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

miggy ask to solved the given quadratic equation x²+8x-20=0 using the quadratic formula,Help miggy to determine the following​

roots of the quadratic 3
discriminant
nature of roots
sum of the roots
product of the roots​

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

roots of the quadratic equation ~

[tex]2 \: \: \: \:a nd \: \: - 10[/tex]

discriminant ~

[tex]144[/tex]

nature of roots ~

[tex]real[/tex]

sum of the roots ~

[tex] - 8[/tex]

product of the roots ~

[tex] - 20[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve he given quadratic equation using quadratic formula ~

Let's consider the following values ~

b (Coefficient of x) = 8

a (Coefficient of x²) = 1

c (Constant term) = -20

According to quadratic formula, the roots are ~

[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

where, ( b² - 4ac ) is known as it's discriminant ~

that is equal to ~

[tex](8) {}^{2} - (4 \times 1 \times - 20)[/tex]

[tex]64 - ( - 80)[/tex]

[tex]64 + 80[/tex]

[tex]144[/tex]

Hence, Discriminant = 144

And since discriminant is positive, then the roots of the quadratic polynomial are real .

Let's find the roots now ~

[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac} }{2a} [/tex]

[tex] \dfrac{ - 8 \pm \sqrt{144} }{2 \times 1}[/tex]

[tex] \dfrac{ - 8 \pm12}{2} [/tex]

[tex] \dfrac{ 2( - 4 \pm6)}{2} [/tex]

[tex] - 4 \pm6[/tex]

So, the two roots are ~

[tex] - 4 + 6[/tex]

[tex]2[/tex]

and

[tex] - 4 - 6[/tex]

[tex] - 10[/tex]

Sum of roots ~

[tex] - 10 + 2[/tex]

[tex] -8[/tex]

product of roots ~

[tex] - 10 \times 2[/tex]

[tex] - 20[/tex]

Yes this can be correct just depends on if you do it

I run 960 hm and my friend run 960 dam. How many km do we run in total?

Answers

Answer:

105.6 km

Step-by-step explanation:

Use: King Henery Doesn't Usually drink chocolate milk

K in king stands for kelo

H in Henery stands for hecto

D in Doesn't stands for deka

U in Usually stands for Meters, Liters, and Grams

d in drink stands for Deci

c in chocolate stands for Centi

And m in milk stands for milli

In a sale, the price of a jacket is reduced.
The jacket has a normal price of £52
The jacket has a sale price of £41.60
Work out the percentage reduction in the price of the jacket.

Answers

Percentage reduction = 80%
J

Pg 118 #11 - 13, 15, 16

Answers

We can't get the answer if there's no problem?

5. Find the triangle similar to AABC at the right.

Answers

Answer:

the answer is b

Step-by-step explanation:

a car travels 30m in 2 minutes whats the speed​

Answers

Answer:

15

Step-by-step explanation:

speed is distance over time so its 30 devided by 2

What is the quotient of 1.155 x 10^5 and 1.65 x 102 expressed in scientific
notation?

Answers

Answer: 7.00x10^2

Step-by-step explanation:

Are you asking for the quotient of (1.155 x 10^5)/(1.65 x 10^2)?

If so, divide (1.155/1.65) = 0.7000.

Then subtract 2 (the bottom exponent from [tex]10^{2}[/tex]) from the top exponent:  [tex]10^{5}[/tex] becomes [tex]10^{3}[/tex].

Combine the two:  0.7000x10^3

Move the decimal point to the right by one:  7.00x10^2 (to 3 sig figs).

7 x 10² is the quotient of 1.155 x 10⁵ and 1.65 x 10² expressed in scientific

notation.

To find the quotient of these two numbers in scientific notation, you divide the two significant figures and then subtract the exponents of 10. The calculation would be as follows:

(1.155 x 10⁵) / (1.65 x 10²)

Dividing the significant figures:

1.155 / 1.65

= 0.7

Subtracting the exponents:

5 - 2 = 3

So, the quotient in scientific notation is approximately:

0.7 x 10³

Which can also be written as:

7 x 10²

Hence, the quotient of 1.155 x 10⁵ and 1.65 x 10² expressed in scientific

notation is 7 x 10².

