how do you find the smallest positive integer k such that 1350k is a perfect cube?

Answers

Answer 1

Final answer:

The smallest positive integer k such that 1350k is a perfect cube is found by prime factorizing 1350 and ensuring that all prime exponents in its factorization are multiples of 3. The missing exponents for 2 and 5 are 2 and 1 respectively, so multiplying by k=20 achieves this.

Explanation:

To find the smallest positive integer k such that 1350k is a perfect cube, we start by factoring 1350 into its prime factors. We have 1350 = 2 × 3^3 × 5^2. In order for a number to be a perfect cube, all the exponents in its prime factorization must be multiples of 3 since a cube of any number is that number multiplied by itself three times. In the prime factorization of 1350, the exponent of 2 is 1 (which is 2 short of a multiple of 3) and the exponent of 5 is 2 (which is 1 short of a multiple of 3).

To make the number a perfect cube, we need to multiply it by a k such that the prime factorization of the result has all exponents as multiples of 3. Therefore, we need one more 2 to make the exponent of 2 equal to 3, and we need one more 5^1 to make the exponent of 5 equal to 3. This gives us a k of 2^2 × 5^1 = 4 × 5 = 20. So, k=20 is the smallest positive integer that, when multiplied by 1350, results in a perfect cube.

Related Questions

The perimeter of a patio is 64. The width of the patio is 12 feet and the length of the patio is (×+6) feet. What is the length of the patio?

Answers

12(2)+(x+6)(2) = 64
12(2) = 24
Distribute the (x+6)(2)= 2x + 12
New equation:
24 + 2x + 12 = 64
Solve for x, and you will get x = 14
Then put that back in to (x+6). 14 plus 6 equals 20. Which L = (x+6)

L = 20
20 is your final answer.

I hope this helped!!

Please help iv added a pic of the work sheet. I have to get this done by tomorrow

Answers

You do this by moving all terms without y to the right hand side, and then divide the whole lot to keep a clean y= on the left hand side.

Moving to the other side is done by subtracting (or adding) a term from both sides. Effectively this looks like you're moving the term and flipping the sign.

So 2y + 18 = 4x changes into 2y +18 -18 = 4x -18 so 2y = 4x - 18. If you forget about the middle step, it looks like the +18 jumped to the other side and changed sign. That's all.

Second step is to change the 2y into y. You do that by dividing everything by 2. So 2y=4x-18 becomes y=2x-9

1. y=2x-9
2. y=3/2x - 6
3. y=4x+18
4. y=2x-12

5. y=-4x+18
6. y=2/3x+4
7. y=-1/4x-18/4
8. y=1/4x-18/4

9. y=1/4x+18/4
10. y=-1/4x+18/4
11. y=-3/2x+6
12. y=3/2x+6

13. y=-3/2x-6
14. y=-2/3x-4
15. y=2/3x+2/3
16. y=18-4x

6(3a+1)-30=3(2a-4) okay i suck at algebra . please help me lol

Answers

So expand your brackets so 6(3a+1)=18a+6 now -30 so 18a-24
3(2a-4) becomes 6a-12
18a-24=6a-12
18a-6a=-12+24
12a=12
a=1

26-38+(-3) what is the answer.

Answers

So basically, first just do this step by step, or subtract 38 from 26 first.

26 - 38 is basically -(38 - 26), or -12.

So then, it becomes -12 + (-3)

A - and a + becomes - because you're adding negative 3.

-12 - 3

Which then becomes -15.

The answer to your question is -15

Anwser. Anwser. Answer. Anwser

Answers

the answer to x is 7 because 4 times 6 is 24 and 7 times 6 is 42

Answer:

i think x to 7 i belive

Step-by-step explanation:

what’s the value of 1 2/3 divided by 1 7/18 In mixed number fraction form someone please help :)

Answers

12/3=4
4 divided by 17/18 equals to 4* 18/17=72/17= 4 4/17
Thus the answer is 4 4/17

Wich is greater 0.48 or 6 15

Answers

6.15 is greater because 0.48 is 48 hundredths

6.15 is greater because its a whole number and 0.48 is a decimal

Explain how you can find 3x584 using expanded form

Answers

I believe what you need to do is multiply 3 by each number.
To start, 3*584 is 1752. Expanded form written out would be (3*500)+(3*80)+(3*4). Simply multiply all the numbers and then add them together. 3*500=1,500; 3*80=240; 3*4=12. 1,500+240=1740+12=1752. Hope this helps! :)

706421 rounded to the nearest thousand

Answers

706,400. Since it is 421 you would round down

The answer to this question is 70600

If 2 more students took the math test and both made a score of 80, what would the picture graph look like?

Answers

If both of them scored 80, then on the graph, both of them will lying on the same points. Say x axis student and y axis is Marks , then for student 1, the point that will be marked is 80 and for student 2 also, the point that will be marked is 80. If both the points are connected, then we will be getting a straight line connecting both the dots. Hence the graph will be a straight line.

