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.

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.

just pick what you think i need more time let me know if this

step-by-step explanation: