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3 years ago

The quotient of 5n^2(m^2+2m-3)/10n(m^2-3m+2) divided by n^2(m^2-3m-18)/4n^2(m^2-8m+12)

1 answer:

7 0

$\dfrac{ 5n^2(m^2+2m-3)}{10n(m^2-3m+2)} \div \dfrac{n^2(m^2-3m-18)}{4n^2(m^2-8m+12)}$

$\dfrac{ 5n^2 (m + 3)(m - 1)}{10n( (m - 1)(m - 2)} \div \dfrac{n^2(m + 3)(m - 6)}{4n^2(m - 2)(m - 6)}$

$\dfrac{ 5n^2 (m + 3)(m - 1)}{10n( (m - 1)(m - 2)} \times \dfrac{4n^2(m - 2)(m - 6)}{n^2(m + 3)(m - 6)}$

$= 2n$

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Find an equation for the nth term of the arithmetic sequence. -15, -6, 3, 12, ...

Mariulka [41]

Answer: $t_{n}=-15+9(n-1)$

Step-by-step explanation:

The formula for finding the nth term of an arithmetic sequence is given as:

$t_{n}=a+(n-1)d$

$a =$ first term = -15

$d =$ common difference = -6 - (-15) = 9

$n =$ number of terms

substituting into the formula , we have :

$t_{n} = -15+(n-1)9$

$t_{n}=-15+9(n-1)$

5 0

3 years ago

Which of the following is not equal to sin⁡(-230°)?

xenn [34]

From trigonometry we know that:

if $sin(\theta)=sin(\alpha)$

then, $\theta=n\pi+(-1)^n\alpha$ (where $n$ is an integer)

This can be rewritten in degrees as:

$\theta=n(180^{\circ})+(-1)^n\alpha$ .............(Equation 1)

Now, in our case, $\alpha=-230^{\circ}$

Therefore, (Equation 1) can be written as:

$\theta=n(180^{\circ})+(-1)^n(-230^{\circ})$ ..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of $\theta$ that match.

For n=2, (Equation 2) gives us: $\theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}$ .

Thus, $sin(230^{\circ})=sin(130^{\circ})$

Now, we know that: $-sin(-50^{\circ})=sin(50^{\circ})$

Let n=-1, then:

$\theta=(-1)\times 180^{\circ}+(-1)^{-1}(-230^{\circ})=-180^{\circ}+230^{\circ}=50^{\circ}$

Thus, $sin(-230^{\circ})=-sin(-50^{\circ})$

Likewise, $sin(-230^{\circ})=sin(50^{\circ})$

Only the last option $sin(-50^{\circ})$ will never match $sin(-230^{\circ})$ because no integral value of $n$ will ever give $\theta=-50^{\circ}$

Thus the last option is the correct option.

3 0

3 years ago

Read 2 more answers

For ΔABC, ∠A = 2x - 2, ∠B = 2x + 2, and ∠C = 5x. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A

Zolol [24]

<h3>Answer:</h3>

A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°

<h3>Explanation:</h3>

The sum of angles in ∆ABC is 180°, so ...

... (2x -2) + (2x +2) + (5x) = 180

... 9x = 180

... x = 20

and the angles of ∆ABC are ∠A = 38°, ∠B = 42°, ∠C = 100°.

___

The sum of angles of ∆A'B'C' is 180°, so ...

... (58 -x) +(3x -18) +(120 -x) = 180

... x +160 = 180

... x = 20

and ∠A' = 38°, ∠B' = 42°, ∠C' = 100°.

_____

The values of angle measures of ∆ABC match those of ∆A'B'C', so we can conclude ...

... A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°

8 0

3 years ago

Which equations have equivalent expressions?

Kazeer [188]

Answer:

A,D,E

Step-by-step explanation:

i. 2t+3t=6t

5t=6t

ii. 2a+2b=4ab

iii. x+3=4x

5 0

3 years ago

Find the value of the function sin 460

rodikova [14]

Answer:

Sin(460 radians)= .97054

sin(460 degrees)= 0.98480775301

Step-by-step explanation:

I'm not sure where you are from, but usually you are allowed to use a calculator. (At least I was when I took Algebra 2/Trig in 6th grade.)

You never specified radians or degrees so I will answer both.

sin(460 radians)= .97054

sin(460 degrees)= 0.98480775301

If you are not allowed to use a calc, then I suggest looking at unit circle videos on Khan Academy.

7 0

3 years ago