Why is it helpful to write a number as a product of primes?

Answers

Answer 1

Because it helps in reducing fractions to their simplest terms and finding the lowest common denominator when adding or subtracting fractions.

Answer 2

With least prime factorization, You can find things like the GCF

Related Questions

The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch. what is the probability that the strength of a sample is less than 38 lb/in2? round your answer to 4 decimal places.

Answers

Given
mean=35 psi
std dev=2 psi
distribution normal

For probability that X<38,
calculate
Z score = (X-mean)/std dev
=(38-35)/2=1.5
P(X<38)
=P(Z<1.5)
=0.9331928 from tables.

So probability that the strength of a random sample <38 pis = 0.9332

Tyquan uses the greatest common factor and the distributive property to rewrite this sum: 75 + 60 What expression does Tyquan write? 3(25 + 20) 5(15 + 12) 25(3 + 60) 15(5 + 4)

Answers

the GCF of 75 and 60 is 15

75/15 = 5
60/15 = 4

so ur expression is : 15(5 + 4) <==

The answer is 15(5+4)

What is 8.038×108 in standard form?

80,308,000

80,380,000

83,800,000

803,800,000

Answers

Okay. I think what you mean by this is 8.038 * 10^8. 10^8 = 100,000,000. When you multiply that by 8.038, you get 803,800,000. The answer is D.

Answer:

803,800,000

Step-by-step explanation:

8.038×10^8 in standard form

To get standard form we multiply the decimal number by 10^8

10^8 is 100000000

Now we multiply

8.038×100000000

Move the decimal number 3 places to the right and add 5 more zeros

803800000

So the standard form of the given expression is

803,800,000

How many pairs of whole numbers have a sum of 99

Answers

does anyone know lol

44 pairs. I believe that's the right answer.

one positive integer is 5 less than another. the product of the two integers is 36. what are the integers?

Answers

let the numbers be x and (x-5)

x(x-5)=36

x^2-5x-36=0

solving the equation we get

x=9 and x= -4

now find out the integers

1st number = x

2nd number = x-5

x*(x-5) = 36

x^2-5x =36

x^2 -5x-36 = 0

factor the polynomial:

(x-9) (x+4)

9-9 = 0, -4 +4 = 0

so x = 9 or -4

the question states a positive number

so x = 9

the 2 numbers are 9 and 4

The following formula relates three quantities force mass and acccelerations
F=ma

Answers

True. Dissect "F=ma" and you'll get "Force," "mass" and "acceleration."

domain of the function

Answers

hello :
y exist : x+6 ≥ 0
x ≥ -6

Jacks has 18 marbles,he loses 6 of them.

What fraction of the marbles does he lose?

Answers

6/18
1/3

Hope this helps!

Which of the following equations is of a parabola with a vertex at (0, 3)?

y = (x - 3) 2
y = (x + 3) 2
y = x 2 - 3
y = x 2 + 3

Answers

The formula for a parabola is (y-k)=(x-h)^2, or y = (x-h)^2 + k, where (h,k) is the vertex. If h=0 and k=3, then the parabola would be y = x^2 + 3

Answer:

Option D.

Step-by-step explanation:

We have to find the equation of the parabola which has vertex at ( 0,3 )

If we write the equation of a parabola in the vertex from then we will write

y = ( x - h )² + (k)²

In this equation ( h, k) will be the vertex.

(a) y = (x-3)² + 0

so ( 3,0) will be the vertex

(b) y = ( x+3)² + 0

or y = [x - (-3)]² + 0

then ( -3,0) will be the vertex

y = ( x-0 )² + (-3)

then ( 0, -3) is the vertex.

(d) y = x² + 3

y = ( x-0 )² + 3

Then ( 0, 3 ) will be the vertex of this parabola.

Option D. is the answer.

I have 5 digits. My 4s are worth 4 [10,000s] and 4 * 10. One of my 3s is worth 3,000. The other is worth 1/10 as much. My other digit is a 2. What number am I?

