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2 years ago

Simplify the expression given below. x+2/4x^2+5x+1 * 4x+1/x^2-4

Mathematics

1 answer:

GenaCL600 [577]2 years ago

8 0

Answer:

$\frac{1}{(x+1)(x-2)}$

Step-by-step explanation:

$\frac{x+2}{4x^2 + 5x + 1} \ \times \ \frac{4x+1}{x^2-4}\\\\=\frac{x+2}{4x^2 + 4x + x + 1} \ \times \ \frac{4x+1}{x^2-2^2}\\\\=\frac{x+2}{4x(x + 1) + 1( x + 1)} \ \times \ \frac{4x+1}{(x - 2)(x + 2)} \ \ \ \ \ \ \ \ [ \ (a^2 - b^2 = (a-b)(a+b) \ ]\\\\\\=\frac{x+2}{(4x + 1)(x+1)} \ \times \ \frac{4x+1}{(x-2)(x+2)}\\\\=\frac{1}{(x+1)} \ \times \ \frac{1}{(x-2)}\\\\= \frac{1}{(x+1)(x-2)}$

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From a point at the waters edge, a bridge arch 53 m away has an angle of elevation of 30, and the top of a yacht mast 14 m away

Arte-miy333 [17]

Answer:

Yes

Step-by-step explanation:

We don't even have to do a calculation.

The arch of the bridge is at point C.

The top of the yacht's mast is at E.

Even though the yacht is much closer to the water's edge, its mast has a much smaller angle of elevation.

The yacht can easily pass under the bridge.

3 0

2 years ago

PLEASE HELP<br> Find the length of the missing side.

BabaBlast [244]

Answer:

use Pythagoras theorem

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Step-by-step explanation:

pythagoras theorem

h^2 = p^2 + b^2

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3025 = b^2

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2 years ago

Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive

PtichkaEL [24]

Looks like the PMF is supposed to be

$\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}$

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

$\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65$

Next,

$\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25$

$\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5$

$\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2$
$\mathbb E(X^2)=\displaystyle\sum_{x\in\{1,2,5\}}x^2\,\mathbb P(X=x)=\dfrac c3+\dfrac{4c}6+\dfrac{25c}3=\dfrac{28c}3=\dfrac{56}5$
$\implies\mathbb V(X)=\dfrac{56}5-\left(\dfrac{14}5\right)^2=\dfrac{84}{25}$

If $Y=X^2+1$ , then $X^2=Y-1\implies X=\sqrt{Y-1}$ , where we take the positive root because we know $X$ can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that $Y$ can take on the values $1^2+1=2$ , $2^2+1=5$ , and $5^2+1=26$ . At these values of $Y$ , we would have the same probability as we did for the respective value of $X$ . That is,

$\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}$

Part (5) is incomplete, so I'll stop here.

8 0

2 years ago

Plz help im an idiot

MrMuchimi

Answer:

3.)138

4.) 149

Step-by-step explanation:

you add the two inside measures together.

5 0

2 years ago

Read 2 more answers

What is the probability of the spinner landing on 2? A spinner is split into 4 equal parts labeled 1, 2, 3, and 4. StartFraction

liubo4ka [24]

Answer:

The probability of the spinner landing on 2 is one fourth.

Step-by-step explanation:

The spinner is split into 4 equal parts labeled 1, 2, 3, 4

The probability of the spinner landing on 2 is given as:

(Possibility of it landing on 2) ÷ (Total possible outcome)

The total possible outcome is 4, because the spinner could land on 1, or 2, or 3, or 4.

It can only land on 2 once, so the possibility of it landing on 2 is 1.

Probability = 1/4

7 0

2 years ago

Read 2 more answers