a/(4√(ab))Rationalize the denominator:-
Answers
Given the expression:
\(\frac{a}{4\sqrt{ab}}\)You can rationalize the denominator by multiplying the numerator and the denominator by the square root in the denominator. Set up that:
\(=\frac{a}{4\sqrt{ab}}\cdot\frac{\sqrt{ab}}{\sqrt{ab}}\)Remember the following Property for Radicals:
\((\sqrt{x})(\sqrt{x})=(\sqrt{x})^2=x\)Then, you get:
\(=\frac{a\sqrt{ab}}{4(\sqrt{ab)^2}}\)\(=\frac{a\sqrt{ab}}{4ab}\)Notice that there is an "a" in the numerator and in the numerator. Knowing that:
\(\frac{a}{a}=1\)You get:
\(=\frac{\sqrt{ab}}{4b}\)Hence, the answer is:
\(=\frac{\sqrt{ab}}{4b}\)Related Questions
help asap, I don't understand
help because I'm failing this class.
Answers
y = (-3/2)x - 1
================================================
Explanation:
The general slope intercept form is y = mx+b
m = slopeb = y interceptThe slope of the original line in the graph is m = 2/3. Flip the fraction and flip the sign to get -3/2 as the perpendicular slope. The original slope and perpendicular slope multiply to -1.
Since the perpendicular slope is -3/2, this narrows the choices between B and D.
We'll plug this perpendicular slope as the new m value, along with the coordinates of the point (-2,2). Then we solve for the y intercept b value.
So,
y = mx+b
2 = (-3/2)*(-2) + b
2 = -1.5*(-2) + b
2 = 3 + b
2-3 = b
-1 = b
b = -1
With m = -3/2 and b = -1, we have the final answer y = (-3/2)x-1 which is choice B
Side notes:
Because -3/2 = -1.5, that equation in bold is the same as y = -1.5x-1The two perpendicular lines intersect at (0,-1). They both have the same y intercept. This won't always happen for any two random perpendicular lines.If you started at P(-2,2) and dropped down 3, and moved to the right 2, then you arrive at (0,-1).What is the scale factor of Figure B to
Figure A? Write your answer as a
simplified fraction.
Answers
Someone help! It is urgent!!!
Answers
Answer:
a. f(-1)=12
b. f(2t)=16t²-6t+5
c. f(t-2)=4t²-19t+27
Step-by-step explanation:
For a, b, c, we are given an input. We plug that into f(x) to find our answers.
a. f(-1)=12
f(-1)=4(-1)²-3(-1)+5
f(-1)=4+3+5
f(-1)=12
-------------------------------------------------------------------------------------------------------------
b. f(2t)=16t²-6t+5
f(2t)=4(2t)²-3(2t)+5
f(2t)=4(4t²)-6t+5
f(2t)=16t²-6t+5
-------------------------------------------------------------------------------------------------------------
c. f(t-2)=4t²-19t+27
f(t-2)=4(t-2)²-3(t-2)+5
f(t-2)=4(t²-4t+4)-3t+6+5
f(t-2)=4t²-16t+16-3t+6+5
f(t-2)=4t²-19t+27
Please I need help with this
Answers
what is 8282 divided by 19 with remainder
Answers
Answer: 8282 / 19 = 435 R 17
*R is Remainder*
Step-by-step explanation:
What would be the equation for a line that is perpendicular to a line of Y = 3X +2
Answers
The equation of the perpendicular line is y = -1/3x
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 3x + 2
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 3
This means that the slope is 2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -1/3
The equation of the line is then calculated as
y = mx
Where
m = -1/3
So, we have
y = -1/3x
Hence, the line has an equation of y = -1/3x
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(X+3)2 + (y-7)2 = 28 what is the radius
Answers
Mr. Adams has 14 boys and 8 girls in his mathematics class. If he chooses two students at random to work on the board, what is the probability that both students chosen are boys? Show your work. (DO NOT GIVE LINKS)
Answers
Answer:
7/11
Step-by-step explanation:
Total students (14+8) = 22
Boys = 14
Probability for boys,
= 14/22
= 7/11
I'm not sure. Hope, this is correct.
Answer:
\(\frac{13}{33}\)
Step-by-step explanation:
14 + 8 = 22
14/22
22 - 1 = 21
14 - 1 = 13
The next time there are 21 students and 13 boys.
