Answer:
The area of the rectangle is 9.
Step-by-step explanation:
The first thing to take into account is that the area of a rectangle is obtained by multiplying its length and width.
[tex]area=length\times width[/tex]
The problem says that the length is [tex]\sqrt[3]{81}[/tex] and the width is [tex]3^{\frac{2}{3}}[/tex]. So, to find the area we must replace the values of length and width into the previous expression.
[tex]area=length\times width[/tex]
[tex]area=(\sqrt[3]{81})\times (3^{\frac{2}{3}})[/tex]
The previous seems to be difficult but with a little of manipulation we can get a result without a calculator.
First step: the term [tex]\sqrt[3]{81}[/tex] could be written as exponential expression.
[tex]area=(81^{\frac{1}{3}})\times (3^{\frac{2}{3}})[/tex]
Second step: the term [tex]3^{\frac{2}{3}}[/tex] could be written in other way.
[tex]area=(81^{\frac{1}{3}})\times ((3^2)^{\frac{1}{3}})[/tex]
Third step: in the same way, the term [tex]81^{\frac{1}{3}}[/tex] could be written in other way taking into account that [tex]81=9^2[/tex].
[tex]area=((9^2)^{\frac{1}{3}})\times ((3^2)^{\frac{1}{3}})[/tex]
Forth step: the two terms must have the same base to apply other exponential rules; for example, the base could be 9.
[tex]area=(9^{\frac{2}{3}})\times (9^{\frac{1}{3}})[/tex]
Fifth step: as both terms have the same base, we must add the exponents and simplify the expression.
[tex]area=9^{\frac{2}{3}}\times 9^{\frac{1}{3}}[/tex]
[tex]area=9^{\frac{2}{3}+\frac{1}{3}}[/tex]
[tex]area=9^{\frac{3}{3}}[/tex]
[tex]area=9^1[/tex]
[tex]area=9[/tex]
Thus, the area of the rectangle is 9.
what is the simplest form of the expression below?
Let us simplify each Expression Separately :
✿ [tex]\mathsf{(\frac{cot\theta.cos\theta}{sin\theta}).tan\theta}[/tex]
[tex]\mathsf{\implies (\frac{cot\theta.tan\theta.cos\theta}{sin\theta})}[/tex]
[tex]\mathsf{We\;know\;that : tan\theta.cot\theta = 1}[/tex]
[tex]\mathsf{\implies (\frac{cos\theta}{sin\theta})}[/tex]
[tex]\mathsf{We\;know\;that : cot\theta = \frac{cos\theta}{sin\theta} }[/tex]
[tex]\mathsf{\implies (\frac{cot\theta.cos\theta}{sin\theta}).tan\theta = cot\theta }[/tex]
✿ [tex]\mathsf{(\frac{sin\theta}{cos\theta.tan\theta})}[/tex]
[tex]\implies \mathsf{(\frac{\frac{sin\theta}{cos\theta}}{tan\theta})}[/tex]
[tex]\mathsf{We\;know\;that : tan\theta = \frac{sin\theta}{cos\theta} }[/tex]
[tex]\implies \mathsf{(\frac{tan\theta}{tan\theta})}[/tex]
[tex]\implies \mathsf{1}[/tex]
[tex]\mathsf{\implies (\frac{sin\theta}{cos\theta.tan\theta}) = 1}[/tex]
[tex]\mathsf{The\;Simplest\;form\;of\;the\;Given\;Expression\;is : cot\theta}[/tex]
The simplifying form of expression by using the trigonometry formula is,
⇒ [tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex] = cot θ
The used formula is,
[tex]\frac{sin \theta }{cos \theta } = tan \theta[/tex]
And, [tex]\frac{cos \theta }{sin \theta } = cot \theta[/tex]
Given that,
The expression is,
[tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex]
Now, by using the trigonometry formula, simplify the expression as,
⇒ [tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex]
Substitute [tex]\frac{sin \theta }{cos \theta } = tan \theta[/tex] And, [tex]\frac{cos \theta }{sin \theta } = cot \theta[/tex],
⇒ [tex]\frac{cot(\theta)}{tan\theta} \times tan\theta \div \frac{tan\theta}{tan\theta}[/tex]
⇒ [tex]cot \theta \div 1[/tex]
Therefore, the solution of expression is,
⇒ cot θ
To learn more about trigonometry visit:
brainly.com/question/13729598
#SPJ4
Find the simple interest and the total amount after three years. Principal =11,750= 11 =11,750 rupees Annual rate of interest 7.5%= Total interest == = rupees Total amount = = = rupeesFind the simple interest and the total amount after three years. Principal =11,750= 11{,}750 =11,750 rupees Annual rate of interest=7.5%=Total interest rupees Total amount rupees
The simple interest after three years is ₹2625 and the total amount is ₹14,375.
Explanation:To find the simple interest and total amount after three years, we can use the formula:
Simple Interest = Principal × Rate × Time
Total Amount = Principal + Simple Interest
Given that the Principal is ₹11,750 and the Annual Rate of Interest is 7.5%, we can calculate the Simple Interest by substituting these values into the formula:
Simple Interest = ₹11,750 × 0.075 × 3
After calculating, we find that the Simple Interest is ₹2625.
To find the Total Amount, we can use the formula:
Total Amount = Principal + Simple Interest
Substituting the values into the formula, we get:
Total Amount = ₹11,750 + ₹2625
After calculation, the Total Amount is ₹14,375.
sarosh receives 8% commission on the final price of the clothing he sells . a customer bought a $45.00 coat the was marked 20% off and a $95.00 suit that was marked 30% off what would sarosh's commission be on that customers purchase?
Answer:
$8.2
Step-by-step explanation:
The final price of the coat = $45 -0.2 * $45 = $36
The final price of the suit = $95 − 0.3 * $95 = $66.5
sarosh's commission = 0.08 * ( $36 + $66 ) = $8.2
Ty takes 1 hour to read 35 pages, 2 hours to read 70 pages, and 3 hours to read 105 pages, is this proportional? Explain
Answer:
Yes it is proportional.
Step-by-step explanation:
35/1 is the same thing as 70/2, as well as 105/3, because they all simplify to 35/1.
How many equivalent fractions can you write for a given fraction?
Answer:
An infinite amount
Step-by-step explanation:
Because numbers stretch on infinitely you literally can keep multiplying the starting value by numbers forever to keep equal fractions.
Hi what’s 7 times 8 again?
Answer:
the ansnwer is 56
mark as brainlest please!!
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
Add 7, 8 times and you'd get 56
The radius of the circle shown below is 7 inches what is the approximate length of AB?
Answer:
16.5 inches
Step-by-step explanation:
WE have arc length formula for a circle as
Arc length = [tex]\frac{x}{360} (2\pi r)[/tex]
where x is the central angle the arc subtends at the centre.
Here x = 135
r= 7 inches
Hence arc length
=[tex]\frac{135}{360} (2\pi )(7) =16.5"[/tex]
Hence option B
16.5 inches is right answer for arc length for a circle of radius 7 inches.
The measure of length of arc AB is 16.5 inches. Therefore, option B is the correct answer.
What is the relationship between a central angle and its arc?An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
Given that, the radius of the circle is 7 inches and measure of arc AB is 135°.
Let O be the center of circle.
So, ∠AOB=135°
We know that, arc length of circle is θ/360° ×2πr
= 135°/360° ×2×3.14×7
= 0.375×2×3.14×7
= 16.485
≈ 16.5 inches
Therefore, the approximate length of AB is 16.5 inches.
To learn more about the circle theorems visit:
https://brainly.com/question/19906313.
#SPJ5
Suppose the radius of a circle is 3 units. what is its circumference ?
Answer:
18.84 (or 19 to 2.s.f)
Step-by-step explanation:
The formula for the circumference of a circle is π * diameter. To find the diameter you multiply the radius by 2:
3 * 2 = 6
Then simply plug the value into the formula:
π * 6 = 6π ≈ 18.84 ≈ 19 to 2.s.f
Answer:The answer is 18.84
Step-by-step explanation:To figure out the circumference of a circle you need to divide the radius by 2. After that you would do [tex]2\pi * ( your number )[/tex] * 2
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
see explanation
Step-by-step explanation:
(1)
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 2, - 5) and (x₂, y₂ ) = (18, - 5)
m = [tex]\frac{-5+5}{18+2}[/tex] = [tex]\frac{0}{20}[/tex] = 0
(2)
divide number of miles travelled by number of gallons used
= [tex]\frac{132}{6}[/tex] = 22 miles per gallon
use the substitution method to solve the system of
equations.choose the correct ordered pair.
3x+y=10
y=x-2
A.(4,2)
B.(5,3)
C.(2,0)
D.(3,1)
Answer:
I THINK THE ANSWER IS D
TELL ME IF I"M WRONG
Step-by-step explanation:
A skydiver falls 144 feet in 3 seconds. How far does he fall per second
Answer:
144/3=48 ft per sec
Step-by-step explanation:
Answer:
48 per second
Step-by-step explanation:
if you divide 144 by 3 you get 43
Which of the following segments is a radius a circle A
Bc
Ac
Cm
Rs
Answer: Segment AC (second choice)
The radius is the segment that goes from the center, point A, to a point on the circle (either B, C or M). Since AB and AM aren't mentioned, this means that only AC is a radius of the four answer choices listed.
