Step-by-step explanation:
Given that:
∛(2) * 2^(-1/13) * ¹²√(32)
= ∛(2) * 2^(-1/13) * ¹²√(2⁵)
[since, ⁿ√(a) = a^(1/n)]
= 2^(1/3) * 2^(-1/13) * 2^{5 * (1/12)}
= 2^(1/3) * 2^(-1/13) * 2^{(5*1)/12}
= 2^(1/3) * 2^(-1/13) * 2^(5/12)
[since, a^m * a^n = a^(m+n)]
= 2^{(1/3) - (1/13) + (5/12)}
Take the LCM of 3, 13 and 12 is 156.
= 2^[{(1*52) - (1*12) + (5*13)}/156]
= 2^{(52 - 12 + 65)/156}
= 2^{(117 - 12)/156}
= 2^(105/156)
Now reduce the power fraction in simplest form by cancelling method.
= 2^(35/52) (or)= {2^(35)}^(1/52) (or)
= ⁵²√{2^(35)}
Answer: Hence, the simplified form of ∛(2) * 2^(-1/13) * ¹²√(32) = ⁵²√{2^(³⁵)}.
Please let me know if you have any other questions.
Applying the law of indices to the roots, we have that
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
So,
[tex]\sqrt[3]{2}[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]\sqrt[12]{32}[/tex] = [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]32^{\frac{1}{12} }[/tex]
= [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex](2^{5} )^{\frac{1}{12} }[/tex]
= [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]2^{\frac{5}{12} }[/tex]
Since we have the same base in all three numbers, we have that from the law of indices, [tex]a^{x}[/tex] × [tex]a^{y}[/tex] = [tex]a^{x + y}[/tex]
= [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]2^{\frac{5}{12} }[/tex]
[tex]= 2^{\frac{1}{3} + (-\frac{1}{13}) + \frac{5}{12} } \\= 2^{\frac{1}{3} - \frac{1}{13} + \frac{5}{12} }[/tex]
Taking L..C.M of the denominators of the exponents, the L.C.M is 156.
So,
[tex]2^{\frac{1}{3} - \frac{1}{13} + \frac{5}{12} }\\= 2^{\frac{52 - 12 + 5 X 13}{156} } \\= 2^{\frac{52 - 12 + 65}{156} }\\= 2^{\frac{40 + 65}{156} }\\= 2^{\frac{105}{156} }[/tex]
Simplifying the exponent, we have
[tex]2^{\frac{105}{156} } \\= 2^{\frac{35}{52} }[/tex]
So, [tex]\sqrt[3]{2}[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]\sqrt[12]{32}[/tex] = [tex]2^{\frac{35}{52} }[/tex]
Learn more about indices here:
https://brainly.com/question/10339517
HELP NEEDED ASAP!!
TT $ 1 = EC $0.43
TT $6.3 = US $1
Use the table above to complete the questions below
1. Convert
a) TT $125 to EC $
b) EC $850.94 to US $
Answer:
a. 0.43*125=
53.75
b. this is a little harder we need to find what the conversane is for ec to us
ec 0.43= 1 tt so
6.3*0.43
2.71 ec=1 us
850.94 divided by 2.71
314 us
Hope This Helps!!!
The Martinez family ate at a restaurant. The cost of the meal was $34.50. The sales tax was 6% of the cost of the meal. They left a tip of 15% of the cost of the meal plus tax. What was the total cost of the meal, tax, and tip?
(I ALREADY KNOW THE ANSWER. BUT I NEED THE WORK FOR THE ANSWER TO SHOW MY TEACHER) (the answer is $42.06 btw)
1. observe problem
The Full price is:
The Subtotal + the Subtotal*tax
so,
34.50+34.50*0.06=
36.57
The Full price plus tip is
Full price + Full price * tip percentage
so,
36.57+36.57*0.15
Which is
$42.0555
Rounded to is
$42.06
Hello. I have tried everything and I still can't find the right answer. Can somebody please explain how to do this to me? Thanks so much!
we know that opposite sides are parallel, or namely that the figure is a parallelogram, meaning as well that opposite sides are equal, Check the picture below.
f-9+4=22
pls some help it's worth 14 points enough for 2 questions pls answer
Answer:
F = 27
Step-by-step explanation:
you subtract 27-9+4
Answer:
f = 27
Step-by-step explanation:
f - 9 + 4 = 22
f-5 = 22
Add the numbers
↓
f = 27
Simplify 5x^2 +x^2+2+x^2+6
Answer:
[tex]=7x^2+8[/tex]
Step-by-step explanation:
[tex]5x^2+x^2+2+x^2+6[/tex]
[tex]=5x^2+x^2+x^2+2+6[/tex]
[tex]=5x^2+x^2+x^2+8[/tex]
[tex]=7x^2+8[/tex]
Brainliest?!
