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n200080 [17]
3 years ago
13

Which three lengths could be the lengths of the sides of a triangle?

Mathematics
1 answer:
faust18 [17]3 years ago
8 0
B. 10 cm, 15 cm, 24 cm
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8) Solve 4^(x - 2)= 8^6 <br><br> A)5 <br><br> B)8 <br><br> C)10 <br><br> D)11
myrzilka [38]

For this case we have the following equation:

4 ^ {(x-2)} = 8 ^ 6

We must create equivalent expressions in the equation, so that they have equal bases:

2 ^ {2 * (x-2)} = 2 ^ {3 * 6}

If the bases are the same, then the two expressions are only equal if the exponents are equal:

2 (x-2) = 3 * 6\\2 (x-2) = 18\\2x-4 = 18\\2x = 18 + 4\\2x = 22\\x = \frac {22} {2}\\x = 11

Answer:

x = 11

Option D

3 0
3 years ago
Read 2 more answers
(2n-9) -5 (-2.4n+4) ...
tatiyna

Answer:

-3< 2-x

Step-by-step explanation:

7 0
3 years ago
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
What is 423 divided by 898?
KiRa [710]

423 divided by 898 is 0.47104677...

Hope I could help! :)

6 0
3 years ago
What’s 20 over 14 as a percentage
sergey [27]

Answer: 14 / 20 = 70%

Step-by-step explanation:

8 0
3 years ago
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