13/21
14/22 × 13/21
13/33
Work out the volume of the prism height of 12 4 and five
Answers
The calculated volume of the prism is 702 cubic cm
Finding the volume of the prismFrom the question, we have the following parameters that can be used in our computation
The trapezoidal prism (see attachment)
The formula of the volume of a trapezoidal prism is
Volume = Base area * Height
Where we have
Base area = 1/2 * (8 + 10) * 6
Evaluate the sum of 8 and 10
Base area = 1/2 * 18 * 6
Evaluate the products of 1/2, 18 and 6
Base area = 54
Also, we have
Height = 13
So, the volume is calculated as
volume = 13 * 54
Evaluate
volume = 702
Hence, the volume of the prism is 702 cubic cm
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construct a 95% confidence interval for the mean number of hours of sleep on a typical night for the students. several studies say humans need an average of 8 hours of sleep per night. you can use technology.
Answers
The confidence interval for mean number of hours of sleep on a typical night for the students is [ 94.58,105.42 ] .
Using the mean, standard deviation, number of samples, and desired confidence interval as inputs, the following formula is used to compute the interval:
X + / -( Z * ( σ / √n))
where z comes from the reference's standard distribution tables and has a 95% confidence interval of 1.96.
100 + / - (1.96 * (17.50/40^1/2))
= [ 94.58,105.42 ]
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean.
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When I triple my number and add three and then subtract double my number and add one I get nine what is my number
Answers
Answer:
i belive if not mistaken 6
Step-by-step explanatio
Answer and Step-by-step explanation:
I will replicate what you said into an algebraic equation.
Your number will be represented as x.
(3x + 3) - (2x + 1) = 9
Distribute the negative.
3x + 3 - 2x - 1 = 9
Combine like terms.
x + 2 = 9
Subtract both sides of the equation by 2.
x = 7
Your number is 7.
Checking my answer:
(3(7) + 3) - (2(7) + 3) = 9
(21 + 3) - (14 + 3) = 9
24 - 17 = 9
9 = 9 ✓
So, your number is 7.
#teamtrees #PAW (Plant And Water)
I hope this helps!
simplified form for 2x(y+3)-4xy?
Answers
Answer:
-2xy+6x
Step-by-step explanation:
The circumference of a circular field is 163.28 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
Answers
Trina has a total of 32 crayons. How much boxes of crayons did she buy.
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Answer:
Depends on the type of box, but most likely one box of crayons because 32 packs are sold.
Do you have answer choices?
HELP ASAP!!!
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
A mapping diagram with one circle labeled x-values containing values negative 4, negative 2, 0, 1, and 3 and another circle labeled y values containing values negative 5, negative 4, negative 3, negative 2, and negative 1 and arrows from negative 4 to negative 5, negative 2 to negative 3, 0 to negative 4, 0 to negative 2, 1 to negative 3, and 3 to negative 1.
Is the relation a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
Answers
Answer:
This relation is not a function. For each input, there is not exactly one output.
The relationship in the given diagram is not a function, because for each input there is not exactly one output. So Option A is correct
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
Values of x and values of y
In given diagram,
for x = 0,
there are two values of y, -4 and -2
but according to definition of y, it should give only one value
Hence, it is not a function
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The height h of an object thrown from the top of a ski lift 1240 feet high after t seconds is h=-16t2 +32t+1240. For what times is the height of the object at least 1000 feet?
←
The height of the object is at least 1000 feet from seconds to seconds.
Answers
Check the picture below.
so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.
\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)
now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.
So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark happened between 0 and 5 seconds.
PLEASE HELP MEEEEEEE
AHHHHHHHHHHHHHHHHHHHHHHHHHHHH
Answers
Answer:
7/48
Step-by-step explanation:
First, you would find common denominator
1/12 + 1/16 = 1*4/12*4 + 1*3/16*3 = 4/48 + 3/48 = 7/48
or
Add 4/48 + 3/48 = 4+3/48= 7/48
lve for m.
-3 + m
9 = 10
A.
-30
B.
63
C.
87
D.
93
Answers
The value of m that satisfies the equation -3 + m = 9 is m = 12.
To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.
-3 + m = 9
To move -3 to the other side, we can add 3 to both sides of the equation:
-3 + 3 + m = 9 + 3
Simplifying, we have:
m = 12
Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.
None of the provided answer options (A, B, C, D) match the correct solution.
for such more question on variable
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Which function is shown in the graph below?
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Answer:
\(for \: x = 0 \\ y = 7 \\ the \: seccond \: answer \: is \: corect \\ for \: x = 0 \\ y = {2}^{2} + 3 = 7\)
One lap around the West Middle School track is one-sixth of a mile. Jane ran 7 laps around the track in 10 minutes 30 seconds.seconds. What was Jane’s average speed in miles per minute?
