Samantha’s rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. she wants to use the same length of ribbon to frame a circular clock. what is the maximum radius of the circular clock? round to the nearest whole number.
(justify)

7 inches

Step-by-step explanation:

The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.

Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches

Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference of the clock should be no more than 44 inches.

Therefore, the maximum radius of the circular clock is 7 inches.

= 7 inches

Step-by-step explanation:

The ribbon covers the perimeter of the gift.

Perimeter of a rectangle= 2L+2W

=2(12)+2(10)

=44 inches

If the same ribbon is used to frame a circular clock, the perimeter remains to be 44 inches.

Perimeter of a circle= 2πr where r is the radius of the circle.

44 inches= 2×π×r

r=44/2π

=7.0 inches

Radius of the circular clock is 7 inches

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1