What are the variables in this expression? f 2 g StartFraction h over 4 EndFraction minus 7 f and g only g and h only f, g, and Negative 7 only f, g, and h only.
Answer:
The variables are F, G and H
Answer:
F,g,h Good luck!
Step-by-step explanation:
NEED HELP ASAP
Given G (-6,5) and H (2, -7), what is the length of GH
[tex]\bold{\huge{\green{\underline{ Solution }}}}[/tex]
[tex]\bold{\underline{ Given}}[/tex]
We have given that the coordinates of the end point G and H are ( -6,5) and ( 2, -7 )[tex]\bold{\underline{To \: Find :- }}[/tex]
We have to find the length of GH[tex]\bold{\underline{Let's \: Begin :- }}[/tex]
The coordinates of G = ( -6 , 5 )
The coordinates of H = ( 2 , - 7 )
According to the distance formula, we get :-
[tex]\purple{\bigstar}\boxed{\sf{Distance\:\:GH=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}[/tex]
Here, x1 = -6 , x2 = 2 and y1 = 5 , y2 = -7Subsitute the required values in the above formula
[tex]\sf{ Distance \:GH = √( -6 - 2)² + ( 5 -(-7))²}[/tex]
[tex]\sf{Distance\:GH= √(-8)^2+(5 + 7)^2}[/tex]
[tex]\sf{Distance\:GH=√(-8)^2+(12)^2}[/tex]
[tex]\sf{ Distance \:GH =√64 + 144 }[/tex]
[tex]\sf{ Distance \:GH =√ 208}[/tex]
[tex]\sf{ Distance\: GH = √ 2 × 2 × 2 × 2 × 13}[/tex]
[tex]\sf{ Distance \:GH = 4√13}[/tex]
[tex]\sf{\red{ Hence\: the \: length\:of \: GH \: is \: 4√13 \: units}}[/tex]
Triangle A has a height of 2.5cm and a base of 1.6cm. The height and base of triangle B are proportional to the height and base of triangle A. Which of the following could be the height and base of triangle B?
Answer:
I THINK ( A ) IS CORRECT ANSWER
I THINK ( A ) IS CORRECT ANSWERHOPE THIS HELPS U!!!
what is 4 3/5 an an improper fraction
Answer:
23/5
Step-by-step explanation:
4 3/5 = 23/5
first multiply 4 x 5 then multiply that answer by 3
then you get 23/5 the denominator stays the same
I hope this helps and I hope this is the right answer for your hw/test
A data set is shown in the table. The line of best fit modeling the data is y = 2. 69x – 7. 95. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries negative 5. 1, negative 3. 2, 1. 0, 2. 3, 5. 6. What is the residual value when x = 3? –0. 88 –0. 12 0. 12 0. 88.
Answer The awnser is the 2x69, by 75 and 35 by 39x4 and 3 5ths .
Step-by-step explanation:
what is an angle? how do you describe an angle?
Answer:
An angle is the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.
"in any triangle, the longest side is opposite the largest angle"
Step-by-step explanation:
Answer:
an angle is a In-plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. An angle is denoted using the symbol. and you can describe an angle by looking for the figure formed by two rays meeting at a common end point.
Step-by-step explanation:
hope this helps you
plz help with iready
Answer:
118
Step-by-step explanation:
150+16%=174
174 - 32% = 118.32
118.32=118(to nearest whole number)
Answer:118
Step-by-step explanation:
I need help with number 9
Answer:
55 ft
Step-by-step explanation:
The mirror is 10 times as far to the dinosaur as it is to Amir: 40 ft = 10×4 ft.
The triangles shown in the diagram are similar, so the height of the dinosaur will be 10 times Amir's eye height. In feet, Amir's eye height is 5 6/12 feet, or 5.5 feet. Ten times that is 55 feet.
The dinosaur is 55 feet tall.