The ordered pairs model an exponential function, where p is the function name and t is the input variable.
{(1,80),(2,240),(3,720),(4,2160)}
What is the function equation in sequence notation?
HURRY!
Answer:
what he said
Step-by-step explanation:
please answer this properly and correctly
at the beginning of school, we had 40 algebra books. We increased our supply by 65%. how many algebra books does the school have now?
Which algebraic expression repesents the phrase? Cindy studied seven more hours than Nikki studied. a. n+7 b. 7-n c. 7n d. n/7
Answer:
Option a is the correct choice.
Step-by-step explanation:
Let n be number of hours studied by Nikki.
We are told that Cindy studied seven more hours than Nikki studied. This means that number of hours studied by Nikki plus 7 hours equals to the number of hours studied by Cindy.
We can represent this information in an expression as :
[tex]\text{The number of hours studied by Cindy}=n+7[/tex]
We can see from our given choices that expression given in option a represents the number of hours studied by Cindy in terms of hours studied by Nikki.
Therefore, option a is the correct choice.
What value of $k$ will make $4x^2 - 20x + k$ the square of a binomial?
Answer:
k = 25
Step-by-step explanation:
(2x - sqrt(k) )^2 Expand this as a binomial
4x^2 - 4x*sqrt(k) + k The middle term must be -20x Solve for k so it is
-4xsqrt(k) = - 20x Divide by -4x
sqrt(k) = -20x/-4x Do the division
sqrt(k) = 5 Square both sides
k = 25
2x2+5x-12 solve this equation
The expression 2x²+ 5x - 12 has infinite many solutions
How to detemrine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
2x²+ 5x - 12
The above is an expression and not an equation
This means that it has infinite many solutions
Hence, the expression 2x²+ 5x - 12 has infinite many solutions
Read more about expressions at
https://brainly.com/question/30492964
#SPJ2
Which of these is a tax form that employers send to their employees?
A. W-2 form
B. 1040EZ form
C. Tax schedule form
Answer:
A. W-2 form
Step-by-step explanation:
What is Distributive property
Answer:
It is when you distribute one number between two numbers like this
Step-by-step explanation:
2(5+3)
5 x 2 and 2 x 3
10 + 6
16
jim and Jon are painting a fence. Jon painted 1/4 of the fence. Jim painted 5/12 of the fence. how much of the fence did they paint in total?
Our first step is the find the lcm of 4 and 12 so we can add the two fractions without having a problem.
The lcm of 4 and 12 is clearly 12 because 12 is a multiple of 4. 12 divided by 4 is 3, so you must multiply by 3/3 to be able to add the two fractions.
1/4*(3/3)=3/12.
So, 3/12+5/12=7/12.
Jim and Jon painted 7/12 of the the fence.
Answer:
2/3 of the fence
Step-by-step explanation:
Jim painted 1/4 of the fence
Jon painted 5/12 of the fence
Together they painted
1/4+5/12 of the fence
We need a common denominator to add the fractions
The common denominator is 12
1/4*3/3 + 5/12
3/12 + 5/12
8/12
This can be simplified by dividing the top and bottom by 4
2/3
Together, they painted 2/3 of the fence.
marco wants to invest his savings in a bank for 3 years. he has £15000 to invest and recieves offers from two banks: bank of peace= 2.5% a year compound interest or bank of trust= 3.8% for 1st year 1% extra for each extra year. which bank should marco choose to get the most interest over the three year period? you must show all your working
Bank of Peace= 15000(1+0.025)³=£16153.36
Bank of Trust=15000(1+0.038)=£15570
£15570(1+0.01)=£15882.95
Bank of Peace is the best choice.
I would choose the Bank of Peace to get the most of my savings.
Formula for calculating the compound value of the savings at the Bank of Peace = FV = P (1 + r)^n
FV = Future value
P = amount deposited
R = interest rate
N = number of years
£15,000 x (1.025)^3 = £16,153.36
Interest earned at the Bank of Trust in the first year = £15,000 x 0.038 = $570
Total amount at the end of the first year = $570 + £15,000 = £15,570.
