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ss7ja [257]
2 years ago
14

Prime factorization of a 4- digit number with at least three distinct factors

Mathematics
1 answer:
denpristay [2]2 years ago
8 0

Answer:

We know that every number can be written as a product of prime numbers.

The method to find the factorized form of a number depends on the number, we just try to find the different factors by dividing by them, for example for the number 1000 we have:

1000 is an even number, then we can divide it by 2 (2 is a prime number)

1000 = 2*500   (so we already found a prime factor)

500 is also an even number, so we can divide it by 2

1000 = 2*500 = 2*2*250  (we found another prime factor)

dividing by 2 again we get:

1000 = 2*2*250 = 2*2*2*125

1000 = (2*2*2)*125

now we just need to factorize 125

we know that 125 is a multiple of 5, such that:

125 = 5*25 = 5*5*5

(5 is a prime number, so it is completely factorized).

Then the factorization of 1000 is:

1000 = (2*2*2)*(5*5*5) = 2^3*5^3

Now with another example, 1422

1422 is an even number, so we again start using the factor 2:

1422 = 2 = 711

then:

1422 = 2*711

we already found a factor.

711 is a multiple of 3 (the sum of its digits is a multiple of 3), then:

711/3 = 237

We can write our number as:

1422 = 2*3*237

237 is also a multiple of 3

237/3 = 79

then:

1422 = 2*3*3*79

and 79 is a prime number, so we already have 1422 completely factorized.

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What is -(2×7)+(4g×9a)
kotykmax [81]
I think its 162 but i dont know so hope this helps sorry if it dont
4 0
3 years ago
A (0, 2) and B (6,6) are points on the straight line ABCD.
elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points (x_1,y_1) and (x_2,y_2), the distance is denoted by: \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}. Let's find the distance between A and B:

d = \sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = \sqrt{(6-a)^2+(6-b)^2}

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0
3 years ago
Read 2 more answers
X+-4+2x=14<br> x=<br> Blank 1:
never [62]

Answer:

6

Step-by-step explanation:

3x-4=14

3x=14+4

3x=18

x=6

6 0
3 years ago
Read 2 more answers
At the beginning of an environmental study, a forest covered an area of 1500km^2. Since then, the area has decreased by 6.3% eac
geniusboy [140]

The <em><u>correct answer</u></em> is:

y=1500(0.937)^t

Explanation:

An exponential function is of the form

y=a\times b^x, where a is the initial population, b is 1 plus the amount of yearly change, and x is the number of years.

For our problem, a, the initial population, is 1500.

The yearly change is 6.3%; 6.3% = 6.3/100 = 0.063.  Since it is decreasing, this is negative; 1+(-0.063) = 0.937.

We use t as the number of years.

This gives us

y=1500(0.937)^t

3 0
3 years ago
Find the solution to the following system using substitution or elimination: y = 3x + 2 y = -2x - 8 O A. (-5,-) OB. (-2,-4) O C.
mr Goodwill [35]

Answer:

B. (-2,-4)

Explanation

Given equations:

   y = 3x + 2

   y = -2x - 8

Solving both equations will yield the values of x and y;

Solution:

   y = 3x + 2    ----- (i)

   y = -2x - 8   ------ (ii)

Using substitution method, input equation i, into ii

    3x + 2 = -2x - 8

Collect like terms and solve;

     3x + 2x = -8 -2

         5x  = -10

            x  = -2

Then put x = -2 into i, to find y

      y = (-2 x 3) + 2

       y = -6 + 2 = -4

So, the solution of the equation is B. (-2,-4)

6 0
3 years ago
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