Answers

The given information are actually the digits and their place values in multiples of 10. To know the identity of the number, simply multiply the digit with its place value. The solution is as follows:

4(10,000) + 4(10) + 3,000 + 3,000(1/10) + 2 = 43,342

Thus, the 5-digit number is 43,342.

if f(x)=x/2-2 and g(x)=2x^2+x-3, find (f+g)(x)

Answers

hello :
If f(x)=x/2-2 and g(x)=2x^2+x-3, find (f+g)(x)
(f+g)(x)= f(x) +g(x) = x/2-2 +2x²+x-3 = x/2 +2x²+x-5
(f+g)(x)= (x+4x²-2x-10) /2
(f+g)(x)= (4x²+3x-10)/2 = 2x²+3/2 x -5

Answer:

B. [tex]2x^2+\frac{3x}{2}-5[/tex]

Step-by-step explanation:

Given functions,

[tex]f(x)=\frac{x}{2}-2[/tex]

[tex]g(x)=2x^2+x-3[/tex]

Since, (f+g)(x) = f(x) + g(x)

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

[tex]=2x^2+\frac{x+2x}{2}-5[/tex] ( combine like terms )

[tex]=2x^2+\frac{3x}{2}-5[/tex]

Option 'B' is correct.

write 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones in standard form

Answers

The correct answer would be 400,000+13,000+1,100+4=414,104.

The standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]

In order to write 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones in standard form, let us write each of the expressions in figures

4 hundred-thousand = 400,000

13 thousand = 13,000

11 hundreds = 11 x 100

11 hundreds = 1100

4 ones = 4 x 1

4 ones = 4

The next step is to sum up all the figures together

400000 + 13000 + 1100 + 4 = 414,104

Convert 414104 to standard form

[tex]414104 = 4.14104 \times10^5[/tex]

Therefore, the standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]

Learn more here: https://brainly.com/question/19169731

what is (9x^4-x^2y^2-5y^4)-(3x^4+2x^2y^2-7y^4)

Answers

(9x⁴ - x²y² - 5y⁴) - (3x⁴ + 2x²y² - 7y⁴)
9x⁴ - x²y² - 5y⁴ - 3x⁴ - 2x²y² + 7y⁴
6x⁴ - 3x²y² + 2y⁴

Which of the following is a true equation?

1) 10 + 3 + 1 = 13 + 6
2) 4 - 3 = 7
3) 4 + 3 - 3 = 7 - 3
4) 4 + 3 = 7 + 3

Answers

4 + 3 - 3 = 7 - 3
4 = 4

answer

3) 4 + 3 - 3 = 7 - 3

What is the value of x?

6 + 8x
-------------- = 5x
2

A) -2
B) -1
C) 1/3
D) 3

Answers

The ans is choice D. since there nothing under 5x, imagine there is a 1 under. After that, you can simply cross multiply, so it would be 1(6+8x)= 2(5x). 6+8x= 10x now combine like terms so subtract 8x from both sides and divide 6 by 2 and you will get 3

I just took the test the answer is D.3

Express the area of each square below as a monomial
14g5h9

Answers

Assuming the side of the square is 14 g^5 h^9, its area as [14 g^5 h^9] ^2.

So, the resulting expression is found using the properties of the power.

=> (14)^2 (g^5)^2 (h^9)^2 = 196 g^10 h^18.

Answer: 196 g^10 h^18

Find the range of the graphed function?

Answers

for finding range pay attention to y axis max of function is 5 and its min is -9
B is true

B is the correct answer

Use the function below to find f(4).

Answers

f(x) = 1/3 * 4^x.......f(4)....so we sub in 4 for x
f(4) = 1/3 * 4^4
f(4) = 1/3 * 256
f(4) = 256/3 <===

Answer: The correct option is (C) [tex]\dfrac{256}{3}.[/tex]

Step-by-step explanation: The given function is

[tex]f(x)=\dfrac{1}{3}\times 4^x.[/tex]

We are to find the value of f(4).

