express 10500 in terms of its prime factors .
determine the smallest positive number P such that 10500P is a perfect cube​

Answers

Answer 1

Answer:

Below

Step-by-step explanation:

Dividing by prime numbers :

2 | 10500

2 |   5250

3 |    2625  

5 |       875

5 |        175

5 |          35

                7.

So 10500 = 2*2*3*5*5*5*7

To find the smallest positive cube  we need to multiply by 2 ( to get 3 2's in the prime factors), another 2 3's and another 2 7's

That is P = 2*3*3*7*7 =  882.

The perfect cube is 2^3*3^3*5*3*7^3 = 9261000.


Related Questions

Bo has $500 in his savings account. He plans to add $150 to his savings account every month. Recently, he purchased a tractor to use on his farm for $4,000. He plans to pay off the total price of the tractor over time by paying $200 a month from a separate account. How much will Bo have in his savings at the time he pays off the tractor in full? A. $3,500 B. $3,000 C. $2,150 D. $2,000.

Answers

Answer:

D. $2,000

Step-by-step explanation:

Found this answer somewhere and it made sense so I hope its correct :D

Answer:

it is 3500 You take 4000 divide by 200 which is 20 months then take 150 times 20 equals 3000 then add 500

Step-by-step explanation:

PLSSSSSSSSS I WILI WILL GIVE BRAINLIEST PLSSSSSSSSSSS
The area of a rectangle is 3/4 square yards. If the width of the rectangle is 3/5, what is the length?
JUST TELL ME HOW TO FIND THE ANSWER

Answers

Answer:

Divide 3/4 by 3/5 to get 1 1/4.

Step-by-step explanation:

To find area, you multiply the length by the width. However, they gave you the area and the width. Therefore, you divide the width by the area (I think).

3/4 divided by 3/5 =  1 1/4

The length is 1 1/4.

plzz helpp what's (12+9⁷)+1284​

Answers

Answer:

4784265

Step-by-step explanation:

(12+9⁷)+1284​

12 + 4782969 + 1284

4784265

Solving:

To resolve this issue first we have to remember the rules to resolve a numeric expression, see:

Power and RadiciationMultiplication and DivisionAddition Sum and Subtraction.

[tex]\sf \left(12+9^7\right)+1284\\\\\\\sf =12+4782969\\\\\\\sf =4782981+1284\\\\\\\to \boxed{\sf 4784265}[/tex]

Okay?!

Find the perimeter.Simplify your answer.

Answers

Answer:

20c+14

Step-by-step explanation:

To find the perimeter we have to add up all the sides

4c+6c+7+4c+6c+7

Combine light terms

20c+14

Answer:

Well your not given C so we just leave that be and we can just add up all 4 sides since perimeter means outside length total. Now when added up,

6c+7+6c+7+4c+4c= 20c+14

20c+14 is the perimeter

Please help me please pleaee

Answers

Hello,

A.i. the circumference of a circle is nothing else but its perimeter which formula is π × diameter = π × 2 × radius

Let π = 22/7 ≈ 3.142857, the egyptian approximation

Then if C is the circumference of the circle i., C = 22/7 × 21 = (22 × 21) / 7 = (22× 7×3 )/7 = 22 ×3 = 66 cm

ii. Applying the same formula for the second circle gives us C = 22/7 × 8 = 176/7 ≈ 25.14 meters, rounded to the nearest hundredth...

Good luck !

Answer:

a) 66cm.       b) 50.28cm. or 50 2/7cm.

Step-by-step explanation:

The circumference of a circle is C=2πr or C=πd.

π=22/7

a)  C=πd

Plugin the diameter.

C=22/7 x 21

=66cm.

b) C=2πr

Plugin the radius.

C=2 x 22/7 x 8

=50.28cm. or 50 2/7cm.

Hope this helps :)

Crystal has played the piano for 15 years. Jane has played for 3 years. How many
times longer has Crystal played the piano I need equation: and answer

Answers

Answer:

15/3=5

Step-by-step explanation:

Crystal has played the piano for 5 times longer than Jane.

The sum of three consecutive numbers is 72.
What IS the smallest of these numbers?

Answers

If the sum of three consecutive numbers is 72 then the smallest of these numbers is 23. Verification = 23 + 24 + 25 = 72.

I don’t really understand this, if you don’t mind please explain.

Answers

Answer:

Roman is wrong because 6/31 is bigger than 9/47

Step-by-step explanation:

no.

i want you to BRING OUT THAT AWESOME CALCULATOR RIGHT NOW! I DONT CARE IF ITS ON YOUR COMPUTER or even an ol fashioned one right in your hands

ok now enter 6 and then divide by (division sign), and then 31. and press Enter or equal sign. now notice that we get  A SUPER LONG NUMBER like this

0.19354838....