Answer:
55ft
Step-by-step explanation:
Laura invests $2,000 in a bank account where she earns simple interest at a rate of 6.4% per year.
1. In total, how much interest will Laura receive after 18 years?
2. In total, how much will be in Laura’s account after 30 years?
1)
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6.4\%\to \frac{6.4}{100}\dotfill &0.064\\ t=years\dotfill &18 \end{cases} \\\\\\ I = (2000)(0.064)(18)\implies I=2304[/tex]
2)
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6.4\%\to \frac{6.4}{100}\dotfill &0.064\\ t=years\dotfill &30 \end{cases} \\\\\\ A=2000[1+(0.064)(30)]\implies A=2000(2.92)\implies A=5840[/tex]
Answer:
after 18 years : $477,685.19
after 30 years: $661,353.82
Step-by-step explanation:
interest formula: A=P(1+r/n)^nt
so...
2000(1+6.4/18)^18 = 477685.1913 rounds to $477,685.19
2000(1+6.4/30)^30 = 661353.8157 rounds to $661,353.82
Which number is greater and by how much: A decreased by 50% and then increased by 50% of the result. sorry for the repost btw also answer it like ___ number is __ greater than the second number.
Answer:
a is greater by 25
Step-by-step explanation:
a is greater by 25 hope it helps
Answer:64
Step-by-step explanation:
a is greater
a is 64
The width of a rectangle is 4t-1.5 feet and the length is 1.5t+5 feet. Find the perimeter of the rectangle.
Answer: P=2(l+w)=2·(1.5+4)=11 is the answr
Step-by-step explanation:
Here’s the explanation!!!!!
Answer:
It's correct
Step-by-step explanation:
(θ‿θ)(θ‿θ)(θ‿θ)
If x < 5, find Ix - 5l.
Help me please
Answer:
b is you answer hope it helps you
25 Points ❣️
Directions: Identify the constant/s and variable/s in each algebraic expression.
Given Constant. Variable
1. 7׳
2. 3a² + 1
3. 10 × + y
4. 25r³ + 10s²
5. 40a⁵b⁴ - 11
Answer:
1. variable = x
2. constant = 1, variable = a
3. variables = x and y
4. variables = r and s
5. constant = -11, variables = a and b
Step-by-step explanation:
Constant: a number on its ownVariable: a symbol for a unknown value. It is usually a letter such as x or yCoefficient: a number used to multiply a variable
1. variable = x
2. constant = 1, variable = a
3. variables = x and y
4. variables = r and s
5. constant = -11, variables = a and b
What is the slope of y = 4x - 7
PLEASE SHOW WORK
ASAP!
The slope of an equation of a line is the number that is in front of the x,,
In y=4x-7 the slope would be 4
Answer: 4
 The square of an odd number is always odd
Try Examples with three odd numbers to check this conjecture And find where it’s false
Do you believe it’s true or false
Explain why it’s true or false
Answer:
True
Step-by-step explanation:
3² = 9 ⇒ odd
7² = 49 ⇒ odd
9² = 81 ⇒ odd
Therefore, the square of an odd number is always odd.
Proof
If n is an odd number, it can be written as n = 2k + 1, for some integer k.
Therefore, n² = (2k + 1)²
= 4k² + 4k + 1
= 2(2k² + 2k) + 1
As 2(2k² + 2k) + 1 is odd, this proves that the square of an odd number is always odd.
Answer 1a please and thank you
Answer:h
Step-by-step explanation:
j
Guavas 25% Oranges 40% Bananas 15% Apples 20% What fractions of students prefer Apples?
Answer:
20/100=1/5 the fraction of students who prefer apples is 1/5
How do you multiply two scientific notation values? Explain the steps you would take to find the product of 6. 7 × 106 and 3. 2 × 105 written in scientific notation.
The product of 6.7 × 10⁶ and 3.2 × 10⁵ can be written in scientific notation is 2.144 × 10¹².
What is multiplication?It is also known as the product. If the object n is given to m times then we just simply multiply them.
The two numbers are [tex]\rm 6.7*10^6 \ and \ 3.2 * 10^5[/tex]
Then find the product of these two numbers.
To multiply these terms is very simple.
