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LenKa [72]
2 years ago
9

The points A, B, and C reside on a line segment. B is the midpoint of AC. If line AB measures 6 units in length, what is the len

gth of line AC?
Mathematics
1 answer:
Nadya [2.5K]2 years ago
6 0

Answer:

12 units

Step-by-step explanation:

A-------6--------B-------?--------C

Midpoint is center that divides the line segment into two equal halves.

∴    AB = BC

If line AB measures 6 units in length, then, line BC will measure 6 units in length.

     AB = BC = 6 units

     AC = AB + BC

     AC = 6 units + 6 units

     AC = 12 units

OR

We can say If B is the midpoint of AC, then AC is twice as long as AB.

     AC = 2AB

     AC = 2 × 6 units

     AC = 12 units        

Therefore, the length of line AC is 12 units.  

You might be interested in
PLZ SHOW ALL WORK
lara31 [8.8K]

Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width:  w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x

Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6

Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224

And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
3 0
3 years ago
The point A(–1, 4) is translated five units right and three units down. Which rule describes the translation?
lozanna [386]

Answer: SECOND OPTION.

Step-by-step explanation:

Given the following point identified as "A":

A(-1,4)

You can identify that the x-coordinate of the point is:

x=-1

And its y-coordinate is:

y=4

According to the exercise, this point is translated five units right and three units down. This means that, in order to find the new coordinates, you need to add 5 to the original x-coordinate and subtract 3 from the original y-coordinate.

Therefore, you can conclude that the rule that best describe the translation of the point A(-1,4) is the following:

(x,y) → (x+5,y-3)

Then, the point translated is:

A'(-1+5,\ 4-3) → A'(4,1)

6 0
3 years ago
Read 2 more answers
I need hard and easy math questions with the answer, i need 10 questions<br><br>thnx
nydimaria [60]

Answer:

https://www.khanacademy.org/

Step-by-step explanation:

I am not entirely sure what you mean however if you sign up for this website and go to whichever grade level you need you can practice all you want

8 0
1 year ago
Multiply (2.0 ⋅ 10−4) ⋅ (3.1 ⋅ 10−20). Express the answer in scientific notation. The options are:
Mkey [24]
(2.0×10^-4)×(3.1×10^-20)
=(2.0×3.1)×(10^4×10^-20)
=6.2×10^(-4+(-20))
=6.2×10^-24. Hope it help!
3 0
2 years ago
The product of a number and 4 increased by 16 is -2
Art [367]
The answer is -4.5

To solve these types of problems it's best to work backwards.
-2 - 16 = -18
4 x (n) = -18
n = -18/4
n = -4.5

3 0
2 years ago
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