To learn more on Number system click:

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Solve for X and find M Find m

Answers

Step-by-step explanation:

3x-28=2x-9

3x-2x=28-9

x=19°

For angle FGH = 2x-9° = 38°-9° = 29°.

For angle HGI = 3x-28° = 57°-28° = 29°.

For angle FGI = 29°+29° = 58°.

hope this helps you.

Winston’s owner increased the amount of dog food he eats every day from 40 grams to 48 grams. By what percentage did Winston increase the amount of dog food he eats?

Answers

Answer:

the answer is 20% increase I used a calculator but you should be able to do that math by taking 40 dividing by five where that ends up being 8 that is 20 percent of 40 so adding that back to the original amount is a 20 percent increase hope this helps

Step-by-step explanation:

can we represent any number on number line

Answers

Answer:

Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the right side of zero (called origin), and negative on left side of origin. The representation of rational numbers on the number line depends on the type of fraction.

Step-by-step explanation:

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left. Here, fractions and decimals have been represented on the number line. A number line can also be used to represent both positive and negative integers as well.

Diana made 143 treats for her visit to the nursing home. There are 37 patients and she wants each person to get the same number of treats. How many more treats will she need to make in order for each patient to receive 4 treats?

Answers

Answer:

5 more treats

Step-by-step explanation:

The total number of treats if she gives each person 4 treats is

. 37 people * 4 treats = 148 treats

Subtract 143 (number of treats she has) from 148 (total number of treats to give out)

. 148 treats - 143 treats = 5 treats

given:

143 treats

37 patients

to find:

how many treats will she need to make in order for each patient to receive 4 treats.

solution:

[tex]4 \times 37[/tex]

[tex] = 148[/tex]

[tex] = 148 - 143[/tex]

[tex] = 5[/tex]

therefore, she'll have to make 5 treats more in order for each patient to receive 4 treats

answer= option D

Matilda and Nancy are miles apart, bicycling toward each other on the same road. Matilda rides miles per hour and Nancy rides at miles per hour. In how many hours will they meet

Answers

Answer:

it will take 3 hours For them to cover 60 miles and meet

Step-by-step explanation:

In pic

(Hope this helps can I pls have brainlist (crown)☺️)

question:To make a certain shade of paint, Anya mixed 2/3 cups of white paint with 2 2/3 cups of blue paint
How many cups of blue paint should she mix with 3 cups of white paint to make the same shade?

Answers

Step-by-step explanation:

2/3 cups white paint mix with 2 2/3 cups = 8/3 cups blue paint.

so, 2/3 / 8/3 = 2×3 / 3×8 = 6/24 = 1/4.

therefore, the mix ratio white/blue paint is 1/4 (1 part white, 4 parts blue).

so, for 3 cups of white paint we need 3×4 = 12 cups of blue paint.

You bought for hamburgers you gave the cashier $50 bill and get $22 change how much was each hamburger

!!!!!!!!5 step plan please!!!!!!!!

Answers

If you have the cashier 50 and got 22 back, each burger would be 7
$50-$22= $28
$28/4hamburgers=$7

An electrician cuts 28 feet piece wire into two pieces one piece is 4 feet longer than the other how long are the pieces

!!!!5 step plan!!!!!

Answers

Answer:

12 and 16

Step-by-step explanation:

Turn it into algebra.

Make one of the pieces x. So x+4 is the piece that is 4 feet longer and x is the piece that it is 4 feet longer than.

So x+4+x=28, which is the total length, and if you simplify it, it makes 2x+4=28.

Then you just solve it, so do 28-4=24, and then divide that by 2, which gets 12.

Then you substitute 12 where x has been substituted for the pieces.

One piece is x feet, so that just stays 12, and another piece is x+4, so 12+4 which is 16.

To make sure it's correct, you can check it by doing 16-12=4 and add 12 and 16 together which gets the correct total of 28.

