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maw [93]
2 years ago
9

Problem 2 Find all the divisors of the number 2,310. How do you know that you found them all?​

Mathematics
1 answer:
elena-s [515]2 years ago
8 0

9514 1404 393

Answer:

  1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42,

  55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310

Step-by-step explanation:

The trailing digit is 0, and the sum of digits is 6, so we know the number is divisible by 2, 3, 5. Dividing out those factors, we get a quotient of 77, which is 7×11. This means the prime factorization is ...

  2×3×5×7×11 = 2310

There are 5 prime factors, each with an exponent of 1, so the total number of divisors is 2^5 = 32. We will have found them all when all 32 are listed.

  1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42,

  55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310

Of course, the pairwise products working toward the center from the ends of the list are all 2310.

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Answer: yes because pi = 22/7 as a fraction and as a decimal that never terminates

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6 0
3 years ago
X-20 = y+20<br>2Y - 44 = X + 22<br>​
nordsb [41]

X-20 = Y+20........    X-Y = 20+20........

X-Y = 40

AND

2Y-44=X+22.............   Y-X= 44+22

Y-X=66

NOW, LET'S FIND X AND Y FROM THESE TWO EQUATIONS....

X-Y =40

Y-X= 66

IF WE COLLECT .......     2Y = 106 AND Y = 53

THEN, USE Y IN ANY EQUATIONS FOR FINDING X

X-53 = 40 ..... X= 53+40 .......... X= 93

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8 0
3 years ago
Find an equation for the perpendicular Bisector of the line segment whose endpoints are (-9,-8) and (7,-4
Alina [70]

equation for the perpendicular Bisector of the line segment whose endpoints are (-9,-8) and (7,-4)

Perpendicular bisector lies at the midpoint of a line

Lets find mid point of  (-9,-8) and (7,-4)

midpoint formula is

\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}

\frac{-9+7}{2} ,\frac{-8+-4}{2}

midpoint is (-1, -6)

Now find the slope of the given line

(-9,-8) and (7,-4)

slope = \frac{y2-y1}{x2-x1} = \frac{-4-(-8)}{7-(-9)}

slope = \frac{-4+8}{7+9}= \frac{4}{16} =\frac{1}{4}

Slope of perpendicular line is negative reciprocal of slope of given line

So slope of perpendicular line is -4

slope = -4  and midpoint is (-1,-6)

y - y1 = m(x-x1)

y - (-6) = -4(x-(-1))

y + 6 = -4(x+1)

y + 6 = -4x -4

Subtract 6 on both sides

y = -4x -4-6

y= -4x -10

equation for the perpendicular Bisector y = -4x - 10


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