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3 years ago

5

Speed cell wireless offers a plan of $40 for the first 400 minutes, and an additional $0.50 for every minute over 400. Let t rep

resent the total talk time in minutes. Write a piecewise-defined function to represent the cost C(t)

1 answer:

Jlenok [28]3 years ago

6 0

Answer:

Step-by-step explanation:

c(t)=40:0≤t≤400

=40+0.50 (t-400):t≥400

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Find the first six terms of the sequence.<br><br> a1 = -4, an = an-1 + 7

maw [93]

$a_n=a_{n-1}+7\\\\a_1=-4\\a_2=-4+7=3\\a_3=3+7=10\\a_4=10+7=17\\a_5=17+7=24\\a_6=24+7=31$

3 0

3 years ago

Read 2 more answers

5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9)

Irina-Kira [14]

Label the points A,B,C

A = (1,2)
B = (4,5)
C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

$A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\$

Segment AB is exactly $3\sqrt{2}$ units long.

Now let's find the distance from B to C

$B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\$

Segment BC is exactly $4\sqrt{2}$ units long.

Adding these segments gives

$AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}$

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

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

$A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\$

AC is exactly $7\sqrt{2}$ units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

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2 years ago

The sum of twice a number n and 8 at most 25

mezya [45]

2n + 8 ≤ 25 |subtract 8 from both sides

2n ≤ 17 |divide both sides by 2

<u>n ≤ 8.5</u>

6 0

3 years ago

Which of the following is the product for (x+4)(x-2)?

larisa86 [58]

Answer:

A

Step-by-step explanation:

X times x is x squared then x times - 2 is - 2x but 4 times x is 4x. So 4x plus - 2x is 2x. Then 4 times - 2 is - 8 put that all together you'll get x^+ 2+2x-8

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3 years ago

What is 73590 rounded to the nearest 10000?

Korolek [52]

It would round to 70,000

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3 years ago