---------------------------------------------------
x^1/3*x^1/5
Apply exponent rule:
x^1/3*x^1/5= x^1/3+1/5
x^1/3+1/5
Add the fractions:
LCM of 3, 5 is 15
5/15 + 3/15
Since the denominators are equal combine the fractions:
5+3/15
Add the numbers 5+3:
5+3= 8
8/15
x^8/15
Your Answer Is x^8/15
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Use DeMoivre’s Theorem to find (3cis(pi/6))^3.
a.) (27sqrt3)/2 +27/2 i
b.) (9sqrt3)/2 +9/2 i
c.) 27i
d.) 9i
Answer:
C. 27iStep-by-step explanation:
Given the complex number in polar coordinate expressed as
z = r(cos∅+isin∅)
zⁿ = {r(cos∅+isin∅)}ⁿ
According to DeMoivre’s Theorem;
zⁿ = rⁿ(cosn∅+isinn∅)
Given the complex number;
(3cis(pi/6))^3
= {3(cosπ/6 + isinπ/6)}^3
Using DeMoivre’s Theorem;
= 3³(cos3π/6 + isin3π/6)
= 3³(cosπ/2 + isinπ/2)
= 3³(0 + i(1))
= 27i
The right answer is 27i
PLEASEEEEE HELPP !!!!!
A lake near Susan's house is predicted to lose water every
day because of a drought. The table shows the estimated
water depth in feet, y, after x days of drought.
Answer:
y = -0.5x + 100
Step-by-step explanation:
Im not really sure what i was supposed to answer but i hope it helped.
Answer:
A. y = −0.5x + 100
Step-by-step explanation:
Pythagorean Theorem: Jason only has room for a TV that is less than 30^ prime prime wide.
Find the width of the TV
Answer:
Step-by-step explanation:
length² + width² = diagonal²
24² + width² = 40²
576 + width² = 1600
width² = 1600 - 576
width² = 1024
width = √1024 = √32*32
width = 32"
Width of the TV is more than 30"
Answer:
32
Step-by-step explanation:
First off, Bruh, 30" is not prime prime. That's 30 inches.
The base of the TV is 32. This is because A^2+B^2=C^2. 24 is A, 40 is C, and the base is B.
So that means that is we take 24^2 and the base^2, we should get 40^2. 40^2 is 1600. 24 squared is 576. So if we take the base and square it and add 576, we should get 1600. Or we could just take 1600 and subtract 576.
1600-576=1024.
So now, the root of 1024 is the base. Which is 32. Hope that helped.
Two number cubes each have sides that are labeled 1 to 6. Jude rolls the 2 number cubes. What is the probability that the sum of the numbers on
cubes will equal 4?
Answer: 3
This is the answer if you think its wrong i don't know its correct i got it right
Can i get some help ♂️
Answer:
[tex]AC=13.5[/tex]
Step-by-step explanation:
Use the Law of Sines as follows:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
Insert the values (use the steps from the last problem):
[tex]\frac{sin25}{14} =\frac{sin24}{b}[/tex]
Isolate b. Multiply both sides by b:
[tex]b*(\frac{sin25}{14} )=b*(\frac{sin24}{b})\\\\b*\frac{sin25}{14}=sin24[/tex]
Multiply both sides by 14:
[tex]14*(b*\frac{sin25}{14})=14*(sin24)\\\\b*sin25=14*sin24[/tex]
Isolate b. Divide both sides by sin 25:
[tex]\frac{b*sin25}{sin25} =\frac{14*sin24}{ysin25} \\\\b=\frac{14*sin24}{sin25}[/tex]
Insert the equation into a calculator and round to the nearest tenth:
[tex]b=13.5[/tex]
The length of AC is 13.5 units.
:Done
3) A box of chocolates contains four milk
chocolates and four dark chocolates. You
randomly pick a chocolate and eat it.
Then you randomly pick another piece.
The first piece is milk chocolate and the
second piece is dark chocolate.
Are the events independent or dependent?
What is the probability?
Answer:
dependent and 2/7
Step-by-step explanation:
dependent because you didn't replace it.
1/2 times 4/7 which is 4/14 which equals to 2/7
Which inequality will have a shaded area below the boundary line?
Answer:
When you change the inequality as the formula of y>ax+b, it is over the boundary line. While the formula is y<ax+b, it is below the boundary line. So we can get the answer is D.
