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2 years ago

11

Find the missing side of the triangle. Side LaTeX: cc is the hypotenuse and sides LaTeX: aa and LaTeX: bb are legs. Leave your a

nswer in simplest radical form. LaTeX: a=2,\:b=4

1 answer:

mylen [45]2 years ago

6 0

Answer:

$c = 2\sqrt{5$

Step-by-step explanation:

Given

$a = 2$

$b = 4$

c = hypotenuse

Required

Find c

Using Pythagoras theorem, we have:

$c^2 = a^2 + b^2$

Substitute values for a and b

$c^2 = 2^2 + 4^2$

$c^2 = 4 + 16$

$c^2 = 20$

Take square roots of both sides:

$c = \sqrt{20$

Express 20 as 4 * 5

$c = \sqrt{4 * 5$

Split surd

$c = \sqrt{4} * \sqrt{5$

Take square root of 4

$c = 2 * \sqrt{5$

$c = 2\sqrt{5$

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Which number can each term of the equation be multiplied by to eliminate the decimals before solving?

Sati [7]

Ok...

5.6 = 56/10 = 560/100

1.1 = 11/10 = 110/100

0.12 = 12/100

--------------

$\frac { 560 }{ 100 } j-\frac { 12 }{ 100 } =4+\frac { 110 }{ 100 } j\\ \\ \\ 100\times \left( \frac { 560 }{ 100 } j-\frac { 12 }{ 100 } \right) =\left( 4+\frac { 110 }{ 100 } j \right) \times 100\\ \\ 560j-12=400+110j\\ \\ 560j-110j=400+12\\ \\ 450j=412\\ \\ j=\frac { 412 }{ 450 }$

So, the answer is: 100

You could multiply both sides of the equation by 100 to get the value of (j) quickly.

6 0

2 years ago

Read 2 more answers

I don't know how to solve it.

Nataly [62]

Step-by-step explanation:

Take the first derivative

$\frac{d}{dx} ( {x}^{3} - 3x)$

$3 {x}^{2} - 3$

Set the derivative equal to 0.

$3 {x}^{2} - 3 = 0$

$3 {x}^{2} = 3$

${x}^{2} = 1$

$x = 1$

or

$x = - 1$

For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).

For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.

Since we are going to Positve to negative slope, we have a local max at x=-1

Plug in -1 for x into the original function

$( - 1) {}^{3} - 3( - 1) = 2$

So the local max is 2 and occurs at x=-1,

For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.

Since we are going to decreasing to increasing, we have minimum at x=1,

Plug in 1 for x into original function

${1}^{3} - 3(1)$

$1 - 3 = - 2$

So the local min occurs at -2, at x=1

8 0

1 year ago

The length of a rectangle is 3 times its width. If the length were increased by 2 inches and the width by 1 inch, the new perime

Dennis_Churaev [7]

Pretty sure it’s the second option because length would be 3w+2
and width would be w+1 and with area you have to multiply so it would just be the (w+1)(3w+2)

5 0

2 years ago

Read 2 more answers

Find the common ratio for the geometric sequence defined by the formula: an=40(2–√)n−1

Maksim231197 [3]

Answer:

b is the answer in your questions

3 0

2 years ago

If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

SCORPION-xisa [38]

<h3>Answer: 31 games</h3>

======================================================

Explanation:

32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
8/2 = 4 games happen in round 3.
4/2 = 2 games in round 4.
2/2 = 1 game as the final championship.

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

----------------

Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

$\displaystyle \sum_{k=1}^{n}2^k = 2^{n+1}-1$

which is equivalent to

$\displaystyle \sum_{k=1}^{n}2^{k-1} = 2^n-1$

3 0

3 years ago