A supplier delivers an order for 20 electric toothbrushes to a store. by accident, three of the electric toothbrushes are defect

Answer:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

y = 2 x + 7

Step-by-step explanation:

Let x denote the smaller number and y denote the larger number.

Part 1

The equation presented indicates that four times some number added to three times a larger number equals 31.

This translates to:

• 4x + 3y = 31

From here, solving for y yields:

• 4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3

    ⇒  y= - 4/3x + 31/3

This indicates the correct response for this scenario:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

Part 2

The statement that seven subtracted from the larger number equals twice the smaller number translates to:

Further, solving for y yields:y-7= 2x ⇒

The correct answer for this equation is:

Answer: Circle C has a radius of 7 cm.

Explanation:

Referring to the illustration below:

Let's denote the radius of circle C as x.

Circle A's radius can be represented as 2x.

Circle B's radius can be expressed as 4x.

The length of side AC in triangle ΔABC becomes x + 2x = 3x.

For side BC of triangle ΔABC, we get 4x + x = 5x.

Similarly, for side AB of triangle ΔABC, it is 4x + 2x = 6x.

Given that the perimeter of triangle ΔABC totals 98 cm.

Remember, the perimeter refers to the total length around the triangle.

Hence, Perimeter = 6x + 5x + 3x = 98 cm.

Thus, 14x = 98.

From this, we find x = .

Therefore, x = 7.

This concludes that the radius of circle C is 7 cm.