Value for the two extra years = $15,570 x (1.01)^2 =$15,882.96
To learn more, please check: https://brainly.com/question/14640433
Carrie buys 6.2 yards of blue fabric and 5.4 yards of red fabric.If the blue and red fabric costs the same amount per yard,and Carrie pays $58 for all of the fabrics ,what is the cost per yard ?
Answer:
5.00 a yard
Step-by-step explanation:
5.4 + 6.2 = 11.6
58.00 divided by 11.6 =
5
5.00 a yard
Answer:
$5 per yard
Step-by-step explanation:
Add 6.2 and 5.4
You get 11.6
Divide 11.6 by 58
The answer is 5
What percent of 94 is 47
Answer:
50%
Step-by-step explanation:
47 is half of 94 which is the same thing as 50% of 94
Answer:
94% of 47 is just 47 x 0.94 ¯\_(ツ)_/¯
So 44.18
Please mark brainliest which would help alot.
Step-by-step explanation:
The variable y is directly proportional to the variable x. If y = 12 when x = 14, what is the value of x when y = 24? A) 26 B) 28 C) 30 D) 32
CORRECT ANSWERS ONLY, ILL MARK YOU THE BRAINLIEST!!!!!!!!!
Hi There!
Answer:
B) 28
Step-by-step explanation:
y = 12 and x = 14 are both proportional.
y = 24 and x = ? are both proportional.
You notice that 24 is twice as much as 12 so we do the same with x.
14 * 2 = 28
They are both proportional when y = 24 and x = 28.
Hope This Helps :)
Answer:
B) 28
Step-by-step explanation:
The equation for direct proportion is
y= kx
If y =12 and x =14
12 = k * 14
Divide each side by 14
12/14 = k
Simplifying
6/7 =k
y =6/7 x
Now if y =24
24 = 6/7 x
Multiply each side by 7/6 to isolate x
24 * 7/6 = 7/6 * 6/7 x
28 =x
Problem 2: Toshi estimates that she needs 2 minutes to read one page. How many minutes longer did she spend reading the 304-page book than Kira-Kira? Explain how you found your answer.
13/10 of a number is what percentage of that number?
[tex]\dfrac{13}{10}=\dfrac{13}{10}\cdot100\%=13\cdot10\%=130\%\\\\\dfrac{13}{10}\ \text{of a number is}\ 130\%\ \text{of a number}.[/tex]
Answer:
130%
Step-by-step explanation:
graph the solution to the inequality 2x-3y<18
<, > - dotted line
≤, ≥ - solid line
[tex]2x-3y<18\qquad\text{subtract 2x from both sides}\\\\-3y<-2x+18\qquad\text{change the signs}\\\\3y>2x-18\qquad\text{divide both sides by 3}\\\\y>\dfrac{2}{3}x-6\\\\y=\dfrac{2}{3}x-6-\text{It's a linear function}\\\\for\ x=0\to y=\dfrac{2}{3}(0)-6=0-6=-6\to(0;\ -6)\\\\for\ x=6\to y=\dfrac{2}{3}(6)-6=2(2)-6=4-6=-2\to(6;\ -2)[/tex]
Consider the sequence 130, 143, 156, 169, ... Write an explicit formula to represent the arithmetic sequence and use it to find the 13th term.
Answer:
a(n) = 130 + (n-1) 13
13th term = 286
Step-by-step explanation:
We are given a sequence of numbers: 130, 143, 156, 169, ... and we are to write an explicit formula to represent the arithmetic sequence and use it to find the 13th term.
We know that the arithmetic sequence can be defined by:
[tex]a_n=d(n-1)+c[/tex]
where [tex]d[/tex] = the common difference between consecutive terms ; and
[tex]c[/tex]=[tex]a_1[/tex]
13th term:
[tex]a_{13}=130+(12)13 = 286[/tex]
Therefore, the formula for this sequence will be a(n) = 130 + (n-1) 13 and 13th term is 286.
One number is 7 more than another.The difference between their squares is 217.What are the numbers?
The problem where one number is 7 more than another and their squares differ by 217 can be solved by creating a system of equations and simplifying to find the numbers are 12 and 19.
Explanation:To solve the problem where one number is 7 more than another and the difference between their squares is 217, we can create a system of equations. Let's assume the first number is x and the second number is x+7. The problem then translates to the equation (x+7)² - x² = 217.
Step-by-step solution:
Expand the left side of the equation: (x+7)² - x² = (x² + 14x + 49) - x².Cancel out the x² terms: 14x + 49 = 217.Subtract 49 from both sides: 14x = 168.Divide both sides by 14: x = 12.Therefore, the first number is 12 and the second number is 12 + 7 = 19.After computing the solution, we find that the two numbers are 12 and 19.