Step-by-step explanation:
math question screen shot down below
Answer:
The correct answer is A, Point P
Step-by-step explanation:
since the additive inverse of 2 is -2 because -2 + 2 = 0 the correct choice must be choice A, Point P.
Order the steps to solve the equation
log(x2 - 15) = log(2x) form 1 to 5.
x² - 2x - 15=0
Potential solutions are -3 and 5
IIIII
x² - 15 = 2x
x - 5 = 0 or x + 3 = 0
(x - 5)(x + 3) = 0
Answer:
Attention for the conditions:
[tex]x^{2} -15>0\\2x>0\\so\\x>0[/tex]
Step-by-step explanation:
we have
[tex]log(x^{2}-15)= log(2x)\\\\x^{2} -15 = 2x\\\\x^{2} -5x+ 3x-15=0\\ (x^{2}-5x)+(3x-15)=0\\ x(x-5)+3(x-5)=0\\(x-5)(x+3)=0\\x-5=0, x=5 \\\\x+3=0, x= -3[/tex]
So the solutions are 5 because x>0
Which shows how the distributive property can be used to evaluate 7x8 4/5?
Answer:
61 3/5
Step-by-step explanation:
we realize that 8 4/5 can be written as [8 + (4/5)]
hence 7 x 8 4/5
= 7 x [8 + (4/5)]
= 7 [8 + (4/5)] (use the distributive property, see attached for reference)
= 7(8) + 7(4/5)
= 56 + 28/5 (convert 28/5 into mixed fraction)
= 56 + 5 3/5
= 61 3/5 (answer)
Financial goal is to purchase a house. To make Marcel’s financial goal of purchasing a house a specific goal, he can . Next, Marcel can make his goal timely by . Lastly, Marcel can make his financial goal measurable by each month.
Answer:
Marcel's financial goal is to purchase a house. To make Marcel's financial goal of purchasing a house a specific goal, he can FOCUS ON SAVING FOR A DOWN PAYMENT. Next, Marcel can make his goal timely by GIVING HIMSELF A DEADLINE. Lastly, Marcel can make his financial goal measurable by TRACKING THE AMOUNT OF MONEY HE SAVES each month.
Which will result in a perfect square trinomial?
Answer:
is there a picture?
Step-by-step explanation:
plz halp meh!!!!!!!
Answer:
M=25-3D
Step-by-step explanation:
Daniel starts with 25 dollars and spends three dollars per day for a d number of days. So the amount of money in his wallet should be equal to the starting number of dollars minus the amount of money he spends. Therefore we get the equation M=25-3D, where M is the amount of money is his wallet, and D us the number of days he buys a drink and chips.
PLS HELP middle school math
Answer: 2,4 4,8 8,16 and so on ...
Step-by-step explanation:
Max pays his rent for $300 on April 28th.
Max mows a different neighbor's lawn on April 29th and they pay him $15.
Max fills up his tank at a gas station on April 30th for $29.80.
Max buys a snack in the gas station for $4.57 the same day.
How much money does Max have on April 30th after he buys the snack?
Jack ran 13.5 miles in 1.5 hours. What was his speed in miles per minute?
Answer:
9
Step-by-step explanation:
13.5 / 1.5 = 9
Answer:
[tex] \boxed{Speed = 0.15 \: miles \: per \: minute} [/tex]
Given:
Distance travelled = 13.5 miles
Time taken = 1.5 hours = 1.5 × 60 = 90 minutes
Step-by-step explanation:
[tex]Speed = \frac{Distance \: travelled}{Time \: taken} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{13.5}{90} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.15 \: miles \: per \: minute[/tex]
If you take out a loan that costs $561 60 over eight years at an interest rate of 9% how much was the loan for?
Answer:
The loan was $28184.81
Step-by-step explanation:
Let the loan amount be x
Rate of interest on Loan = 9%
Time = 8 years
Amount of loan over 8 years = $56160
Formula : [tex]A=P(1+r)^t[/tex]
Where A = Amount =56160
P = Principal = x
r = rate of interest = 9% = 0.09
t = time = 8 years
Substitute the values in the formula :
So,[tex]56160=x(1+0.09)^8[/tex]
[tex]\frac{56160}{(1+0.09)^8}=x[/tex]
$28184.81=x
Hence The loan was $28184.81
Find the volume of the cone
Answer:
12π
Step-by-step explanation:
Volume of the cone is πr^2 * h / 3
r = 3
h = 4
9π * 4 / 3 = 12π
Answer: 37.6991118
Step-by-step explanation:
A man wants to hike two trails. The length of one trail is 7.709 km. The length of the other trail is 9.0309 km. What is the total length of the two trails?
