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3 years ago

14

A triangle has a priemeter of 39 units . Each side of this triangle is the same length. What is the length of one side of the tr

iangle in units

1 answer:

Readme [11.4K]3 years ago

3 0

This is easier to understand with a picture...

We know that a triangle has 3 sides right?

Well, if the perimeter is 39 and there are 3 sides you would divide 39 by the 3 sides

39/3=13

Therefore, one side of the triangle would equal 13

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Factor the expression below

Mazyrski [523]

Answer:

(2x² + 5x + 2) = (2x + 1)(x +2)

Step-by-step explanation:

Given expression is (2x² + 5x + 2).

We have to factorize the given expression.

(2x²+ 5x + 2) = 2x² + 4x + x + 2

= 2x(x + 2) + 1(x + 2)

= (2x + 1)(x + 2)

So the factored form of the given expression will be (2x + 1)(x + 2).

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2 years ago

The sum of two numbers is 11. Their difference is 3. Find the numbers

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The answer is 7 and 4/ 7+4+11 and 7-4=3!

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3 years ago

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Step-by-step explanation:

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3 years ago

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The proportion of left handed people in the population is about 0.10. Suppose a random sample of 300 people is observed. (a) Wha

pantera1 [17]

Answer: $(\hat{p})\sim N(0.10,\ 0.017)$

Step-by-step explanation:

Sampling distribution of the sample proportion $(\hat{p})$ :

$(\hat{p})\sim N(p,\ \sqrt{\dfrac{p(1-p)}{n}})$

The sampling distribution of the sample proportion $(\hat{p})$ has mean = $\mu_{\hat{p}}=p$ and standard deviation = $\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}$ .

Given : The proportion of left handed people in the population is about 0.10.

i.e. p=0.10

sample size : n= 300

Then , the sampling distribution of the sample proportion $(\hat{p})$ will be :-

$(\hat{p})\sim N(0.10,\ \sqrt{\dfrac{0.10(1-0.10)}{300}})$

$(\hat{p})\sim N(0.10,\ \sqrt{0.0003})$

$(\hat{p})\sim N(0.10,\ 0.017)$ (approx)

Hence, the sampling distribution of the sample proportion $(\hat{p})$ is $(\hat{p})\sim N(0.10,\ 0.017)$

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3 years ago

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficie

Dvinal [7]

For part (a), you have

$\dfrac x{x^2+x-6}=\dfrac x{(x+3)(x-2)}=\dfrac a{x+3}+\dfrac b{x-2}$
$x=a(x-2)+b(x+3)$

If $x=2$ , then $2=b(2-3)\implies b=-2$ .

If $x=-3$ , then $-3=a(-3-2)\implies a=\dfrac35$ .

So,

$\dfrac x{x^2+x-6}=\dfrac 3{5(x+3)}-\dfrac 2{x-2}$

For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.

$\dfrac{x^2}{x^2+x+2}=\dfrac{x^2+x+2-x-2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}$

In the remainder term, the denominator $x^2+x+2$ can't be factorized into linear components with real coefficients, since the discriminant is negative $(1-4\times1\times2=-7)$ . However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.

$x^2+x+2=0\implies x=-\dfrac12\pm\dfrac{\sqrt7}2i$
$\implies x^2+x+2=\left(x-\left(-\dfrac12+\dfrac{\sqrt7}2i\right)\right)\left(x-\left(-\dfrac12-\dfrac{\sqrt7}2i\right)\right)$
$\implies x^2+x+2=\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)$

Then you have

$\dfrac{x+2}{x^2+x+2}=\dfrac a{x+\dfrac12-\dfrac{\sqrt7}2i}+\dfrac b{x+\dfrac12+\dfrac{\sqrt7}2i}$
$x+2=a\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)+b\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)$

When $x=-\dfrac12-\dfrac{\sqrt7}2i$ , you have

$-\dfrac12-\dfrac{\sqrt7}2i+2=b\left(-\dfrac12-\dfrac{\sqrt7}2i+\dfrac12-\dfrac{\sqrt7}2i\right)$
$\dfrac32-\dfrac{\sqrt7}2i=-\sqrt7ib$
$b=\dfrac12+\dfrac3{2\sqrt7}i=\dfrac1{14}(7+3\sqrt7i)$

When $x=-\dfrac12+\dfrac{\sqrt7}2i$ , you have

$-\dfrac12+\dfrac{\sqrt7}2i+2=a\left(-\dfrac12+\dfrac{\sqrt7}2i+\dfrac12+\dfrac{\sqrt7}2i\right)$
$\dfrac32+\dfrac{\sqrt7}2i=\sqrt7ia$
$a=\dfrac12-\dfrac3{2\sqrt7}i=\dfrac1{14}(7-3\sqrt7i)$

So, you could write

$\dfrac{x^2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}=1-\dfrac {7-3\sqrt7i}{14\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)}-\dfrac {7+3\sqrt7i}{14\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)}$

but that may or may not be considered acceptable by that webpage.

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3 years ago

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