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3 years ago

. Find the greatest common factor and the least common multiple of each of the following sets of numbers. 12 and 7

Mathematics

2 answers:

Nana76 [90]3 years ago

5 0

Answer:

LCM = 84 GCF = 1

Step-by-step explanation:

LCM of 7 and 12 is 84.

GCF(7,12) = 1

LCM(7,12) = ( 7 × 12) / 1

LCM(7,12) = 84 / 1

LCM(7,12) = 84

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

GCF of 7 and 12 is 1. Now calculate the prime factors of 7 and 12, then find the greatest common factor (greatest common divisor) of the numbers.

To find the GCF of two numbers: List the prime factors of each number. Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Levart [38]3 years ago

3 0

Answer:

HCF: 1

LCM: 84

Step-by-step explanation:

7 is a prime number. Nothing but 1 and 7 divide into which means that twelve and 7 have no highest common factor but 1.

The lowest common multiply (because 12 and 7 are prime to each other ) is 12 * 7 = 84

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Lera25 [3.4K]

Answer: $x=\frac{\pi}{4}\ or\ \frac{7\pi}{4}$

Step-by-step explanation:

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3 years ago

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Arlecino [84]

9514 1404 393

Answer:

3 (7e) f(x) = -3(x +2)^2 +1; D: (-∞, ∞); R: (-∞, 1]

4 (8) g(x) = 4(x -3)^2 -5; x = 3; (3, -5); min: -5; D: (-∞, ∞); R: [-5, ∞)

5 (10) A(175) = 31,250 m^2

Step-by-step explanation:

Q3. (7e) f(x) = -3x^2 -12x -11 = -3(x^2 +4x) -11 = -3(x^2 +4x +4) -11 +3(4)

f(x) = -3(x +2)^2 +1

Domain: all real numbers; Range: y ≤ 1

Expanded: -3(x^2 +4x +4) +1 = -3x^2 -12x -11

Q4. (8a) g(x) = 4(x^2 -6x) +31 = 4(x^2 -6x +9) +31 -4(9)

g(x) = 4(x -3)^2 -5

8b) x = 3 . . . axis of symmetry

8c) (3, -5) . . . coordinates of vertex

8d) minimum: -5 (parabola opens upward from vertex, which is the minimum)

8e) any quadratic has a domain of "all real numbers"

8f) the range is upward from the minimum: y ≥ -5

8g) see attached

Q5. (10) A(x) = 700x -2x^2 = -2(x^2 -350x +30625) +2(30625)

A(x) = -2(x -175)^2 +31,250

The maximum area that can be enclosed is 31,250 square meters.

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<em>Additional comment</em>

The process of "completing the square" can be done using the following steps. (a) Factor out the leading coefficient from the variable terms; (b) determine the linear term coefficient inside parentheses, and add the square of half of it inside parentheses; (c) add the opposite of the same quantity outside parentheses (make sure the leading coefficient is properly factored in; (d) rewrite the parentheses as a square, and collect terms outside parentheses. In the final form a(x -h)^2 +k, the vertex is (h, k).