DO THE SAME THING WITH 9 divided by 47!!

0.19148936....

ok notice. take a look at the third number from the decimal point for each result. they are different. for some SILLY REASON, Roman decided to ignore the rest of the numbers.

6/31 is bigger than 9/47!!!!

Can someone help me with this? (Do not upload through file only text please!)

Answers

Answer:

-6

Step-by-step explanation:

f(0) =  5(0) -6

f(0) = -6

mrs peele has 11 1/4 pounds of cookie dough a batch of cookies requires 2 1/2 of cookie dough how many batchesof cookie dough can mrs peele make

Answers

Answer:

4.5 lbs

Step-by-step explanation:

just divide 11.25 by 2.5

Noah’s recipe for one batch of sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water. If someone uses 455 liters of soda water, how much orange juice would they need? And then how many batches would that make?

Answers

Answer:364

Step-by-step explanation:

At the market you spent $21 for 5 bags of chips and 3 bottles of mango juice. Your buddy
spent $12 for 2 bags of chips and 3 bottles of mango juice. How much does each item cost?

Answers

Answer:

$2 for each bottle of mango juice and 3$ for each bag of chips

Step-by-step explanation:

hope it can help you lovelots

The base of the following pyramid is a square. If the volume of
the pyramid is 360 feet^3, what is the missing length? Round the
answer to the nearest hundredth.

Answers

Answer:

h = 12.52 ft

Step-by-step explanation:

volume of pyramid is 1/3*b*l. b is the base and l is the height we know that this equals 360 because it is given in the text. we also know b=8^2 since the base is a square so b=64. divide 360 by 1/3*64*pi to get l, l=5.3715. next we will use the pythagorean theorem to find h. first find the diagonal of the base: 8sqrt(2), now using the pythagorean theorem, we have h^2=5.3715^2 + (8sqrt(2))^2= 28.8528+128=156.8528. square root to get12.5241

Help Me Within 7 Minutes for brainliest. I already have a sorta guess But I'm not positive, A little help here? I want to confirm my answers and it seems no one else ever posted this question out.

Answers

y=3x+5

m=3

Parallel lines has equal slope .

So equation of parallel line also have slope 3

Take the 2nd option

[tex]\\ \sf\longmapsto 6x+2y=12[/tex]

Cut 3

[tex]\\ \sf\longmapsto 3x+y=4[/tex]

[tex]\\ \sf\longmapsto y=-3x+4[/tex]

Note the answer

Take 3rd option

[tex]\\ \sf\longmapsto -3x+y=8[/tex]

[tex]\\ \sf\longmapsto y=3x+8[/tex]

Take the 1st option

[tex]\\ \sf\longmapsto 3y=9x[/tex]

[tex]\\ \sf\longmapsto y=3x[/tex]

Option C and A is correct

Answer:

C and A

Step-by-step explanation:

Parallel means same slope, which is 3. Just solve for y in each equation, and see if 3 is the slope.

a. 3y = 9x

y = 3x

---

b. 6x + 2y = 12

2y = -6x + 12

y = -3x + 6

---

c. -3x + y = 8

y = 3x + 8

---

d. y = -1/3 x

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!8

Answers

Answer:

C

Step-by-step explanation:

Slope can truly be anything as long as they're equal

Answer:

c.their slopes are equal

Lindsay got her hair cut. The cost of a haircut
is $16. If she wants to tip her hairstylist 20%,
how much should she leave for the tip?

Answers

16 x .20 add the .20 value for the total price

Plz help don't understand
1 thru 4------Don't mind the other writing------

Answers

Hi there friend, I hope this helps explain a little better. Let me know if you have questions.

convert 250 Angtrums to centimeters

Answers

2.5x-10^6 is the answer

Can someone help me with this please?

Answers

Answer:

Step-by-step explanation:

At 12:05, a

parachutist is 8000 feet above the ground.

At 12:08, the parachutist is 5400 feet

above the ground. Find the average rate of

change in feet per minute.

Answers

Above the ground at goo feet

-4y + 12 = -7y + 24
I’ll give Brain whoever solves
PLEASE DO IT STEP BY STEP

Answers

Answer:

y - 4

Step-by-step explanation:

subtract 12 from both sides of the equation

4y+12-12= -7y +24 - 12

-4y = -7y +24 - 12

subtract

-4y +-7y + 12

add 7y to both sides of the equation

-4y + 7y = -7y +12 + 7y

simplify

3y + -7y  +12 + 7y

combine like terms.

