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3 years ago

Least Common Multiple for 6 and 10.

Mathematics

2 answers:

Alik [6]3 years ago

5 0

Oh the LCM is 30. I know this because 6 times 5 is 30 and 10 times three is 30

IrinaVladis [17]3 years ago

4 0

The least common multiple of any two numbers is the first number they both have in common.
A multiple of any number means the number is self-adding, or creating multiples.

With this information, lets get ready to solve.

We'll do the first 5 of each number.

6 = 6, 12, 18, 24, 30.

10 = 10, 20, 30, 40, 50.

They both have 30 in common first, so 30 is the least common multiple.

I hope this helps!

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2 tan 30°<br>II<br>1 + tan- 300

shusha [124]

Question:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Answer:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

Step-by-step explanation:

Given

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Required

Simplify

In trigonometry:

$tan(30^{\circ}) = \frac{1}{\sqrt{3}}$

So, the expression becomes:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}$

Simplify the denominator

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}$

Express the fraction as:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} / \frac{4}{3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} * \frac{3}{4}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{1}{\sqrt 3} * \frac{3}{2}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3}$

Rationalize

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3\sqrt{3}}{2* 3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\sqrt{3}}{2}$

In trigonometry:

$sin(60^{\circ}) = \frac{\sqrt{3}}{2}$

Hence:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

3 0

3 years ago

Plz help me thank you so much

BartSMP [9]

Answer:

7. b

8. a

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

1. Write a quadratic function, in standard form, that fits the set of points. Solve it as a system of three equations

sasho [114]

Answer:

The equation is $y=2x^2+4x-7$

Step-by-step explanation:

Let the quadratic function be

$y=ax^2+bx+c$

The point (-4,9) must satisfy this function,

$\Rightarrow a(-4)^2+b(-4)+c=9$

$\Rightarrow 16a-4b+c=9...(1)$

The point (0,-7) must also satisfy this function,

$\Rightarrow a(0)^2+b(0)+c=-7$

$\Rightarrow c=-7...(2)$

The point (1,-1) must also satisfy this function,

$\Rightarrow a(1)^2+b(1)+c=-1$

$\Rightarrow a+b+c=-1...(3)$

We put equation 2 into equation 1 to get;

$\Rightarrow 16a-4b-7=9$

$\Rightarrow 16a-4b=16$

$\Rightarrow 4a-b=4...(5)$

We again put equation 2 into equation 3 to get;

$\Rightarrow a+b-7=-1$

$\Rightarrow a+b=6...(6)$

We add equation 5 and 6 to get;

$5a=10$

$\Rightarrow a=2$

We put $a=2$ into equation 6 to get;

$2+b=6$

$\Rightarrow b=6-2$

$\Rightarrow b=4$

The equation is therefore $y=2x^2+4x-7$

5 0

2 years ago

Which expression can be used to determine 50% of 42?<br> 42-2 ,42÷2,42÷10,42-10<br>

evablogger [386]

Answer:

42÷2

Step-by-step explanation:

3 0

3 years ago

The ordered pair (a, b) gives the location of point P on the coordinate plane. The values of a and b have

Mama L [17]

Answer:

Since a and b = (a, b) = (x, y) have the same sign.....P will lie either in the 1st quadrant of the Cartesian plane or the 3rd quadrant of the Cartesian plane.

6 0

3 years ago