Question

Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). Will they intersect?

Answer 1

Yes, at positive x coordinates
Yes, at negative x coordinates
Yes, at negative and positive x coordinates
No, they will not intersect

Answer 2

we have to write the equation for the function \(g(x)\), first

Answer 3

since \(g(x)\) is a \(linear\) function, then we can write:(g(x)=ax+b\), wherein \(a,b\) are 2 real numbers which can be determinaed using data you provided

Answer 4

Ok so then you plug it in ?

Answer 5

if we use the first ordered pair, namely x=-1, and y=-22, then I substitute such values into my equation above, so I get:
\(-22=-a+b\)

Answer 6

Alternatively, just plot the 3 points given you in this table. Either the resulting line intersects the circle or it does not, in 2 places, 1 place or no place.

Answer 7

(Draw a line thru your 3 points, obviously.)

Answer 8

I know that the point of intersection is (8, -4) i just can't put it to an answer choices above.

Answer 9

whereas if I use the second ordered pair x=0, y=-20
then after a substitution, I get:
\(-20=b\)
so we get this system:
\[\left\{ \begin{gathered}
- 22 = - a + b \hfill \\
- 20 = b \hfill \\
\end{gathered} \right.\]
please solve for \(a\) and \(b\)

Answer 10

Again, please plot the 3 points, and draw a line thru them. What do you notice?

Answer 11

that they are negative?

Answer 12

from second equation, we get \(b=-20\)

Answer 13

and from first equation, we get:
\[\begin{gathered}
- 22 = - a + b \hfill \\
\hfill \\
- 22 = - a - 20 \hfill \\
\end{gathered} \]
plese solve for \(a\)

Answer 14

please*

Answer 15

-42?

Answer 16

hint:
if I add 20 to both sides, I get:
\[ - 22 + 20 = - a - 20 + 20\]
please simplify

Answer 17

-2 :-)

Answer 18

we get this:
\[ - 2 = - a\]

Answer 19

and then:
\(a=+2\)

Answer 20

so its a positive answer A?

Answer 21

no, we have determined the equation for g(x), namely:
\(g(x)=2x-20\)

Answer 22

do i have to solve for x? (-10)?

Answer 23

no, we have to substitute \(y=2x-20\) into the equation of the circle, namely:
\[\begin{gathered}
{x^2} + {y^2} = 100 \hfill \\
{x^2} + {\left( {2x - 20} \right)^2} = 100 \hfill \\
\end{gathered} \]

Answer 24

Oh that makes sense !! So substituting it would provide us with a positive integer gx
Answer c?

Answer 25

Im not very good at algebra but i appreciate you helping me

Answer 26

after a substitution, we get this:
\[\begin{gathered}
{x^2} + 4{x^2} + 400 - 80x = 100 \hfill \\
\hfill \\
5{x^2} - 80x + 300 = 0 \hfill \\
\end{gathered} \]

Answer 27

I have computed the square of the binomial \(2x-20\)

Answer 28

I understand the steps of the problem and i know when they intersect i just don't know how how to translate it to the answers above

Answer 29

Because they both intersect at positive x coordinated it would be A, correct?

Answer 30

here is the final step:
the discrimant of the last equation is :
\[\Delta = {80^2} - \left( {5 \cdot 4 \cdot 300} \right) = 6400 - 6000 = 400 > 0\]
so such equation admits 2 distinct solutions \(x\), and, if we apply the \(Cartesio\) rule, we can say that both values of \(x\) are positive

Answer 31

so you are right, it is option A

Answer 32

Thank you so much. How do you medal I'm new on open study

Answer 33

you click best response :)

Answer 34

Thank you

Answer 35

:)

Answer 36

your welcome!!