Answer:
Its addition I think so the answer would we 16.7399km for both trials
Step-by-step explanation:
Find , to the nearest tenth of a foot , the height of the tree represented in the accompanying diagram.
Answer:
Height of tree = 28.2 ft (Approx)
Step-by-step explanation:
Given:
Angle from ground to top of the tree = 62°
Distance from a point to base of tree = 15 ft
Height of tree = [tex]X[/tex]
Find:
Height of tree = [tex]X[/tex]
Computation:
Using trigonometric application:
[tex]Tan\ 62 = \frac{Height\ of\ tree}{Distance\ from\ a\ point\ to\ base\ of\ tree} \\\\Using\ calculator\ , Tan62 = 1.88\\\\1.88=\frac{Height\ of\ tree}{15} \\\\Height\ of\ tree=28.2ft[/tex]
Height of tree = 28.2 ft (Approx)
The parabola opens to the right. The focus is given as
F (p,0) and directrix x = -p. The distance between the
focus and point P is equal to the distance between the
directrex and point P. Continue to simplify the equation to
solve for y2. THE ANSWER IS 4px!! :)
Answer:
Step-by-step explanation:
We have that the focus is at (p,0) and that the directrix is x=-p. Take the point (-p,0) of the directrix. We know that the vertex of the parabola is at the middle point ot the line segment that joins the points (p,0) and (-p,0). To get the middle piont, we take the average coordinate by coordinate. That is, the middle point is [tex](\frac{-p+p}{2}, \frac{0+0}{2}) = (0,0)[/tex]. The general formula of a parabola of vertex (h,k) that opens to the right or to the left is given by
[tex](y-k)^2 = 4p(x-h)[/tex]
Where |p| is the distance from the focus to the vertex. If the parabola opens to the right, then p>0 and p<0 otherwise. In our case, h =0=k, so we get that
[tex]y^2 = 4px[/tex]
Answer:
y^2 = 4px
Step-by-step explanation:
edg 2021
Of all 25 marbles in a bag, 3 of the marbles are white. What is the probability that a white marble will be randomly selected from the bag without looking? Write your answer as a percent.
Step-by-step explanation:
Total marbles = 25
Probability of white marble = 3/ 25 = 0.12
The half-life of a certain radioactive element is 35 hours. If there are 904 grams of this element, how much will be left after 70 hours? PLEASE HELP I MIGHT FAIL MATH.
===========================================================
Explanation:
The half-life is 35 hours. This means every 35 hours, the amount of the substance is cut in half. If we started with 100 grams, then 35 hours later, we will have 50 grams. Then another 35 hours later we will then have 25 grams, and so on.
In this case, we start with 904 grams and follow this sequence:
904, 452, 226, 113, ...
Each term is cut in half. Going from term to term it takes 35 hours each. The third term 226 is the result of waiting two half-lives, which is 2*35 = 70 hours that have elapsed total.
--------------
If you want to use a formula, then it would be
[tex]y = A*\left(\frac{1}{2}\right)^{x/H}[/tex]
where,
H = half-life duration (in this case, it is 35)
A = starting amount (which is 904 in this case)
x = amount of time that has elapsed (we will plug in x = 70)
y = final amount after x units of time has elapsed
note that x and H must have the same time unit. Both are in terms of hours in this case.
------------
So we will plug A = 904, x = 70, H = 35 into the formula to get...
[tex]y = A*\left(\frac{1}{2}\right)^{x/H}\\\\y = 904*\left(\frac{1}{2}\right)^{70/35}\\\\y = 904*(0.5)^{2}\\\\y = 904*(0.25)\\\\y = 226\\\\[/tex]
We see that x = 70 leads to y = 226. This means after 70 hours, there is 226 grams of the material left.
Is this SAS or Not SAS?
Answer:
SAS
Step-by-step explanation:
Is (1, -2) a solution of y> -6x – 3?
Choose 1 answer:
Yes
No
Answer:
Yes
Step-by-step explanation:
(1, -2)
y > -6x – 3
-2 > -6(1) - 3
-2 > -6 - 3
-2 > -9 Yes
Solve the inequality for X.
