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MissTica
2 years ago
15

Find the least common denominator for the group of fractions. 5/12, 9/14, 2/5, 1/10

Mathematics
1 answer:
makkiz [27]2 years ago
5 0

9514 1404 393

Answer:

  420

Step-by-step explanation:

The prime factors of each denominator are ...

  12 = 2²×3

  14 = 2×7

  5 = 5

  10 = 2×5

The unique factors are 2²×3×5×7 = 420.

The least common denominator of these fractions is 420.

_____

<em>Additional comment</em>

  • 5/12 = 175/420
  • 9/14 = 270/420
  • 2/5 = 168/420
  • 1/10 = 42/420
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The difference between the roots of the quadratic equation x2 -14x +q =0 is 6. Find q
Irina-Kira [14]

9514 1404 393

Answer:

  q = 40

Step-by-step explanation:

When the quadratic has roots p and r, it can be factored as ...

  (x -p)(x -r) = x² -(p+r)x +pr

So, the sum of the roots is 14, and their difference is 6. This lets us find the roots from ...

  p + r = 14

  p - r = 6

  2p = 20 . . . add the two equations

  p = 10

  r = 14 -p = 4

The value of interest is then ...

  q = pr = (10)(4)

  q = 40

__

The graph shows the roots to be 4 and 10, as we found.

3 0
3 years ago
Evaluate 3x+5(y+3) when x is 2 less than the quotient of y and 3, and y=12
myrzilka [38]

Answer:

81

Step-by-step explanation:

12/3 = 4

4 - 2 = 2

x = 2

using the order of operations, you would first have to do y + 3

y = 12

12 + 3 = 15

the equation simplified is 3 x 2 + 5 x 15

3 x 2 = 6

5 x 15 = 75

75 + 6 = 81

8 0
3 years ago
the sum of the reversed number and the original number is 154. Find the original number, if the ones digit in it is 2 less than
VladimirAG [237]

Answer:

The number is 86

Step-by-step explanation:

Let the number be  xy, then the reverse is yx

The sum of the reversed number and the original number is 154,

\implies (10x+y)+(10y+x)=154

We simplify this to get:

\implies 11x+11y=154....eqn(1)

If the ones digit in it is 2 less than the tens digit, then

y=x-2....eqn(2)

Putt equation (2) in (1)

\implies 11x+11(x-2)=154

\implies 11x+11x-22=154

\implies 11x+11x=154+22

\implies 22x=176

\implies x=8

Put x=8 in the second equation:

y=8-2=6

The original number is 86

7 0
3 years ago
Read 2 more answers
What is the image of (-5, -1) after a reflection over the x-axis?​
elena55 [62]

Answer:

(-5,1)

Step-by-step explanation:

solved by graphing

5 0
3 years ago
Read 2 more answers
Noelle used 17 lemons to make lemonade. This was 85% of all the lemons
LuckyWell [14K]

Answer:

20 lemons

Step-by-step explanation:

Let the number of lemons = 'x'

85% of x = 17

\frac{85}{100}*x = 17\\\\x = \frac{17*100}{85}\\x = 20

6 0
2 years ago
Read 2 more answers
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