To find the value of f(4), we need to substitute the value of x as 4 in the given definition of function f(x).

Substituting x = 4 in f(x), we have

[tex]f(4)=\dfrac{1}{3}\times 4^4=\dfrac{1}{3}\times 256=\dfrac{256}{3}.[/tex]

Therefore, the value of f(4) is [tex]\dfrac{256}{3}.[/tex]

Option (C) is correct.

which
of the following is the least?
A.0.105
B.0.501
c.o.015
D.0.15

Answers

Is C 0.015? If so, then C, because if you imagine all of the numbers to the right as whole numbers, you get, in order from least to greatest, c, a, d, b. C is the answer.

Distributive property of 68/4

Answers

Start with 68/4. Rewrite 68 as (4)(17)/4. Cancel the 4s. Result: 17.

The trick here is to rewrite 68 as 4(17).

There are six different sixth roots of 64. That is, there are six complex numbers that solve x^6=64

Please help

Answers

There are two possible solutions:

1)
When we know that:

[tex]\sqrt[n]{z}=\sqrt[n]{|z|}\Big(\cos\frac{\phi+2k\pi}{n}+i\sin\frac{\phi+2k\pi}{n}\Big)\qquad\text{for}\quad k=0,1,\ldots,n-1[/tex]

when [tex]z=|z|(\cos\phi+i\sin\phi)[/tex]

then:

[tex]x^6=64\quad|\sqrt[6]{(\ldots)}\\\\x=\sqrt[6]{64}[/tex]

For [tex]x=64[/tex] we have:

[tex]64=|64|(\cos0+i\sin0)\quad\Rightarrow\quad \phi=0[/tex]

and:

[tex]\sqrt[6]{64}=\sqrt[6]{64}\Big(\cos\frac{0+2k\pi}{6}+i\sin\frac{0+2k\pi}{6}\Big)\qquad\text{for}\quad k=0,1,\ldots,5\\\\\\ \sqrt[6]{64}=2\Big(\cos\frac{k\pi}{3}+i\sin\frac{k\pi}{3}\Big)\qquad\text{for}\quad k=0,1,\ldots,5 [/tex]

k = 0

[tex]2\Big(\cos\frac{0}{3}+i\sin\frac{0}{3}\Big)=2(1+0i)=2\cdot1=\boxed{2}[/tex]

k = 1

[tex]2\Big(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\Big)=2\Big(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{1+i\sqrt{3}}[/tex]

k = 2

[tex]2\Big(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\Big)=2\Big(-\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{-1+i\sqrt{3}}[/tex]

k = 3

[tex]2\Big(\cos\frac{3\pi}{3}+i\sin\frac{3\pi}{3}\Big)=2\Big(\cos\pi+i\sin\pi\Big)=2(-1+0i)=\boxed{-2}[/tex]

k = 4

[tex]2\Big(\cos\frac{4\pi}{3}+i\sin\frac{4\pi}{3}\Big)=2\Big(-\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{-1-i\sqrt{3}}[/tex]

k = 5

[tex]2\Big(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3}\Big)=2\Big(\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{1-i\sqrt{3}}[/tex]

So the answer is:

[tex]x=\{2,\,1+i\sqrt{3},\,-1+i\sqrt{3},\,-2,\,-1-i\sqrt{3},\,1-i\sqrt{3}\}[/tex]

2)
We don't know method (1). If so, we could use following identities:

[tex](1)\quad a^2-b^2=(a+b)(a-b)\\\\(2)\quad a^3-b^3=(a-b)(a^2+ab+b^2)\\\\(3)\quad a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

There will be:

[tex]x^6=64\\\\x^6-64=0\\\\(x^3)^2-8^2=0 \qquad\text{from (1)}\\\\(x^3+8)(x^3-8)=0\\\\(x^3+2^3)(x^3-2^3)=0\qquad\text{from (2) and (3)}\\\\ (x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\qquad(\star)[/tex]