-3x - 3 <-63
es
A)
x > 20
B)
x > 22
9.
x < 20
D)
x < 22
------------------------------------------------
-3x - 3 <-63
Add 3 to both sides:
-3x-3+3 < -63+ 3
Simplify:
-3x < -60
Multiply both sides by -1:
(reverse the inequality)
(-3x)(-1) > (-60)(-1)
Simplify:
3x > 60
Divide both sides by 3:
3x/3 > 60/3
Simplify:'
x > 20
Your Answer Is x > 20
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The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8(n + 2)(n + 4) = 1,144.
Answer the following questions about the equation modeling the volume of the shipping box.
Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If you get two solutions, are they both reasonable?
Answer:
see below
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
FOIL
8(n^2 +2n+4n+8) = 1144
Divide each side by 8
8/8(n^2 +2n+4n+8) = 1144/8
(n^2 +2n+4n+8) = 143
Combine like terms
n^2 +6n+8 = 143
Subtract 143 from each side
n^2 +6n+8 -143= 0
Combine like terms
n^2 +6n -135 =0
Factor
What two terms multiply to -135 and add to 6
-9*15 =-135
-9+15 = 6
(n-9) (n+15) =0
Using the zero product property
n-9 =0 n+15=0
n = 9 n=-15
The length cannot be negative so n = -15 cannot be a solution
n =9
Answer:
n = 9
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n² + 2n + 4n + 8 = 143
n² + 6n - 135 = 0
n² + 15n - 9n - 135 = 0
n(n + 15) - 9(n + 15) = 0
(n - 9)(n + 15) = 0
n = 9, -15
since n is a length, it can not be negative
Therefore the only solution is n = 9
factorise 15x- 10x^3
Answer:
5x (3-2x^2)
Step-by-step explanation:
so all you have to do is 15x-10x=5x right?, then all you have to do is 15/5=3. 10x/5x=2x. then subtract 1 from the exponents. then you get the answer. okay Im sure about the fist part and the divison but not the exponents, I did use a calculator to check it though.
The factorize equation is, [tex]\rm 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0[/tex].
The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
Given that,
Equation; [tex]\rm 15x - 10x^3[/tex]
We have to determine,
Factorize the equation and factor of the equation.
According to the question,
To factorize the equation and determine the factor of the equation following all the steps given below.
Equation; [tex]\rm 15x - 10x^3[/tex]
Step1; Taking the term 5x common from the equation,[tex]\rm = 15x - 10x^3 = 0 \\\\= 5x (3-2x^2) = 0[/tex]
Step2; Simplify the equation,[tex]\rm = 5x (3-2x^2) = 0\\\\ = 5x (\sqrt{3} - \sqrt{2x}) (\sqrt{3}+\sqrt{2x}) = 0[/tex]
Step3; The roots of the equation are,[tex]\rm = 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0\\\\ The \ roots \ of \ the \ equation \ are;\\\\5x = 0, \ x = \dfrac{0}{5}, \ x =0\\\\\\[/tex]
[tex]\sqrt{3} - \sqrt{2x} = 0, \sqrt{2}x = \sqrt{3}, \ x = \dfrac{\sqrt{3} }{\sqrt{2} }\\\\ \sqrt{3} +\sqrt{2x} = 0, \sqrt{2}x = -\sqrt{3}, \ x =- \dfrac{\sqrt{3} }{\sqrt{2} }[/tex]
Hence, The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
For more details refer to the link given below.
https://brainly.com/question/11540485
Please Answer Quick i'm in a rush please ill give brainliest!!!!!!!
The map shows the location of the houses of Dan, Joe, Lee, and Roy:
Coordinate grid shown from negative 5 to positive 5 on x-axis and negative 5 to positive 5 on y-axis. A point labeled Dan is shown on ordered pair 1, 4. A point labeled Joe is shown on ordered pair negative 3, 4. A point labeled Lee is shown on ordered pair negative 3, negative 4. A point labeled Roy is shown on ordered pair 2, negative 3.
The coordinates of the community center are (5, −1). Who has a house in the same quadrant as the community center?
Dan
Joe
Lee
Roy
Answer:
roy is in the same quadrant
Step-by-step explanation:
↙↘⤵⤵⤵⤵⤵⤵⤵⤵⤵⤵⤵⤵⤵
Answer:
roy
Step-by-step explanation:
Simplify.
2(m + 11)
2m + 11
2m + 22
24m
22m
Answer:
You distribute the 2 to the m=2m
Then you distribute the 2 to the 11 which gives you 22
ANSWER: 2m+22
