How did this expression get simplified to this?

1 answer:

8 0

(leave the 15 alone for the duration of the sum)

= 5*675 - 5*3*210 - 210 ------------------------------ time's out bracket
=5*675 -210(5*3 +1) ---------------------------- took out common "-210" out of last
two terms'
= 5*675 -210(15+1)
= 5*675 -210(16)
=5*675 -210*16

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In how many different ways can a ski club consisting of 20 people select a person for its officers? the positions available are

LUCKY_DIMON [66]

There are 116,280 ways to select the officers.

Since order is important, we use permutations:

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3 years ago

A line includes the points (4,1) and (8, 2). What is its equation in slope-intercept form?

Alisiya [41]

Answer:

$y = \frac{1}{4} x$

Step-by-step explanation:

1) First, find the slope of the equation. Use the slope formula $m= \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(2)-(1)}{(8)-(4)} \\m = \frac{2-1}{8-4}\\m = \frac{1}{4}$

Thus, the slope is $\frac{1}{4}$ .

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation in point-slope form (from there we can convert it to slope-intercept). Substitute values for $m$ , $x_1$ , and $y_1$ .

Since $m$ represents the slope, substitute $\frac{1}{4}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, the end result will be the same) and substitute its x and y values into the formula as well. (I chose (4,1), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the answer.

$y-(1) = \frac{1}{4} (x-4)\\y-1 = \frac{1}{4} x-1\\y = \frac{1}{4} x+0\\y=\frac{1}{4}x$