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3 years ago

What number is the least common multiple of 6 and 8? A. 48 B. 2 C. 12 D. 24

Mathematics

2 answers:

rosijanka [135]3 years ago

4 0

The answer is D. 24 if you need me to show my work i will but you did not specify

yanalaym [24]3 years ago

4 0

The answer is D.
6*4 = 24
8*3 =24

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2 years ago

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Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

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2 years ago

An abstract sculpture in the form of a triangle has a base 21 meters and a height of 12 meters. Find the are of the triangle.

charle [14.2K]

The area of a triangle could be determined using the following formula
$\boxed{a= \frac{1}{2} \times b \times h}$

plug in the numbers
$a = \frac{1}{2} \times 21 \times 12$
$a = \frac{1}{2} \times 252$
$a= \frac{252}{2}$
a = 126

The area of the triangle is 126 square meters

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