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babymother [125]
2 years ago
5

Which Angle measurements create a Triangle?

Mathematics
1 answer:
sladkih [1.3K]2 years ago
7 0
I think the answer is C
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Can someone help me with this? I need to find the points of discontinuity/limits for each of these. I think one point is 4, but
Debora [2.8K]
The answers are shown in the attached image

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

Explanation:

Set the denominator x^4-8x^3+16x^2 equal to zero and solve for x

x^4-8x^3+16x^2 = 0
x^2(x^2-8x+16) = 0
x^2(x-4)^2 = 0
x^2 = 0 or (x-4)^2 = 0
x = 0 or x-4 = 0
x = 0 or x = 4

The x values 0 and 4 make the denominator zero

These x values lead to asymptote discontinuities because the numerator 8x-24 = 8(x-3) has no common factors which cancel with the denominator factors.

There are two vertical asymptotes

Let's see what happens when we plug in a value to the left of x = 0, say x = -1, we'd get
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(-1) = (8(-1)-24)/((-1)^4-8(-1)^3+16(-1)^2)
f(-1) = -1.28
So as x gets closer and closer to x = 0 from the left side, the f(x) is heading to negative infinity

Now plug in some value to the right of x = 0. I'm going to pick x = 1
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(1) = (8(1)-24)/((1)^4-8(1)^3+16(1)^2)
f(1) = -1.78 (approximate)
So as x gets closer and closer to x = 0 from the right side, the f(x) is heading to negative infinity

Overall, as x approaches 0 from either the left or right side of x = 0, the y value is heading off to negative infinity

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

Repeat for values to the left and right of x = 4
We can't use x = 1 as it turns out that x = 3 is a root
But we can use something like x = 3.5 to find that...
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(3.5) = (8(3.5)-24)/((3.5)^4-8(3.5)^3+16(3.5)^2)
f(3.5) = 1.31 approx
So as x gets closer to x = 4 from the left, y is getting closer to positive infinity

Plug in x = 5 to find that
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(5) = (8(5)-24)/((5)^4-8(5)^3+16(5)^2)
f(5) = 0.64
which has the same behavior as the left side

So overall, as we approach x = 4, the y value is heading off to positive infinity

Again everything is summarized in the image attachment

Note: you could make a table of more values but they would effectively say what has already been said. It would be redundant busy work. However, its always good practice for function evaluation. 

6 0
2 years ago
A restaurant has 20 and 1/2 pounds of bananas to make smoothies a check uses 1/8 lb of bananas per smoothie. how many smoothies
torisob [31]

Step-by-step explanation:

I assume you meant :

the restaurant has 20 1/2 pounds of bananas.

one smoothie uses 1/8 pound of bananas.

how many smoothies can be made with the amount of available bananas ?

the answer is as many as the times 1/8 fit into 20 1/2.

so, we actually calculate

(20 1/2) / (1/8)

first we will convert the mixed number into a true fraction :

20 1/2 = 40/2 + 1/2 = 41/2

so we have

41/2 / 1/8

and then, when dividing fractions we have 2 choices (they do both the same, of course, but start looking differently) :

a/b / c/d = a×d / b×c

a/b / c/d = a/b × d/c = a×d / b×c

so,

41/2 / 1/8 = 41×8 / 2×1 = 41×4 = 164

they can make 164 smoothies.

7 0
1 year ago
24:12 in its simplest form
natima [27]

Answer: 2/1

Step-by-step explanation:

24 divided by 12 equals: 2/1

6 0
2 years ago
Read 2 more answers
What conversion factor would you use to solve thikproblem?
ira [324]

Conversion factor is the term that is to be multiplied to a variable when converting between units. The conversion factor is: 2.20lbs /kg

Given that:

54kg \to x\ lbs

From standard unit of conversion:

1kg = 2.20lbs

So, we have:

54kg \to x\ lbs

1kg = 2.20lbs

Cross multiply

54kg \times 2.20lbs = xlbs \times 1kg

Divide both sides by 1kg

54kg \times 2.20lbs /kg= xlbs

Rewrite as:

x = 54kg \times 2.20lbs /kg

Hence, the conversion factor is: 2.20lbs /kg

Read more about conversion factors at:

brainly.com/question/6988886

8 0
2 years ago
The diagonals of a parallelogram bisect each other.
Montano1993 [528]
each diagonal cuts the other into two equal parts.
7 0
2 years ago
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