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1 year ago

Find the value of the variable that results in congruent triangles

Mathematics

1 answer:

sdas [7]1 year ago

8 0

Answer:

y = 5

Step-by-step explanation:

The triangles will be congruent when corresponding sides are congruent. __

We already have ...

KL ≅ NP . . . = 15 mm

JL ≅ MP . . . = 22 mm

So, we need ...

JK ≅ MN

4y +12 = 32 . . . . substitute given values

This will be the case when ...

4y = 20 . . . . . subtract 12

y = 5 . . . . . . . divide by 4

The value of y that makes the triangles congruent is 5.

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What is the sum of the polynomials?

Allisa [31]

Answer:

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2 years ago

Read 2 more answers

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. In the equation√n+5

Yuki888 [10]

Answer:

n = 59

Step-by-step explanation:

The given equation of n is $\sqrt{n + 5} - \sqrt{n - 10} = 1$ and we have to solve it for n.

$\sqrt{n + 5} - \sqrt{n - 10} = 1$ ........... (1)

⇒ $\frac{(n + 5) - (n - 10)}{\sqrt{n + 5} + \sqrt{n - 10}} = 1$

{Rationalizing the numerator}

⇒ $\sqrt{n + 5} + \sqrt{n - 10} = 15$ .............. (2)

Now, adding (1) and (2) we get

$2\sqrt{n + 5} = 16$

⇒ n + 5 = 64 {Squaring both sides}

⇒ n = 59 (Answer)

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2 years ago

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2 years ago

Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 +

timama [110]

Looks like your function is

$f(x)=\dfrac x{6x^2+1}$

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$f(x)=\dfrac x{1-(-6x^2)}$

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$\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n$

If we replace $x$ with $-6x^2$ , we get

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By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2$

Solving for $x$ gives the interval of convergence,

$|x|^2$

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.

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2 years ago