The given expression 4 sqrt(16x^11y^8/81x^7y^6) simplifies to (4/9) * x^2 * y by taking the square root of each term separately and then simplifying the powers of x and y.
Explanation:The expression given is 4 sqrt(16x^11y^8/81x^7y^6). To simplify this expression, we need to apply the square root to both the numerator and the denominator separately and simplify any like terms, as well as using the property of exponents to simplify the powers of x and y.
We start by simplifying the square root of each component:
Square root of 16 is 4.x^11 under the square root becomes x^(11/2).Similarly, y^8 under the square root becomes y^(8/2), which is y^4.The square root of 81 is 9.x^7 under the square root becomes x^(7/2).y^6 under the square root becomes y^(6/2), which is y^3.Now, divide and simplify:
(4 * x^(11/2) * y^4) / (9 * x^(7/2) * y^3) = (4/9) * x^((11/2) - (7/2)) * y^(4 - 3)
Therefore, we get:
(4/9) * x^2 * y
Which regular polygon would have each of its interior angles measure 120°? hexagon heptagon octagon nonagon?
Which graph would help solve the equation 5log(x+3)=5
The value of x is 7 for the given equation.
What is logarithm?Logarithm, a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.
For the given situation,
The equation is 5log(x+3)=5.
On solving this equation, we can get value of x.
⇒ [tex]5log(x+3)=5[/tex]
⇒ [tex]log(x+3)=1[/tex]
We know that, log 10 = 1
Then,
⇒ [tex]log(x+3)=log10[/tex]
⇒ [tex]x+3=10[/tex]
⇒ [tex]x=7[/tex]
Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.
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The measure of an angle is 8 times the measure of its complement. tina writes an equation and finds the correct measure of each angle. which shows the equation tina could have written and the angle measures she could have found?
The measure of angles are 10 and 80 degree.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
We have,
let the complementary angle = x
and, the another angle is = 8x
We know the complementary angle sum to 90 degree.
So, x + 8x = 90
9x = 90
x =10
Thus, the measure of angles are 10 and 80 degree.
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what expression is equivalent to the division expression 3/4 divided by 4/5
Answer:
3/4 ÷ 4/5 = .75 ÷ .80
Step-by-step explanation:
3/4 ÷ 4/5
= .75 ÷ .80
= 0.9375
NEED HELP ASAP!
Subtract.
(4x^2+8x−2)−(2x^2−4x+3)
Answer in standard form
Karen is considering taking out a 20-year loan with monthly payments of $260 at an APR of 5.5%, compounded monthly, and this equates to a loan of $37,796.89. Assuming that the APR and the length of the loan remain fixed, which of these is a correct statement?
The correct statement is A;If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
How to calculate EMI?The EMI formula is :
[tex]\dfrac{pr(1 + r)^n}{(1 + r)^n - 1}[/tex]
Where r = 5.5/12/100 = 0.00425
p = 37,796.89
and n = 20 x 12 = 240
Putting the values in formula we get'
= (37,796.89x 0.00425 x 2.767)/1.767
= $350
Hence,
The correct statement is A; If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
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Answer:If Karen's monthly payment were $240, the amount of the loan that she is considering taking out would be less than $37,796.89.
Step-by-step explanation:
An equiangular triangle can be scalene. A. True B. False
Which equation in point-slope form contains the point (4, –1) and has slope 3? y – 1 = 3(x + 4) y – 4 = 3(x + 1) y + 1 = 3(x – 4)
Answer:
the answer is option d y+1 =3 (x-4)
Roman saves $500 each year in account earning interest at an account earning interest at an annual rate of 4% compounded annually.How much interest will the account earn at the end of each of the first 3 years?
Please someone help Me with this problem. I really need help.
Subtract.
(x + 1) − (−2x − 5)
Answer:
3x+6
Step-by-step explanation:
you have to distribute the negative to get the parentheses away and simplify
can someone help me on trigonometry ?
sketch one cycle of the cosine function y=-cos 3 theta
Answer with explanation:
The given cosine function is
y= - cos 3 (theta)= -3 cos A, where , theta =A.