First, multiple 6.7 and 3.2 simply. And the power of 10 gets added. That is
[tex](6.7*10^6) * (3.2 * 10^5) = 6.7 * 3.2 * 10^6 *10^5\\\\(6.7*10^6) * (3.2 * 10^5) = 21.44* 10^{6+5}\\\\(6.7*10^6) * (3.2 * 10^5) = 21.44 *10^{11}\\\\(6.7*10^6) * (3.2 * 10^5) = 2.144* 10^{12}[/tex]
The product of 6.7 × 10⁶ and 3.2 × 10⁵ can be written in scientific notation is 2.144 × 10¹².
More about the multiplication link is given below.
https://brainly.com/question/19943359
Which equation represents the relationship between r and s? A) s = 1 6 r B) r = s - 5 6 C) s = r - 5 6 D) r = 1 6 s
Answer:
a because that what I got
Can someone please help me? I will give brainliest!
Answer:The height is 12ft
The length of the rug is 10ft and the height of the parallelogram is 12ft
The width of the rug is 6ft wide and the parallelogram is 9ft wide
Yes the rug will fit
Step-by-step explanation:
What’s the perimeter of a rectangle with a length of 4.2cm and a width of 2.8cm
How do you find measure arc SG
Answer:
mS.G = 68
*NOTE: If units are needed, then put a degree symbol (68°), but since the measure of the other arc which is arc F.G has no degree symbol, then I didn't use a degree symbol.
Step-by-step explanation:
It wouldn't let me submit my explanation, but I took a screenshot, so here
1. A buoy floats 19 yards from the eastern most point of a boat and 15 yards from the western most point of a second boat. The angle formed from the buoy to the two boats 108o. What is the other angle measure that is formed with the buoy? (Law of Sines or Law of Cosines Problem)
2. A helicopter flies between two islands that are 20 miles apart. The angle of elevation with one island is 15o and 35o with the second island. What is the mileage of the helicopter? Round your answer to the nearest tenth of a mile. (Law of Sines or Law of Cosines Problem)
The laws of cosines and law of sines can be used given that two sides
and an included angle, or two angles a side are known.
Response:
1. The other angles in the triangle formed by the buoy are approximately;
31.1° and 40.9°2. Distance of the helicopter from the first island is approximately;
14.5 milesHow is the Law of Sines and Cosines used?Given parameters are;
Distance of the buoy from the easternmost point of a boat = 19 yards
Distance of the buoy from the westernmost point of the other boat = 15 yards
Angle formed from the buoy to the two boats = 108°
Distance between the two boats, d, is given by the law of cosines, as follows;
d² = 19² + 15² - 2 × 19 × 15 × cos(108°) = 586 - 570·cos(108°)
d = √(586 - 570·cos(108°))
By the law of Sines, we have;
[tex]\dfrac{d}{sin(108^{\circ})} = \mathbf{\dfrac{15}{sin(Angle \ formed \ from \ the \ boat \ on \ the \ West, \ \theta_1)}}[/tex]
Which gives;
[tex]sin(\theta_1) = \mathbf{ \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} }}[/tex]
The o
[tex]\theta_1 = arcsin \left( \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} } \right) \approx \mathbf{31.1^{\circ}}[/tex]
The other angles formed in the triangle containing the buoy are;
θ₁ ≈ 31.1θ₂ ≈ 180° - 108° - 31.1° ≈ 40.9°2. Distance between the two islands = 20 miles
Angle of elevation with one island = 15°
Angle of elevation with the second island = 35°
Required:
The mileage (distance travelled) of the helicopter.
Solution:
Let A represent the island that has an angle of elevation to the helicopter
of 15°, and let B represent the other island.
Angle formed by the helicopter and the two island, θ, is found as follows;
θ = 180° - (15° + 35°) = 130°
By the Law of Sines, we have;
[tex]\dfrac{20}{sin(130^{\circ})} = \mathbf{ \dfrac{Distance \ from \ island \ A }{sin(35^{\circ})}}[/tex]
Which gives;
[tex]Distance \ of \ helicopter \ from \ island \ A = \mathbf{ \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ})}[/tex]
[tex]Mileage \ from \ island \ A = \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ}) \times cos(15^{\circ}) \approx 14.5[/tex]
The mileage of the helicopter from the first island is approximately 14.5 milesLearn more about the Law of Sines and Cosines here:
https://brainly.com/question/8242520
https://brainly.com/question/2491835
Ira enters a competition to guess how many buttons are in a jar. Ira’s guess is 200 buttons. The actual number of buttons is 250. What is the percent error of Ira’s guess?.