[tex]12.\underbrace{25}_{2}=\dfrac{1225}{1\underbrace{00}_2}=\dfrac{1225:25}{100:25}=\dfrac{49}{4}\\\\12.25=12+0.25=12+\dfrac{25}{100}=12+\dfrac{25:25}{100:25}=12+\dfrac{1}{4}\\\\=\dfrac{12\cdot4}{4}+\dfrac{1}{4}=\dfrac{48+1}{4}=\dfrac{49}{4}[/tex]
Please help me with this problem.
Answers
Answer:
3
Step-by-step explanation:
You know that ...
1000 = 10³
when you take the logarithm to base 10, you get
log₁₀(1000) = 3
HELP PLEASE! ONLY 5 MORE MINUTES! Look at the following shape below: Please find the PERIMETER of the following shape using the correct formulas. Use 3.14 for pi.
Answers
Answer:
The perimeter is [tex]P=73.12\ cm[/tex]
Step-by-step explanation:
we know that
The perimeter of the figure is equal to the circumference of a semicircle
plus the perimeter of a square minus the diameter of the circle
so
[tex]P=\pi r+4(b)-D[/tex]
we have
[tex]r=8\ cm[/tex]
[tex]b=16\ cm[/tex]
[tex]D=16\ cm[/tex]
The diameter of the circle is equal to the length side of the square
substitute
[tex]P=(3.14)(8)+4(16)-16[/tex]
[tex]P=25.12+64-16[/tex]
[tex]P=73.12\ cm[/tex]
On a number line the directed line segment from Q to S has endpoints Q at -14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio.
Which expression correctly used the formula, to find the location of point R?
Answers
Answer:
Step-by-step explanation:
The distance from Q to S is 2 - (-14), or 16.
We start at point Q. Note how 3 and 5 add up to 8, which allows us to write:
R = Q + (3/8)(16), or R = -14 + 6, or R = -8.
From R to S it is (5/8)(16), or 10 units.
The directed line segment is partitioned into segments of lengths 6 and 10, whose combined length is 16, as expected.
Answer:
14/5 or A
Step-by-step explanation:
I just took this assignment.
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answers
Answer:
D. 64 and 81
Step-by-step explanation:
The best benchmarks are the ones that are the closest to the value you want the root of. Perfect squares in that neighborhood are ...
7² = 498² = 64your number = 709² = 8110² = 100The closest are 64 and 81.