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3 years ago

Find c such that (−3,−8), (−7,−6), and (c,4) lie on a line.

1 answer:

Nutka1998 [239]3 years ago

8 0

If the 3 points are collinear, then the slopes of all line segments connecting the points are the same.

Thus,

-6 - (-8) 2
m = ------------- = -------- = -1/2
-7 - (-3) -4

Then the following must be true:

4-(-6) 10
-1/2 = ------------ = ---------
c - (-7) c + 7

Cross multiplying, -(c+7) = 20, and c+7 = -20, so that c = -27

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Find the following function of B

levacccp [35]

G(x) = 2x + 1
f(x) = x + 2

B wants you to find g of f of x, or, in other words, g(f(x)).

g(x + 2) = 2(x + 2) + 1
g(x + 2) = 2x + 4 + 1
g(f(x)) = 2x + 5

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3 years ago

What is a common dominator for 5/6+1/6

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2 years ago

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35 less than seven times a certain number is fifty-three more than 3 times that number. What is the number?

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3 years ago

A restaurant offers three sizes of coffee and four differerſt types of coffee.

Kruka [31]

<h3>Answer: 864</h3>

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

Work Shown:

There are,

3 sizes of coffee
4 types of coffee
2 choices for cream (you pick it or you leave it out)
2 choices for sugar (same idea as the cream)

This means there are 3*4*2*2 = 12*4 = 48 different coffees. We'll use this value later, so let A = 48.

There are 6 bagel options. Also, there are 3 choices in terms of if you order the bagel plain, with butter, or with cream cheese. This leads to 6*3 = 18 different ways to order a bagel. Let B = 18.

Multiply the values of A and B to get the final answer

A*B = 48*18 = 864

There are 864 ways to order a coffee and bagel at this restaurant.

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

If you're curious why you multiply the values out, consider this smaller example.

Let's say you had 3 choices of coffee and 2 choices for a bagel. Form a table with 3 rows and 2 columns. Place the different coffee choices along the left to form each row. Along the top, we'll have the two different bagel choices (one for each column).

This 3 by 2 table leads to 3*2 = 6 individual table cells inside. Each cell in the table represents a coffee+bagel combo. This idea is applied to the section above, but we have a lot more options.

3 0

2 years ago

What is the equation of the line that passes through (-3, -1) and has a slope of 2/5? Put your answer in slope-intercept form.

Zanzabum

Hi there!

The general formula of A line in slope-intercept form is the following:
$y = mx + n$

In this formula m represents the slope of the line. Therefore, we can conclude that m = 2/5.
$y = \frac{2}{5} x + n$

We also know that the line passes through the point (-3, -1) and we can therefore substitute this coordinate into the formula of the line.
x = -3 and y = -1

$- 1 = \frac{2}{5} \times - 3 + n$

Multiply first.
$- 1 = - 1\frac{1}{5} + n$

And finally add 1 1/5 to both sides of the equation.
$\frac{1}{5} = n$

We can now switch sides.
$n = \frac{1}{5}$

Now we've found our value of n, which we can substitute into the formula of our line. Hence, in slope-intercept form, we find the following:
$y = \frac{2}{5} x + \frac{1}{5}$

7 0

3 years ago