What is the equation of this line in slope intercept form? -x- 5y = 10

A) y= -1/5x-2
B) y= -1/5x + 10
C) y= 1/5x + 10
D) y= 5x - 2
NO FILES NO LINKS PLEASE​

Answers

Answer:

D 22ilsjjssiksksksksksksks

Step-by-step explanation:

212

I need help please each number has its own equation number it off please

Answers

4. 22 ≤ 5x - 3

5. x/8 - 5 > -6/10

6. 2 + x ≥ 4 * 12

find the the equations of the circle passing through (1, 4) and having the diameters of 3x-4y=1 and 2x+y=8?

Answers

Answer:

In order to write the equation of a circle, we need two things their centre as well as the radius. so….diameter always intersect each other at the centre of the circle, hence after solving the equation of diameter, we get the intersecting point(x, y)=(3,2). now, we have already given one point…and as per the question circle passing through that point itself. so by applying distance formula, we can obtain the value of radius. thus we get radius 2√2. now we have required things to get the equation of a circle. we know the standard equation of circle having centre =(x1,y1) and radius = r is (x-x1)²+(y-y1)²=r² hence we can find the equation of circle by putting the coordinate (x1,y1)=(3,2) and radius =2√2 in the above mentioned standard equation.

Step-by-step explanation:

:3

9. Using a twenty sided number cube, what is the probability that you will roll an even number or
an odd prime number? The number 1 isn't an odd prime. Round to three decimals.
(1 point)

Answers

Answer:

0.85

Step-by-step explanation:

total samples cases = 20

chances that are even or odd prime are 17 chances

2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20

probability = 17/20

= 0.85

Consider the function given by the graph. What are
these values?
fl-2) =
10) =
f(4) =

Answers

Answer:

f(-2) = 2

f(0) = 4

f(4) = -1

Step-by-step explanation:

Given the graph of a piecewise function:

[tex]\displaystyle\mathsf{f(x) = \left \{ {{x\:+\:4\quad if\:\:x\leq \:0} \atop {-\frac{1}{2}x\:+\:1\quad if\:\:x\: >\:0}} \right.}\\[/tex]

Side note:

I used the method of finding the linear equations in slope-intercept form to establish the piecewise function. First, I solved for the slope by choosing two points in each defined interval. Then, I plugged in the y-intercepts of each interval, for f(x) = x + 4: the y-intercept is (0, 4) where b = 4; for f(x) = -½x + 1, the y-intercept is (0, 1) where b = 1.

Explanation:

There are two methods for determining the range values of the given domain values.  

Method 1: The first method is using the graph to find the corresponding range values of the given domain {-2, 0, 4}.  

Method 2: Alternatively, we could use the rules provided by the piecewise function in evaluating the following domain values.  This post will use the second method (using the piecewise function) to evaluate the input values.

Regardless of the method used, the results will remain the same.

f(-2)

Since the input value is x = -2, then we must use the function, f(x) = x + 4:

f(x) = x + 4

f(-2) = -2 + 4

f(-2) = 2

Therefore, the range value given the domain, x = -2 is 2, or simply: f(-2) = 2.

f(0)

Given the input value is x = 0, then we must also use the function, f(x) = x + 4:

f(x) = x + 4

f(0) = 0 + 4

f(0) = 4

Therefore, the range value given the domain, x = 0 is 4, or  f(0) = 4.

f(4)

Since the input value is x = 4, then we must use the function, f(x) = -½x + 1:

f(x) = -½x + 1

f(4) = -½(4) + 1

f(4) = -2 + 1

f(4) = -1

Therefore, the range value given the domain, x = 4 is -1, or  f(4) = -1.

What does this graph represent?
Question options:
not moving
acceleration
constant speed

Answers

Answer:

A or C

Step-by-step explanation:

help please??????????????????

Answers

Answer:

-5 and 2

-2 and -1

-3 and 0

There is no shortcut to solving this type of problem. You just have to use trial and error.

:)

Answer:

-2+ (-3)

-5+ 0

-1+ (-2)+ (-2)

Hope this helps!

LMK if it does

Select all the equations that have {6} as its solution set.

15−x=54x

8+3x=6x−10

x2+2=7x−4

43−4x=3x−1

Answers

ANSWER:

The ANSWER IS 2. if two solutions are allowed then 2. AND 3. and if your rounding, then 2. 3. and 4.