Now, we complete the square for:

[tex]x^2-2x+4=x^2-2x+1+3=(x^2-2x+1)+3=(x-1)^2+3=\\\\=(x-1)^2+(\sqrt{3})^2=(x-1)^2-(-1)(\sqrt{3})^2=(x-1)^2-i^2(\sqrt{3})^2=\\\\=(x-1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x-1-i\sqrt{3})(x-1+i\sqrt{3})}[/tex]

and for:

[tex]x^2+2x+4=x^2-2x+1+3=(x^2+2x+1)+3=(x+1)^2+3=\\\\=(x+1)^2+(\sqrt{3})^2=(x+1)^2-(-1)(\sqrt{3})^2=(x+1)^2-i^2(\sqrt{3})^2=\\\\=(x+1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x+1-i\sqrt{3})(x+1+i\sqrt{3})}[/tex]

When we return to [tex](\star)[/tex]:

[tex](x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\\\\(x+2)(x-1-i\sqrt{3})(x-1+i\sqrt{3})(x-2)(x+1-i\sqrt{3})(x+1+i\sqrt{3})=\\=0[/tex]

And we have answer:

[tex]x=\{-2,\,1+i\sqrt{3},\,1-i\sqrt{3},\,2,\,-1+i\sqrt{3},\,-1-i\sqrt{3}\} [/tex]

To find the six sixth roots of 64, you can use polar form and De Moivre's Theorem to calculate the complex numbers. The roots are 2, 1+i√3, -1+i√3, -2, -1-i√3, and 1-i√3.

[tex]X^6 = 64[/tex]

The sixth roots of 64 are complex numbers and can be found by writing 64 in polar form and applying De Moivre's Theorem. Let's find the six roots:

First root: 2(cos(0) + i sin(0)) = 2

Second root: 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + i√3

Third root: 2(cos(2π/3) + i sin(2π/3)) = 2(-1/2 + i√3/2) = -1 + i√3

Fourth root: -2

Fifth root: -2(cos(-π/3) + i sin(-π/3)) = -2(1/2 - i√3/2) = -1 - i√3

Sixth root: -2(cos(-2π/3) + i sin(-2π/3)) = -2(-1/2 - i√3/2) = 1 - i√3

Find the equation in standard form of the line with slope
[tex] \frac{7}{2} [/tex] that passes through the point (5,7)
Please explain as well

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 7}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{7}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=\cfrac{7}{2}(x-5)\implies y-7=\cfrac{7}{2}x-\cfrac{35}{2} \\\\\\ y=\cfrac{7}{2}x-\cfrac{35}{2}+7\implies \stackrel{standard~form}{-\cfrac{7}{2}x+y=-\cfrac{21}{2}}[/tex]

Between two tenths of a mile will the second relay exchange occur? Explain.

Answers

yes it will occur because two tenths of a mile the second relay will exchange

2/10

There is one tenth in a mile. I have the same question. But I am just guessing.

pls I help I need answers and work shown

Answers

0.30 as a fraction is 30/100 = 3/10

0.30 as a percent = 0.30 * 100 = 30%

answer is D. 3/10 and 30%

.30 is .3

do .30 divided by 1 and you get 3/10

Percentage= move the decimal 2 places to the right and you get 30%

So your answer is D.

You want to replace the countertops in a kitchen. One counter measures 24 inches by 6 feet. The other is 30 inches by 4 feet. If the new countertop costs $42.00 per square foot, what will be the cost of the new top?

Answers

First, multiply to find the total square footage of the counter.

2 ft x 6 ft=12 square feet
2.5 ft x 4 ft=10 square feet
Total square feet of the counter is 22 square feet.

To find the total cost, just multiply the area by the cost per square foot.
$42 x 22=$924

Answer:

The cost of the new top $924.

