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const2013 [10]
3 years ago
11

20POINTS! HELP ME PLZZ I NEED HELP WITH THIS IT IS DUE TOMORROW !!

Mathematics
1 answer:
ANTONII [103]3 years ago
8 0

Step-by-step explanation:

The denominators are 2, 3, and 4.  The least common denominator is the least common multiple (LCM) of these numbers.

To find the LCM, first write the prime factorizations.

2 = 2¹

3 = 3¹

4 = 2²

The LCM is therefore 2² × 3 = 12.

Rewrite the fractions with a denominator of 12.

⁷/₄ + ¹/₂ + ⁵/₃ + ¹/₃ + ¹/₄ + ¹/₂

= ²¹/₁₂ + ⁶/₁₂ + ²⁰/₁₂ + ⁴/₁₂ + ³/₁₂ + ⁶/₁₂

Now that the denominators are the same, we can simply add the numerators.

= ⁽²¹⁺⁶⁺²⁰⁺⁴⁺³⁺⁶⁾/₁₂

= ⁶⁰/₁₂

= 5

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Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)
Lisa [10]

Answer:

f(x) = 4x^2 - 3x + 6

Step-by-step explanation:

Quadratic function is given as f(x) = ax^2 + bx + c

Let's find a, b and c:

Substituting (0, 6):

6 = a(0)^2 + b(0) + c

6 = 0 + 0 + c

c = 6

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

f(x) = ax^2 + bx + c

16 = a(2)^2 + b(2) + 6

16 = 4a + 2b + 6

16 - 6 = 4a + 2b + 6 - 6

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10 = 2(2a + b)

\frac{10}{2} = \frac{2(2a + b)}{2}

5 = 2a + b

2a + b = 5 => (Equation 1)

Substituting (3, 33), and c = 6

f(x) = ax^2 + bx + x

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27 = 9a + 3b

27 = 3(3a + b)

\frac{27}{3} = \frac{3(3a + b)}{3}

9 = 3a + b

3a + b = 9 => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

3a + b = 9

2a + b = 5

a = 4

Replace a with 4 in equation 2.

2a + b = 5

2(4) + b = 5

8 + b = 5

8 + b - 8 = 5 - 8

b = -3

The quadratic function that represents the given 3 points would be as follows:

f(x) = ax^2 + bx + c

f(x) = (4)x^2 + (-3)x + 6

f(x) = 4x^2 - 3x + 6

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Answer:

10+4=14

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