→→Domain of Cos A
= All Real number
= Period is from (-π , π)
Range of Cos A=[-1, 1]
→Domain of Cos 3 A,will be also, all real number.
Period is from,
[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]
But range of Cos 3A,will be same as ,Cos A which is equal to ,[-1,1].
→Plotted the graph of ,y=-cos 3 A, having cycle ,
[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]
A math book sells for $106.50. (a) find the amount of sales tax, to the nearest cent, if the sales tax rate is 8.5%. (b) find the total purchase price
what is 3 ^9? how to solve?
The cross-sectional area parallel to the bases of the two figures above is the same at every level. Find the volume of the cone, to the nearest tenth.
A.26.5cm3
B.44.2cm3
C.79.5cm3
D.132.5cm3
Find the Mean Median Mode and range of each data set that is obtained after adding the given constant. 12,10,15,17,15,9,10,15,12,14,+9. Please show work.
Mean: 12.545454545455
Median: 12
Range: 8
Mode: 15, appeared 3 times
Largest: 17
Smallest: 9
Sum: 138
Count: 11
If a scare as side lengths of 5 inches what is the lengths of the diagonal to the nearest 10th of in inch
Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. What is the speed of the train, if it is 5 km/h greater than the speed of the car?
[tex]\\ \text{Let the speed of the car is x km/h}\\ \text{Then, the speed of the train is x+5 km/hr}\\ \text{Now, 4 hr is the time of the car}\\ \text{and 7 hour is the time of the train}\\ \text{We know the formula}\\ \text{Distance }= \text{Velocity }\times \text{ time}\\ \text{Distance travelled by car is 4x}\\ \text{Distance travelled by train is }7(x+5)\\ \text{The total distance is given by 255 km. Hence, we have}\\ 4x+7(x+5)=255\\ 4x+7x+35=255\\ 11x=220\\ x=20[/tex]
The speed of the car is 20 km/hr and hence the speed of the train is 2+5=25 km/hr.
The speed of the train is given by 25 km/hr.
how do you do 27?????
Can someone help me in this trig question, please? thanks
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12
The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).
The positionSince the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°
So, substituting the value of θ into the positions, we have
(20cos75°, 20sin75°)
The value of 20cos75°
20cos75° = 20cos(45 + 30)
Using the compound angle formula
cos(A + B) = cosAcosB - sinAsinB
With A = 45 and B = 30
cos(45 + 30) = cos45cos30 - sin45sin30
= 1/√2 × √3/2 - 1/√2 × 1/2
= 1/2√2(√3 - 1)
= 1/2√2(√3 - 1) × √2/√2
= √2(√3 - 1)/4
= (√6 - √2)/4
= (-√2 + √6)/4
So, 20cos75° = 20 × (-√2 + √6)/4
= 5 (-√2 + √6)
The value of 20sin75°
20sin75° = sin(45 + 30)
Using the compound angle formula
sin(A + B) = sinAcosB + cosAsinB
With A = 45 and B = 30
sin(45 + 30) = sin45cos30 + cos45sin30
= 1/√2 × √3/2 + 1/√2 × 1/2
= 1/2√2(√3 + 1)
= 1/2√2(√3 + 1) × √2/√2
= √2(√3 + 1)/4
= (√6 + √2)/4
= (√2 + √6)/4
So, 20sin75° = 20 × (√2 + √6)/4
= 5(√2 + √6)
Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).
So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).
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Determine whether quantities vary directly or inversely and find the constant of variation. If 5 bushels of wheat weigh 136 kg, how much do 3.5 bushels of wheat weigh?
Let the bushels of wheat is b and weight of the wheat is w.
We can say that more the bushels of wheat more will be the weight of the wheat.
Hence, the quantities vary directly.
Therefore, we have
[tex]b=kw[/tex], where k is the constant of variation.