Answers
Answer: \(\dfrac19\text{ miles per minute}\)
Step-by-step explanation:
Given: Length of one lap = \(\dfrac16\) mile.
Jane ran 7 laps, Total distance covered = \(7\times\dfrac16=\dfrac76\text{ miles}\)
Time taken = 10 minutes 30 seconds
\(=\text{ 10 minutes}+\dfrac{30}{60}\text{ minutes}\text{ [1 minute = 60 seconds]}\\\\=(10+\dfrac{1}{2})\text{ minutes}\\\\=\dfrac{21}{2}\text{ minutes}\)
Jane's average speed = \(\dfrac{\text{Total distance covered}}{\text{ Time taken}}\)
\(=\dfrac{\dfrac76}{\dfrac{21}{2}}\\\\=\dfrac{7}{6}\times\dfrac{2}{21}\\\\=\dfrac{1}{9}\text{ miles per minute}\)
Hence, Jane’s average speed = \(\dfrac19\text{ miles per minute}\)
Based on the number of laps that Jane ran and the time she ran it in, her average speed per minute must have been 0.11 miles per minute.
First convert the number of laps ran to miles:
= Number of laps x Conversion factor
= 7 x 1/6
= 7/6 miles
The number of minutes was:
= 10 minutes 30 seconds
= 10.5 minutes
The speed in miles per minute is:
= Number of miles / Number of minutes
= 7/6 ÷ 10.5
= 0.11 miles per minute
In conclusion, find out more at 0.11 miles per minute.
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Sphere A has a radius of 24 centimeters, and sphere B has a diameter of 42 centimeters. The radius of sphere A is
multiplied by what factor to produce the radius of sphere B?
0을
o
Noo
100
Na
Answers
Is 4 a terminating, repeating, or non-repeating decimal?
A Repeating
B Terminating
c) Non-repeating
D) Cannot tell
Answers
(っ◔◡◔)っ ♥ Answer:
⁎ B) Terminating
Explanation:
⁎ Termination means to Stop ( have an end point ) also called "finite" numbers.
Repeating means that it just keeps on going.
A word from me:
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hope this helps :))
7.71 divided by 10 I don’t get how to do this
Answers
Answer: 0.771 you are welcome
Get this riddle correct and earn your prize
Goodluck!!
You find me once in the morning, twice in the afternoon but never in the evening. What am I?
Answers
Answer: o
Step-by-step explanation:
Answer:
the letter '0' ..........
Megan is reading a book about the tallest tree in the world, the redwood tree. One of the trees she reads about grew 300 feet tall over 150 years. If the tree grew at a steady rate, how many inches did it grow each year?
Answers
Answer:
24 inches per year
Step-by-step explanation:
Given that the growth of the red wood tree is about :
300 feet tall in over 150 years ;
Given a steady growth ;
The growth per year is given by :
Height / number of years
300 fts / 150 years
= 2 feets per year
1 Feet = 12 inches
2 feets per year = 24 inches per year
10th grade Geometry Question, I will give brainliest. NEED HELP ASAP!
Answers
Answer:
- 1 + 5 + 2 y is your answer I am the teacher
Leo is a barber.
He charges £5 for a haircut.
He charges 10% extra for hair gel.
One day 25 customers have a haircut.
16 of these ask for hair gel.
Work out the total amount that Leo charges his customers that day.
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25 x £5 = £125
16 x £5.50 = £88
£125 + £88=£213
Answer: £213 (I think)
(I may well be wrong and I’m so sorry if I am)
pls help i don’t get it , ill mark brainlist
Answers
Answer:
2 Radical 50
Step-by-step explanation:
Now we need to reduce the 100,since 2 is not reducible its automatically goes outside the radical. To reduce the 100 we can multiply 50 times 2.You can see now that the 2 in the radical is also not reducible so that also has to go outside the radical. When you get two numbers that are alike you don't necessarily combine them but only use one of them.
Simplify by removing parentheses and collecting like terms.
-8(a+3)-8(a-8)
Answers
Answer:
-16a
Step-by-step explanation:
-8(a+3)-8(a-3)
-8a-24-8a+24
-16a
84.4% of what number is 19.412?
Answers
Answer: 22.4402
Step-by-step explanation:
Answer:
84.4% of 23 is 19.412.
Step-by-step explanation:
Let the unknown number be x.
Now, 84.4% of x = 19.412.
∴ (84.4 ÷ 100) × x = 19.412.
By simplifying the equation,
x = (19.412 × 100) ÷ 84.4
x = 1941.2 ÷ 84.4
∴ x = 23
Thus, 84.4% of 23 is 19.412.
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