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alukav5142 [94]

2 years ago

6

There are 16 ounces in 1 pound. Juan is mailing a package that weighs 96 ounces. he wants to know the weight of the package in p

ounds

1 answer:

pav-90 [236]2 years ago

6 0

The answer is 6 pounds

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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.

7 0

2 years ago

Solve for the missing angle with the question mark

mash [69]

Answer:

it's 60

Step-by-step explanation:

I have done that before

4 0

3 years ago

Write 321x64 in long muliplication

makkiz [27]

Step by step:
3 2 1
× 6 4
————————————-
+ 1 2 8 4
+ 1 9 2 6 0
————————————-
= 2 0 5 4 4

4 0

2 years ago

the perimeter of a rectangle is 60 meters. if the length of the rectangle is 14 meters. what is the width of the rectangle.,

Ray Of Light [21]

Perimeter is 2width+2length
Therefore since you already know that the perimeter is 60 and the length is 14 you can set up the equation;
60= 2w+14
with this you then need to find w so;
60=2w+14
-14 -14
46=2w
(46/2)=(2w/2)
13=w
The width is 13

8 0

3 years ago

Read 2 more answers

4 / 3 is equal to 12 / k<br> What does k equal?

Natali5045456 [20]

Answer:

k=9

Step-by-step explanation:

4/3 = 8/6 = 12/9

8 0

3 years ago

Read 2 more answers