3y = 12

divide

3y/3

=12/3

simplify      

y=12 3

y = 4

Answer:

y = 4

Step-by-step explanation:

Given the algebraic equation, -4y + 12 = -7y + 24, the goal is to solve for the value of y by isolating it to either sides of the equation.  

Start by adding 7y to both sides of the equation:

-4y + 7y + 12 = -7y + 7y + 24

3y + 12 = 0 + 24

3y + 12 = 24

Next, subtract 12 from both sides:

3y + 12 - 12 = 24 - 12

3y = 12

Divide both sides by 3 to isolate and solve for y:

[tex]\frac{3y}{3} = \frac{12}{3}[/tex]

y = 4

Double-check whether the value of y will provide a true statement if plugged into the equation:

-4y + 12 = -7y + 24

-4(4) + 12 = -7(4) + 24

-16 + 12 = -28 + 24

-4 = -4 (True statement).

Therefore, the value of y = 4.

(1 point) Water is leaking out of an inverted conical tank at a rate of 8500.0 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 14.0 m and the the diameter at the top is 7.0 m. If the water level is rising at a rate of 29.0 cm/min when the height of the water is 1.5 m, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answers

Answer:

2030.4

Step-by-step explanation:

divided 85 and 7.0

What is the slope-intercept form and slope and y-intercept of the problem: -4x+2y=10?

Answers

Answer:

slope intercept is y=mx+b where m is the slope and b is the y intercept

so the slope is 2 and the y intercept is 5 so the equation is y=2x+5

Step-by-step explanation:

7(x+2)-5(x+3=9(4-x)

Answers

Answer:

x = 37/11

Step-by-step explanation:

7(x + 2) - 5(x + 3) = 9(4 - x)

=> 7x + 14 - 5x - 15 = 36 - 9x

=> 2x - 1 = 36 - 9x

=> 11x = 37

=> x = 37/11

Hoped this helped.

Convert 9 km into cm

Answers

Answer:

900,000

Step-by-step explanation:

1 Solve for the unknown variable:

Answers

Answer:

Approximately 6.4

Step-by-step explanation:

We can use the pythagorean thereom here, that tells us (a^2)+(b^2)=c^2. C is the hypotenuse, the side opposite from the right angle, while a and b are the other sides. We can insert 5 and 4 as a and b, and solve for c

:(5^2)+(4^2)=c^2

:25+16=c^2

:41=c^2

:sqrt(41)=6.4=c              (We square rooted both sides. 6.4 is only rounded to the nearest hundredths place.) Hope this helps!

Answer:

c = 6.4

Step-by-step explanation:

To find c, we need to use Pythagoras theorem which is:

[tex]a^2 + b^2 = c^2[/tex]

Plug known variables in:

[tex]5^2 + 4^2 = c^2\\25 + 16 = c^2\\\sqrt{25 + 16} = c\\\sqrt{41} = c \\c = 6.403\\c = 6.4[/tex]

Hope this helps!

plssss help picture down below

Answers

Answer:

it is (-4,1)

Step-by-step explanation:

Hope this helps:)

I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY NOOOO SCAMS

Answers

Answer:

8

Step-by-step explanation:

Ik it is cus ik my number lines

PLS MARK ME BRAINLIEST

Answer:

I think it's 8 I'm not sure

100 POINTS!! WILL MARK BRAINLIEST
NEED RESPONSE ASAP PLEASE AND THANK YOU!!

Consider the function f (x) = 3x^3 + 10x^2 - 13x - 20

(a) Determine the x-intercepts of f (x)
(b) Determine the y-intercepts of f (x)
(c) Identify a point in between each of the x-intercepts of f(x)
(d) Determine the end behavior of f (x)
(e) Use the points and end behavior from parts (a) - (d) to graph f (x)
Label the scale of each axis.

All help is greatly appreciated!

Answers

A) (-4,0) (-1,0) (1.667,0)

B) (0, -20)

C) In between (-4, 0) and (-1, 0) is (-3, 0) and in between (-1, 0) and (1.667, 0) is (0, 0)

D) in the right end of the x-axis, x approaches +∞. And in the left end of the x-axis, x approaches −∞.

E) (Is shown in the image)

0.000456 in scientific notation (Please answer fast this is on my final math exam!)

Answers

Answer:

0.000456 in scientific notation

= 4.56 × 10-4

Step-by-step explanation:

Can I have brainliest?

0.000456 in scientific notation is 4.56 × 10-4

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