Barbie is analyzing a circle, y2 + x2 = 16, and a linear function g(x). Will they intersect?

y2 + x2 = 16 g(x)
graph of the function y squared plus x squared equals 16
x g(x)
0 6
1 3
2 0
Yes, at positive x‐coordinates
Yes, at negative x‐coordinates or zero
Yes, at negative and positive x‐coordinates or zero
No, they will not intersect

Yes, at positive x-coordinates.

Step-by-step explanation:

Finding the equation for g(x):

Slope = (3-6)/ (1-0) = -3

y-intercept =  y value when x = 0 = 6.

So g(x) = -3x + 6

Solve them simultaneously:

x^2 + y^2 = 16

g(x) : y =  -3x + 6

Substitute for y in the first equation:

x^2 + (-3x + 6)^2 = 16

x^2 + ( 9x^2 - 36x + 36) = 16

10x^2 - 36x + 20 = 0

5x^2 - 18x + 10 = 0

x = [-(-18) +/- sqrt ( (-18)^2 - 4 * -18 * 10)] / (5*2)

= ( 18 +/- sqrt 124 )/ 10

= (1.8) +/- 1,114

These 2 roots are both positive.

i would need to see the dot plot : )

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.