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Sindrei [870]
3 years ago
8

What is the maximum number of possible solutions for the system shown below?

Mathematics
2 answers:
Fudgin [204]3 years ago
8 0

Answer:

2

Step-by-step explanation:

The first equation is that of a an ellipse. The second equation is that of a line.

Attached is the graphs of both of these equations.

<em>If you think about it, there can only be 2 possible ways of solutions (intersection points) of an ellipse and a line.</em>

<em>1. The line will not intersect the ellipse at all, so no solution</em>

<em>2. The line will intersect the ellipse at 2 points maximum</em>

<em />

So, we can clearly see from the reasoning that the maximum number of possible solutions would be 2. The graph attached confirms this as well.

romanna [79]3 years ago
3 0

Answer:

The maximum number of solutions that the system can have are 2

Step-by-step explanation:

We have a system of equations composed of an ellipse of equation x ^ 2 + 4y ^ 2 = 64 and a line of equation x + y = 5.

The solution to the system of equations gives information about when the values of both equations coincide. In other words, the solutions of the system of equations give information about the number of times that the line x + y = 5. touch or intercept the graph of the ellipse x ^ 2 + 4y ^ 2 = 64

Graphically you can verify that a line can only touch an ellipse once or can intercept an ellipse a maximum of two times, or never touch it

Therefore, the maximum number of solutions that the system can have are 2.

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Find the circumference of the following circle. Use 3.14 for π. Round to the nearest hundredth, if necessary.
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Step-by-step explanation:

3.14 · 6

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3 years ago
Find three consecutive odd integers whose sum is 489
miss Akunina [59]

Answer:

162, 163, and 164.

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 489

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 489

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162 + 163 + 164 = 489

We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.

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