Simplify the expression 4^3 + 2(3 - 2)

Answers

4 x 4 x 4 = 16 x 4 = 64

64 + 2(1) = 64 +2 = 66

66 is your answer

hope this helps

[tex]4^3 + 2(3-2) 4^3 + 2(1) 64 + 2 66 _________________ Thus, the answer is: 66 You're welcome. [/tex]

how can adding. doubles help you multiply by 2 give an example

Answers

Since you add a number x amount of times by itself when you multiply it by x, we have, for example, 3*2=3+3=6. In addition, 3*3=3+3+3=9 and 3*4=3+3+3+3 (4 times)=12.

I'm a bit confused on how to get x, the example doesn't make sense either.

Answers

We know that A=l*w and we also know that these two rectangles have to have the same area. This means we set the two area formulas equal to each other:
[tex](x)(12)=(16)(x-2)[/tex]
[tex]12x=16x-32[/tex]
[tex]-4x=-32[/tex]
[tex]x=8[/tex]

how can i show my work for 0.4 divide 1.44

Answers

Draw a picture showing the groups

Percent of change
original:35
new:70

Answers

Hello, the formula to find a percent of change is [(new value - start value) / start value] × 100

[(70-35) / 35] × 100 = (35 / 35) × 100 = 1 × 100 = 100%

Answer = 100%

Unite price batteries size 4pk and total price 2.97 how come unite price

Answers

To find the unit price, divide the unit by the the total amount:

2.97/4
0.7425

Round this to the nearest cent:

$0.74

Hope this helps!

Answer:

divide the unit by the the total amount

The answer is 0. 74

please help me with this

Ernesto built a wooden car for a soap box derby. He is painting the top of the car blue and the sides black. He already has enough black paint, but needs to buy blue paint. He needs to know the approximate area of the top of the car to determine the size of the container of blue paint he should buy. He measured the length to be 9 feet 11.25 inches, and the width to be 0.5 inches less than 3 feet. Draw a diagram and label the measurements. What is the area of the top of the car? What is the most accurate area Ernesto can use to buy his paint?

Answers

Google it and see what you get

The product of a number m and 1.7 is 6.63. Determine what an equation would be and solve for m. What is the value of m?

Answers

The equation would be m*1.7=6.63, because 6.63 is the *product* (showing that you need to multiply). and to find m you would need to divide 6.63 by 1.7 to do inverse operations. M equal 3.9.

Mrs. Synder must choose two of her homeroom students to be class representatives. The class consists of 13 girls and 9 boys. Approximately what percent chance is there that the first student chosen is a boy and the second student chosen is a girl? (Round to the nearest percent)

A. 10%

B. 25%

C. 22%

D. 15%

Answers

9/22 x 13/21 = 0.25 = 25% B

Answer: B. 25%

Step-by-step explanation:

Given : Number of boys in the class = 13

Number of girls in the class = 9

Total students = 13+9=22

Now, the number of ways to choose first boy then a girl =[tex]13\times9=117[/tex] (1)

Number of ways to choose nay two students :-

[tex]{22}P_{2}=\dfrac{22!}{(22-2)!}\\\\=\dfrac{22\times21\times20!}{20!}=462[/tex] (2)

Now, the probability that the first student chosen is a boy and the second student chosen is a girl :-

[tex]\dfrac{117}{462}=0.253246753247\approx0.25[/tex] [Divide (1) by (2)]

In percent , [tex]0.25\times100=25\%[/tex]

Hence, approximately 25% chance that the first student chosen is a boy and the second student chosen is a girl.

Is 0.09 greater than 0.7

Answers

no, 0.7 is greater than 0.09

0.70 > 0.09

hope this helps

Think of 0.7 as 0.70

In terms of money, 0.09 dollars is the same as 9 cents
Similarly, 0.70 dollars is the same as 70 cents

So the value 0.70 is larger

The cost to rent a car is $30 per day. Write an expression for the cost of renting a car d days. Make a table to find how much it will cost to rent a car for 3, 5, 7, and 10 days.

Answers

d = day
c = cost

c = 30d

Day(d) | c = 30d    | Cost(c)
3 | 90=30(3)   | $90
5 | 150=30(5)   | $150
7    | 210=30(7) | $210
10    | 300=30(10)  | $300

Answer:The expression for the cost of renting a car d days is:

[tex]c=30d[/tex]

The table can be made as follows:

Number of days Cost

3 90

5 150

7 210

10 300

Step-by-step explanation:

It is given that:

The cost to rent a car is $30 per day.