Now, we have been given that 5 bushels of wheat weigh 136 kg. Thus, we have
[tex]5=136k\\ \\ k=\frac{5}{136}[/tex]
Thus, the constant of variation is [tex]\frac{5}{136}[/tex]
Now, we have been given 3.5 bushels of wheat. Hence, we have
[tex]3.5=\frac{5}{136} w\\ \\ w=\frac{136\times 3.5}{5} \\ \\ w=95.2[/tex]
Therefore, 3.5 bushels of wheat weigh 95.2 kg
CAN SOMEONE HELP ME ON THIS
At noon joyce drove to the lake at 30 mph, but she made the long walk back home at 4 mph. how many hours did she walk if she was gone for 17 hours
Answer:
i just did this on a quiz the answer was 15 hours
Step-by-step explanation:
What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.
To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.
HELP!! Drag values to complete each equation.
Answer:
a.[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]
b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]
Step-by-step explanation:
We have to complete each equation
We are given that
[tex]((12)^2)^3\cdot (12)^{-4}[/tex]
[tex](12)^6\cdot (12)^{-4}[/tex]
Using identity
[tex](a^x)^y=a^{xy}[/tex]
[tex](12)^{6-4}=(12)^2[/tex]
Using identity: [tex]a^x\cdot a^y=a^{x+y}[/tex]
[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]
b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}[/tex]
[tex]\frac{(12)^2}{(12)^2}[/tex]
[tex](12)^{2-2}=(12)^0=1[/tex]
Using identity: [tex]\frac{a^x}{a^y}=a^{x-y},a^0=1[/tex]
[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]
A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)
A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)
Solution:
We have 48 [tex] \frac{miles}{hour} [/tex]
To convert, miles to centimeters.
Let us convert miles to feet and then inches and then centimeters.
1miles=5280feet
And, 1 foot=12inches
So, 5280 feet or 1 miles =12*5280inches
So, 1miles=63360inches
Now, Let us convert inches to centimeters
1centimeter=0.39inches
Or, 1 inch= [tex] \frac{1}{0.39} [/tex] centimeter
So, 63360inches (or 1 mile)= [tex] \frac{63360}{0.39} [/tex] centimeter
1mile or 63360inches=162461.54centimeter
1mile=162461.54 centimeter
We have, 48 [tex] \frac{miles}{hour} [/tex]
We have, 48 *[tex] \frac{162461.54 centimeter}{60minutes} [/tex]
We have, 48* [tex] \frac{162461.54 centimeter}{60*60seconds} [/tex]
So, We have, 48* [tex] \frac{162461.54 centimeter}{3600seconds} [/tex]
=48*[tex] \frac{162461.54}{3600} [/tex][tex] \frac{centimeters}{second} [/tex]
=48*45.13[tex] \frac{centimeters}{second} [/tex]
=2166.15[tex] \frac{centimeters}{second} [/tex]
Answer:= Speed of the car in centimeters per second is 2166.15 centimeters/second
the probability of winning the game is 7/10. What is the probability that they will lose?
The probability of losing the game is 3/10 or 0.3 when the probability of winning is 7/10, because the total probability must always equal 1.
If the probability of winning the game is 7/10, then the probability of losing the game is the complement of the probability of winning. This means we subtract the probability of winning from 1. Therefore, the probability of losing the game is 1 - 7/10 = 3/10 or 0.3. This is because the sum of the probabilities of all possible outcomes in a probability distribution must equal 1.
help! I will give thanks!
If p(x) = 2x^3 - 3x + 5, what is the remainder of p(x) divided by (x - 5)
Final answer:
Using the Remainder Theorem, after substituting 5 into the polynomial p(x), we find that the remainder when p(x) is divided by (x - 5) is 240.
Explanation:
To find the remainder of p(x) divided by (x - 5), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial p(x) divided by (x - a) is p(a). Thus, we need to evaluate p(5).
Let's substitute x with 5 in the polynomial p(x):
p(5) = 2(5)^3 - 3(5) + 5
= 2(125) - 15 + 5
= 250 - 15 + 5
= 240.
Therefore, the remainder when p(x) is divided by (x - 5) is 240.