Step-by-step explanation:

For the first one it is: 0.27... or 3/11

For the second one it is: 6

For the third one it is: 1 or 6, meaning it has two solutions

For the fourth one it is: 6.285714, or 44/7

for the first one: 15-x=54x -> add x to both sides: 15=55x -> then divide both sides by 55: x=3/11

for the second one: 8+3x=6x-10 -> subtract 6x from both sides: 8-3x=-10 -> subtract 8 from both sides: -3x=-18 -> divide both sides by -3: x=6

I'm actually supposed to be doing school, so I don't have time to explain the last two, but I wanted to help, so please give 4 stars or brainliest. and thanks for waiting patiently.

The equation 8+3x=6x−10 has {6} as its solution set. Option B is correct.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

The equations that have {6} as its solution set is,

We have to solve the equation in order to find the value of x,

Equation 1,

15−x=54x

54x+x=15

55x=15

x=0.27

Equation 2,

8+3x=6x−10

6x-3x=-10+8

3x=18

x=6

Equation 3,

x²+2=7x−4

x²-7x+6=0

x²+6x+x+6=0

x(x+6)+1(x+6)=0

(x+1)=0 , x=-1

(x+6)=0, x=-6

Equation 4,

43−4x=3x−1

4x+3x=43+1

7x=44

x=44/7

x=6.285

Thus, the equation 8+3x=6x−10 has {6} as its solution set. Option B is correct.

Learn more about the equation here,

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You have already saved $75 dollars for a new TV. You are
week from now on. Write an equation to model the amount of your savings.
If the TV costs $250, how many weeks will you need to save?

Answers

U will need to save 3 and a half weeks so 3 weeks and 3 days and u will have probably a little over 250
How much are you gaining each week? You need to know that to be able to make an equation, but it looks like that part cuts off

Pls help and explain, will give brainliest!

-5+3 + (-1/6)+ 5/6 in fractions form

Answers

Answer:

Step-by-step explanation:

-5+3 + (-1/6)+ 5/6

-2 - 1/6 + 5/6

-2 + 4/6 (do this boring math)

Answer:

[tex]-1\frac{1}{3}[/tex] aka [tex]\frac{-4}{3}[/tex]

Step-by-step explanation:

-5+3+(-1/6)+ 5/6

Ok soo -5+3 is -2 So then

-2-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex]

-2+(-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex])

-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex]=[tex]\frac{4}{6}[/tex] or [tex]\frac{2}{3}[/tex]

-2+[tex]\frac{2}{3}[/tex]=-1[tex]\frac{1}{3}[/tex]

The Guiness Book of World Records holder for Fastest Rapper is a guy
from Seattle named NoClue. He can rap 70 syllables in just 5 seconds. (He
actually did 723 in 51.27 seconds). What is his speed in syllables per
second?

Answers

Answer:

Write a ratio.

70 : 5

x : 1

To solve for x, cross multiply.

70 : 5x

Divide both sides by 5.

14 = x

So, NoClue can rap 14 syllables per second.

:)

how to find the slope of 1,4 and 0,11

Answers

Answer:

y2-y1 over x2-x1, typically the second or set of the higher numbers would be #2 so im taking 0,11 as #2

Step-by-step explanation:

7 i believe

Answer:

y2-y1/x2-x1

11-4/1-0

7/1

slope = 7

60 divided by the ratio of 7:3

Answers

First find the total of the ratio:
7 + 3 = 10

Now we can divide 60 by 10:
60 divided by 10 is 6

Finally we can multiply both 7 and 3 by 6:
7 x 6 = 42
3 x 6 = 18

To check we can add 42 and 18: this gives us 60.

Answer: 42:18

Hope this helps!

find the percentage change of 20 to 25​

Answers

Answer:

Percentage change should be 25%

Step-by-step explanation:

25 - 20

---------- x 100%

20

5

---- x 100% = 25% increase

20

25 percent increase

Solve the system of linear equations by elimination.

3x−30=y
7y−6=3x

























Solve the system of linear equations by elimination.

3x−30=y
7y−6=3x

Answers

Hey! Hopefully this helped :)
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