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3 years ago

What is the solution set to the following system? X+y=4 X^2+y^2=16

1 answer:

7 0

X+y = 4, -----> y=4 - x
x² +(4-x)² =16
x² +16-2*4x+x² =16
2x² - 8x = 0
x(2x-8) = 0
2x-4=0, 2x=8, x=4
x=0 or x=4

If x=0, y=4-x=4-0=4.
If x=4, y= 4-x=4-4=0.

(0,4) or (4,0)

Check
x² +y² =16
For (0,4)
0²+4² =16
16 =16 True

For (4,0)
4² +0²=16
16=16 True

Answer (0, 4) and (4,0).

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Line segment AB has endpoints A(1, 2) and B(5, 3). Find the coordinates of the point that divides the line segment directed from

ikadub [295]

Now despite what you may think, 1:3 is not 1/3 in this situation, but rather it's "1 equal part to 3 equal parts", which is a total of 4 equal parts. In short, they want the point that is at the 1/4 mark from A to B.

Firstly, how many units apart is 1 to 5 (the x-coordinates)? That would be 4 units apart. Multiply 1/4 by 4:

$\frac{1}{4}\times \frac{4}{1}=\frac{4}{4}=1$

Next, how many units apart is 2 to 3 (the y-coordinates)? That would be 1 unit apart. Multiply 1/4 by 1:

$\frac{1}{4}\times \frac{1}{1}=\frac{1}{4}$

Next, since from 1 to 5 you are increasing, add 1 to 1.

$1+1=2$

2 is the x-coordinate of the new point.

Next, since from 2 to 3 you are increasing, add 1/4 to 2.

$2+\frac{1}{4}=2\frac{1}{4}=\frac{9}{4}$

9/4 is the y-coordinate of the new point.

Putting it together, the point which divides AB into a 1:3 ratio is (2, 9/4), or D.

4 0

3 years ago

I need to solve the three representations (the table, rule/equation, and the graph)

Hitman42 [59]

Figure #5 shows 5 squares which I would assume means (5, 5)
In the table you have the point (3, 7)
From this you can find the slope: (7 - 5)/(3 - 5) = -1
Completions of table:
x y
0 10
1 9
2 8
3 7
4 6
5 5
6 4

Rule/Equation:
y = -x + 10

Graph: Plot the ordered pairs from the table

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3 years ago

What is the importance of polynomial functions and how this real life applications improve or contribute to the value of life

-Dominant- [34]

Answer:

What is the importance of polynomial functions?

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How these real-life applications improve or contribute to the value of life?

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Engineers use polynomials to graph the curves of roller coasters and bridges.

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3 years ago

Multiplying 5 and 3 does NOT tell you the total number of flash cards in the 5 piles. Which is the reason why?

erica [24]

5 * 3 does not tell you the total number of flash cards in 5 piles because you don't know how many cards are in each pile.

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3 years ago

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pychu [463]

Answer:

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3 years ago