A straight line ,L, passes through the points (2,9) and (3,5) Find the equation of the line L.

Mathematics

1 answer:

Ugo [173]3 years ago

4 0

Answer:

y-9=-4(x-2) or y=-4x-1

Step-by-step explanation:

First we must find the slope. Using the slope formula (diff y/diff x), we plug in using the given points;

(9-5)/(2-3)

=>4/-1 or just -4

Now, using the point slope formula, pick any point and plug into the formula y-y_1=m(x-x_1);

y-9=-4(x-2)

You can leave it just as this, if it asks specifically for slope-intercept form (y=mx+b) then just expand and simplify;

y-9=-4x+8

=> y=-4x-1

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How many ways are there to fill either the pitcher or catcher field position (but not both) from among the 25 players (leaving t

Artemon [7]

Using the permutation formula, it is found that there are 600 ways to fill the pitcher and catcher positions.

The order is important, as one player is the pitcher and the other is the catcher, hence the <em>permutation formula </em>is used to solve this question.

<h3>What is the permutation formula?</h3>

The number of possible permutations of x elements from a set of n elements is given by:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

2 players are taken from a set of 25, hence the number of ways is given by:

$P_{(25,2)} = \frac{25!}{23!} = 600$ .

More can be learned about the permutation formula at brainly.com/question/25925367

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4 0

2 years ago

Pleaseeee help w these math questions! please show work!!!<br><br> 50 points

Schach [20]

9. You need an exact answer. So I will give you it but I'll also give you an approximation because it might help you understand it more.

Because we know the cosine fo theta, we can evaluate the inverse cosine of -2/3 first to find theta.

$sin^{-1}(-2/3)$ = 131.81° approx.

Because 131.81° is in the second quadrant its third quadrant partner is 228.19°. Which would make the sine 0.75 approximately.

But we need an exact answer I suppose so which is this disgusting mess... $sin(2\pi -cos^{-1}(\frac{-2}{3}))$ . I know it looks scary but it is basically all the steps we just did but without evaluating anything.