Now, the expression which is used to represent the cost for renting a car d days is:

[tex]c=30d[/tex]

where c is the cost of renting a car.

when d=3 we have:

c=90

( Since, 30×3=90 )

when d=5

c=150

( Since, 30×5=150 )

when d=7

c=210

( Since, 30×7=210 )

when d=10

c=300

( Since, 30×10=300 )

slove the equation y=mx+b for m

a)m=y-b-m
b)m=(y-b)m
c)m=y+b/x
d)m=y-b/x

Answers

Subtracting b from both sides, we get y-b=mx. Next, we can divide x from both sides to get (y-b)/x=m. This does not fit into any option, however, as y-b/x is different from (y-b)/x due to that in the former, you first do b/x while in the latter you have to subtract b from y first

how are rates and ratios related?

Answers

Fundamentally, a ratio is a ratio, a rate is a ratio with time as the denominator and a period is the inverse of a rate.

Of course, there are differential forms of these concepts, where it is not a ratio truly, but it is a “ratio” of differential elements.

Evaluate the function
f(x)= 7.45x + 33.7 at x= -4.3

Answers

First, you have to substitute for x, which would make the problem f(x)=7.45(-4.3)+33.7
Now, you just have to use the PEMDAS method (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)
f(x)= -32.035+33.7
f(x)=1.665

PLEASEEEE HELP MY LIFE :((((

Answers

Since he gets 10$ per shirt, his revenue is 10y if y represents the shirts sold as he adds 10$ with every purchase. His expenses start with the base cost of 1500, then he also has to pay 3 dollars for each shirt, so his expenses add up to 1500+3y. Since he wants to make as much as he spent, his revenue has to equal his expenses and 10y=1500+3y. Subtracting 3y from both sides, we get 7y=1500. Dividing both sides by 7, we get y=214.something=215 by rounding up

the break even point is when ur expenses = ur revenue...there is no profit

1. expenses (what it costs steve ) are 1500 plus x shirts for $ 3
revenue(what steve makes from selling shirts) are x shirts for $ 10
so ur 2 equations would be : y = 3x + 1500 and y = 10x

2. 3x + 1500 = 10x
1500 = 10x - 3x
1500 = 7x
1500/7 = 214.28....so he would have to sell 215 shirts.

PLease help!!
Use the figure to the right to find the value of PT. T is the midpoint of PQ
PT=3x+2 and TQ= 5x - 8
Simplify your answer

Answers

3x+2=5x-8 so 2x=10 therefore the answer is x=5

There are 300 apples and peaches for sale at a farmer's market. The ratio of the number of apples to the number of peaches is 7 : 8. If 50 apples and 40 peaches are sold, what is the ratio of the remaining apples to peaches?

Answers

7:8.....added = 15

7/15(300) = 2100/15 = 140 apples
8/15(300) = 2400/15 = 160 peaches

if 50 apples and 40 peaches are sold....
apples : 140 - 50 = 90
peaches : 160 - 40 = 120

ratio of remaining is : 90/120 which reduces to 3/4 or 3:4 or 3 to 4 <==

4.3t-2.1t-2.3=7.6
Solve equation

Answers

If your solving for t then t = 4.5

Final answer:

The equation can be solved by combining like terms, isolating the variable t, then dividing by the coefficient of the variable. The solution to the equation is t = 4.5.

Explanation:

The given equation in this problem is 4.3t - 2.1t - 2.3 = 7.6. To solve the equation, first we need to combine like terms, meaning we would subtract 2.1t from 4.3t.

This leaves us with 2.2t - 2.3 = 7.6. After that, we must isolate t by adding 2.3 to both sides of the equation. This results in 2.2t = 9.9. Finally, we divide both sides by 2.2 to solve for t, which gives us t = 4.5.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ2

What do you add to 2 3/8 to make 6

Answers

29 because first u add 5 then 8 3 times.

A sack full of medals contains gold, silver, and bronze. If selected at random, the probability of picking a gold medal is 5/12. The probability of picking a silver medal is 1/3. What is the probability of picking a bronze medal? Express the probability as a number between 0 and 1.

Answers

Final answer:

The probability of picking a bronze medal is found by subtracting the probabilities of picking a gold and a silver medal from 1. As the probability of picking gold is 5/12 and silver is 1/3 (or 4/12), the probability of picking bronze is 1 - (5/12 + 4/12) = 1/4 or 0.25.

Explanation:

The probability of picking each type of medal from the sack adds up to 1 since one of the medals must be picked. Given the probability of picking a gold medal is 5/12 and the probability of picking a silver medal is 1/3, we can calculate the probability of picking a bronze medal by subtracting the probabilities of picking a gold or silver medal from 1.

First, let's find a common denominator for 5/12 and 1/3, which is 12. The probability of picking a silver medal expressed with the denominator 12 is 4/12 (since 1/3 equals 4/12).

Now, we add the probabilities of picking a gold or silver medal: 5/12 + 4/12 = 9/12.

Finally, we subtract this sum from 1 to find the probability of picking a bronze medal:
1 - 9/12 = 3/12, which simplifies to 1/4.

Therefore, the probability of picking a bronze medal is 1/4, or 0.25 when expressed as a number between 0 and 1.

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