Recall the question for a circle with center. (H, k) and Radius r. At what point in the first quadrant does the line with equation y=1.5x+1 intersect with radius 3 and center (0,1)

the point lies at (1.7, 3.6) in the first quadrant.

Step-by-step explanation:

The formula for a circle with centre (h,k) and radius (r) can be expressed as :

(x-h)² + (y-k)² = r²

Now for the expression of the circle with radius 3 and center (0,1), we have:

(x - 0)² + (y - 1)² = 3²

x² + (y-1)² = 9

replacing y = 1.5x + 1 in the above equation, we have:

x² + (( 1.5x + 1 ) - 1 )² = 9

x² + ( 1.5x +1 - 1)² = 9

x² + (1.5x)² = 9

x² + 2.25x² = 9

3.25x² = 9

x² = 9/3.25

x = 1.7 in the positive x - axis

Recall that:

y = 1.5x + 1

y = 1.5 (1.7) +1

y = 2.55 +1

y = 3.55

y = 3.6

Therefore, the point lies at (1.7, 3.6) in the first quadrant.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

16.80 times .20= 3.36

step-by-step explanation: