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2 years ago

What is the LCM of 6, 12 and 15

Mathematics

2 answers:

Wewaii [24]2 years ago

8 0

3 is the least common multiple

alexandr402 [8]2 years ago

8 0

60 is the Least common denominator

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alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS

serious [3.7K]

Answer:

$k=\frac{-11}{2}$ .

Step-by-step explanation:

We are given $\alpha$ and $\beta$ are zeros of the polynomial $x^2-(k+6)x+2(2k-1)$ .

We want to find the value of $k$ if $\alpha+\beta=\frac{1}{2}$ .

Lets use veita's formula.

By that formula we have the following equations:

$\alpha+\beta=\frac{-(-(k+6))}{1}$ (-b/a where the quadratic is ax^2+bx+c)

$\alpha \cdot \beta=\frac{2(2k-1)}{1}$ (c/a)

Let's simplify those equations:

$\alpha+\beta=k+6$

$\alpha \cdot \beta=4k-2$

If $\alpha+\beta=k+6$ and $\alpha+\beta=\frac{1}{2}$ , then $k+6=\frac{1}{2}$ .

Let's solve this for k:

Subtract 6 on both sides:

$k=\frac{1}{2}-6$

Find a common denominator:

$k=\frac{1}{2}-\frac{12}{2}$

Simplify:

$k=\frac{-11}{2}$ .

7 0

3 years ago

What effect does decreasing the temperature of a room have on a lifespan of a battery?

Leni [432]

This question is incomplete. There are options in the question (from reference) and no highlight in the red bolded text in the question.

What effect does decreasing the temperature of a room have on a lifespan of a battery?

Which variable is highlighted in red, bolded tex?

a . Independent

b . Dependent

c . Control

d . None

But the answer to both the independent and dependent variables will be provided and explained in detail.

Answer:

Independent variable: decrease in temperature

Dependent variable: lifespan of battery

Step-by-step explanation:

The independent variable in an experiment is defined as the variable that can be changed or manipulated in order to find an outcome while the dependent variable is defined as the variable that is influenced by the changes in the independent variable.

In the given example, a decrease in temperature is the dependent variable as it is changing and the lifespan of battery is the dependent variable as it is responding to the independent variable ?9decrease in temperature).

8 0

2 years ago

The diagram shows a rhombus inside a regular hexagon work out the angle x

kvv77 [185]

Answer:

Step-by-step explanation:

The rest of the question is the attached figure.

And it is required to find the angle x.

As shown, a rhombus inside a regular hexagon.

The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°

So, the measure of one angle of the regular hexagon = 720/6 = 120°

The rhombus have 2 obtuse angles and 2 acute angles.