Step-by-step explanation:

You want to replace the counter-tops in a kitchen.

The dimensions of the first counter is 24 inches by 6 feet.

i.e [tex]24 \text{ inch} \times 6 \text{ feet}[/tex]

or [tex]2\text{ feet} \times 6 \text{ feet}[/tex]

As 1 feet =12 inches

Hence the area of the counter is [tex]2\times 6=12\text{ feet}^2[/tex]

The dimensions of the second counter is 30 inches by 4 feet.

i.e [tex]30 \text{ inch} \times 4 \text{ feet}[/tex]

or [tex]2.5\text{ feet} \times 4 \text{ feet}[/tex]

Hence the area of the counter is [tex]2.5\times 4=10\text{ feet}^2[/tex]

Hence, the total area will be [tex]12+10=22 \text{ feet}^2[/tex]

The unit cost of the counter-top is [tex]\$42.00\text{ feet}^2[/tex]

So the net cost will be,

[tex]=42\times 22=\$924[/tex]

Simplify the expression 3 1/3/3 1/3. Explain how the expression and its simplified form show that the set of irrational numbers is not closed under division

Answers

The expression given is ambiguous according to the standard rules of math (PEMDAS) due to the lack of appropriate parentheses and probably the exponentiation symbol ^.

From the context, I assume it to mean
(3^(1/3)) / (3^(1/3)) = 1

Since 3^(1/3) is the cube-root of 3, and is thus irrational.
However, the quotient is exactly 1, which is a rational number.

The example is therefore a counter-example for the statement that "set of irrational numbers is closed under division", or stated differently,
"the set of irrational numbers is not closed under division"

There are 60 minutes in 1 hour. What fraction of an hour is 4 minutes? Write your answer in lowest terms.

Answers

4 minutes/60 minutes

Divide the numerator and denominator by 4
1/15

Final answer: 1/15

The fraction of an hour is 4 minutes in lowest terms is 1/15.

What fraction of an hour is 4 minutes in lowest terms?

To find the fraction of an hour that 4 minutes represents, we need to compare the number of minutes to the total number of minutes in an hour, which is 60.

We can set up a fraction where the numerator represents the number of minutes we want to find the fraction for (4 minutes) and the denominator represents the total number of minutes in an hour (60 minutes).

So, the fraction can be written as 4/60.

To simplify the fraction to its lowest terms, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 60 is 4.

Dividing both the numerator and denominator by 4, we get:

4/60 = (4 ÷ 4) / (60 ÷ 4) = 1/15.

Therefore, 4 minutes in lowest terms is equal to 1/15th of an hour.

Read more about lowest terms here: https://brainly.com/question/28635285

#SPJ2

Express each repeating decimal as a fraction.

1.
1.8[4]

2.
2.1[26]

Answers

Hello,

1.8444444....=1.8+1/10*0.44444....
=1.8+1/10*4/9
=1.8+4/90
=162/90+4/90
=166/90
=83/45

2.126262626...=2.1+1/10*0.262626...
=2.1+1/10*26/99
=2.1+26/990
=2079/990+26/990
=2105/990
=421/198

Answer:

1.8444444....=1.8+1/10*0.44444....

=1.8+1/10*4/9

=1.8+4/90

=162/90+4/90

=166/90

=83/45

2.126262626...=2.1+1/10*0.262626...

=2.1+1/10*26/99

=2.1+26/990

=2079/990+26/990

=2105/990

=421/198

Rational numbers are _____ natural numbers.

always
sometimes
never

Answers

Rational numbers are sometimes natural numbers.

Sometimes is the answer meh dude

Solve For L: A = L ⋅ W ⋅ H

L=aw/h

L=wh/a

L=a/wh

L=w/ha

Answers

Ok so what you're trying to do is get L by itself so to do this you move everything to the other side:
A=L*WH
[tex] \frac{A}{WH} [/tex]=L
So you answer would be: C

your answer would be the third one C

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