What is the simplified form of √10000x^64 ? 5000x^32 5000x^8 100x^8 100x^32
Answer:
Option (d) is correct.
[tex]\sqrt{10000x^{64}}=100x^{32}[/tex]
Step-by-step explanation:
Given : Expression [tex]\sqrt{10000x^{64}}[/tex]
We have to write a simplified form of the given expression [tex]\sqrt{10000x^{64}}[/tex]
Consider the given expression [tex]\sqrt{10000x^{64}}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0[/tex]
[tex]=\sqrt{10000}\sqrt{x^{64}}[/tex]
Factor 10000 as [tex]10000=100^2[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]
[tex]\sqrt{100^2}=100[/tex]
also, [tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
We have,
[tex]\sqrt{x^{64}}=x^{\frac{64}{2}}=x^{32}[/tex]
Thus, [tex]\sqrt{10000x^{64}}=100x^{32}[/tex]
Answer: D. 100x32
Step-by-step explanation:
it is a fraction. it is greater than 0.5 and less than 0.9. its denominator is a square number.its numerator number is a prime number. what could be the mystery number be?
Fraction with numerator as prime number and denominator as a square number between 0.5 and 0.9 is equals to 7/9.
What is fraction?"Fraction is defined as the part of whole number divided into equal parts."
According to the question,
'x / y' represents the required fraction
'x' represents numerator of the given fraction
'y' represents denominator of the given fraction
Condition given,
0.5 < ( x / y) < 0.9
Denominator is squared number
Numerator is a prime number
(5 / 10) < ( 6 / 10) <( 7 / 10) < (7 / 9)< ( 9 / 10)
Hence, required fraction as per condition is ( 7 / 9).
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randy made a business trip of 204 miles. he averaged 52 mph for the first part of the trip and 50 mph for the second part. if the trip took 4 hours, how long did he travel at each rate?
x+y = 4
x=4-y
52x+50y=204
52(4-y)+50y=204
208-52y+50y=204
208-2y=204
-2y=-4
y=2
x= 4-2=2
check 52*2=104
50*2 = 100
104+100=204
so he traveled 2 hours at both 50 and 52 mph
how do you solve f + 15 = 35
So what we do to one side of the equal sign, we must do to the other side as well.
We want to solve for f, so we need to subtract 15 on both sides of the equal sign in order to get f alone by itself on the left side:
[tex] f=20 [/tex]
So now we know that f = 20.
f + 15 = 35
Isolate the variable (f). Note the equal sign. What you do to one side, you do to the other.
Subtract 15 from both sides
f + 15 (-15) = 35 (-15)
f = 35 - 15
Simplify
f = 20
f = 20 is your answer
hope this helps
When adding or subtracting two decimals, what is the first thing you must do
If trap is an isosceles trapezoid, what is the value of x
Answer:
Option E ⇒ x = 19
Step-by-step explanation:
See the attached figure.
TRAP is an isosceles trapezoid
The shown angles are supplementary angles
So, the sum of (5x+9) and (4x) is 180
So, 5x+9 + 4x = 180
solve for x
9x + 9 = 180
9x = 180-9 = 171
x = 171/9 = 19
The answer is option E
91 more than the square of a number in verbal form
If the area of a rectangle is 24a2b and the length is 8ab2, what would be the width of the rectangle, given that width is found by dividing area by length? Simplify the answer.
the quantity of 3 times a all over b
b over the quantity 3 times a
3 over the quantity a times b
3ab
Answer:
Option the quantity of [tex]3[/tex] times a all over b
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
where
L is the length side of rectangle
W is the width side of rectangle
In this problem we have
[tex]A=24a^{2}b\ units^{2}[/tex]
[tex]L=8ab^{2}\ units[/tex]
Remember that
[tex]W=\frac{A}{L}[/tex]
substitute
[tex]W=\frac{24a^{2}b}{8ab^{2}}=\frac{3a}{b}\ units[/tex]
If you triple 4 and subtract 2 each day, how many days until you have zero?* 2 6 8 12
triple 4 = 4x3 = 12
divide 12 by 2: 12/2 =6
it will take 6 days
The following information is obtained from two independent samples selected from two normally distributed populations.
n1 = 18 x1 = 7.82 σ1 = 2.35
n2 =15 x2 =5.99 σ2 =3.17
A. What is the point estimate of μ1 − μ2? Round to two decimal places.
B. Construct a 99% confidence interval for μ1 − μ2. Find the margin of error for this estimate.
Round to two decimal places.
A. The point estimate of μ1 − μ2 is calculated using the value of x1 - x2, therefore:
μ1 − μ2 = x1 – x2 = 7.82 – 5.99
μ1 − μ2 = 1.83
B. The formula for confidence interval is given as:
Confidence interval = (x1 –x2) ± z σ
where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58
and σ is calculated using the formula:
σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]
σ = sqrt [(2.35^2 / 18) + (3.17^2 / 15)]
σ = 0.988297
Going back to the confidence interval:
Confidence interval = 1.83 ± (2.58) (0.988297)
Confidence interval = 1.83 ± 2.55
Confidence interval = -0.72, 4.38
The cruise control feature on a car is set to maintain a speed of 65 miles per hour. The car’s actual speed never varies by more than three mph. Select the inequality that represents the speed of the car while cruise control is being used.
Final answer:
The inequality that represents the speed of the car while cruise control is being used is 62 ≤ s ≤ 68, where s is the car's speed and it shows the car's speed will be at least 62 mph and at most 68 mph.
Explanation:
The cruise control feature on a car is designed to maintain a steady speed, in this case, 65 miles per hour. However, it is acknowledged that the car's actual speed can fluctuate slightly. The question asks for an inequality that represents the potential speed of the car while cruise control is in use.
Considering the car's speed can vary by up to 3 mph more or less than the cruise control setting, we can set up an inequality to describe this range of speeds. The car's speed (s) should be no more than 3 mph above 65 mph and no less than 3 mph below 65 mph. Therefore, the inequality that represents the speed s of the car would be:
62 ≤ s ≤ 68
This inequality shows that the car's speed will be at least 62 mph and at most 68 mph, encompassing the 3 mph range of variation allowed by the cruise control setting.
Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
Solve the equation for 10 points
6x+7=8x−15
You need to pump water out of a flooded basement, using two 50-gallon-per-minute (gpm) pumps. The basement has the dimensions shown and is flooded to a depth of 16 inches. How long will it take to pump the water out of the basement?
How do you turn 1/8 into a fraction
A girl wants to count the steps of a moving escalator which is going up. If she is going up on it, she counts 60 steps. If she is walking down, taking the same time per step, then she counts 90 steps. How many steps would she have to take in either direction, if the escalator were standing still?
explain the place value relationship when the same two digits are next to each other in a multidigit number
Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parentheses 6 minus 6 i close parentheses.
the diagram show a straight line ABC . Find the value of p
Mr. Wilson has 3000 in his bacon count Mrs. Nelson has 10 times as much money in her bank account as Mr. Wilson has in his big and count how much money does Mrs. Nelson have in her bank account
The tickets in a box are numbered from 1 to 20 inclusive. If a ticket is drawn at random and replaced, and then a second ticket is drawn at random, what is the probability that the sum of their numbers is even?
Answer:
1/2
Step-by-step explanation:
no guarantees but the guy before me said 10/20 and of course if you divide 10 and 20 you get 0.5, and 0.5 is equal to 1/2.
In which situation is the distance traveled proportional to time?
A car moving in stop-and-go traffic
A person biking on a trail at 12
miles per hour for 20
minutes
A baseball hit to center field
A race car slowing down after crossing the finish line
Answer: a person on a trail at 12 miles per hour for 20 minutes
Step-by-step explanation:
just go it right!!!
Plz help me answer this
Complete the steps in order to write the inverse of f(x) = x + 5
To find the inverse of a function, replace f(x) with y, swap x and y, then solve for y. Thus, the inverse of f(x) = x + 5 is f^-1(x) = x - 5.
Explanation:To find the inverse of a function like f(x) = x + 5, we use the following steps:
Replace the function notation f(x) with y. So, we get y = x + 5.
Swap the roles of x and y. This changes the equation to x = y + 5.
Solve for y to get the inverse function. By subtracting 5 from both sides, we acquire y = x - 5.
This implies that the inverse of the function f(x) = x + 5 is f-1(x) = x - 5.
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What is 25 degrees lower than 57
solve the system of equations using elimination. 3p+9q=6 5p-5q=30
8x-12y=84 into slope intercept form
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what else would you need yo show that ABC DEF by ASA APEX ?