All categories

3 years ago

Guys I really need help geometry hw 21 and 22

Mathematics

1 answer:

mario62 [17]3 years ago

4 0

These can be a bit of a mind-twister. A fairly straightforward approach is to define a variable (x) to be the angle, then use 90-x for the complement and 180-x for the supplement. Write the relations given in the text, solve for x, then calculate the measure of the angle asked for by the problem statement.

You don't have to do it that way. In 21, you can work directly with "the complement of the angle." You know that an angle and its complement make 90°, and that an angle and its supplement make 180°. This means the supplement is 90° more than the complement—a fact you can use here.

<h2>21.</h2><h3>Given</h3>

The supplement of an angle is 4 times the complement of the angle.

The complement of the angle.

<h3>Solution</h3>

Let x represent the complement of the angle (what the question asks for). Then the supplement of the angle is x+90.

The supplement is 4 × the complement

... x + 90 = 4x

... 90 = 3x . . . . . . . subtract x

... 30 = x

The complement of the angle is 30°.

_____

<u>Check</u>

The angle is 60°; its complement is 30°, and its supplement is 120°. 120° is 4 times 30°, as required.

<h2>22.</h2><h3>Given</h3>

5 times the complement of an angle less 2 times the supplement is 40°

the supplement of the angle

<h3>Solution</h3>

We can do this as we did in the previous problem. We are asked to find the supplement of the angle. Let x represent the supplement of the angle. As discussed above, then the complement of the angle is x-90°.

... 5 × (the complement) - 2 × (the supplement) = 40

... 5(x-90) -2x = 40 . . . . . . . . . filling in the variable expressions for complement and supplement

... 5x -450 -2x = 40 . . . . . . . . eliminate parentheses

... 3x = 490 . . . . . . . . . . . . . . . collect terms, add 450

... x = 163 1/3

The supplement of the angle is 163 1/3°.

_____

<u>Check</u>

The angle is 16 2/3°. Its complement is 73 1/3°.

5 times the complement is 366 2/3°. 2 times the supplement is 326 2/3°. The latter subtracted from the former is 366 2/3 - 326 2/3 = 40, as required.

You might be interested in

Identifying the Graph of an Inequality

Norma-Jean [14]

Answer:

The point-slope form of the equation of a line is ...

y -h = m(x -k)

for a line with slope m through point (h, k).

Comparing this to the given equation, you see that ...

h = -2, m = 1, k = -4

The line has a slope of 1 and goes through the point (-4, -2). This information is useful for graphing.

You can also rearrange the equation to slope-intercept form by subtracting 2 from both sides.

y = x +2

This has a slope of 1 and crosses the y-axis at y=2. It graphs the same as the above.

7 0

4 years ago

A poker hand is a set of 5 cards randomly chosen from a deck of 52 cards. Find the probability of a (a) royal flush (ten, jack,

zysi [14]

Answer:

a) 0.000001539

b) 0.00001385

c) 0.0002401

d) 0.001441

e) 0.001966

Step-by-step explanation:

Since there are 52 deck of cards, and the hand of the poker is 5 set, then the total number of hands achievable would be

T = 52! / 5!(52 - 5)!

T = 52! / 5! 47 !

T = 2598560 possibilities.

a) There are 4 ways of getting a royal flush. So the probability of getting a royal flush is

4 / 2598560 =

0.000001539

b) There are 9 hands from the 5 card hands, and also, there are 4 possible suits. So then, the probability is

9 * 4 / 2598560 =

36 / 2598560 =

0.00001385

c) There are 13 possible ways to get a four of a kind, since there are 5 cards with the poker, the remaining would be taken from the 48 remaining cards, thus

13 * 48 / 2598560 =

624 / 2598560 =

0.0002401

d) 3 of a kind in conjunction with a pair is needed to form a full house. This 3 of a kind can be gotten from any 4 suits. Then again, the pair has two cards with the same face value. So,

4! / 2! (4 - 2)! =

4! / 2! 2! = 6

That means, there are 6 possible ways to get our needed suits. Then, the probability of getting a full house is

13 * 4 * 12 * 6 / 2598560 =

3744 / 2598560 =

0.001441

e) To get a flush, all the 5 cards in the hand needs to have the same suit. Now, there are 13 different types of cards with only 5 cards being in the hand, thus

13! / 5! (13 - 5)! =

13! / 5! 8! = 1287

Now, recall that the question specifically asked us not to include any straight. There are 10 straights that can be gotten, and thus, we subtract it.

1287 - 10 = 1277

Since there are 4 suits, the probability of getting a flush is

1277 * 4 / 2598560 =

5108 / 2598560 = 0.001966

5 0

4 years ago

PLZ HELP

Pani-rosa [81]

Answer:

$a = - 25.5 \\ b = - 4 \\ c = 12 \\ d = - 8$

5 0

3 years ago

Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.