At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A

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:

Response:

Detailed explanation:

The length of the pool is longer than its width by 8 meters.

If we designate L as length and W as width, we can express this as:

L = 8 + W

We also know that the area amounts to 105 m squared.

Note:

Area of a Rectangle = Length x Width

Thus, 105 = (8 + W) x W

To adjust the equation, subtract 105 from both sides:

Response:

When combining two fractions that each exceeds 1/2, their sum will invariably exceed 1.

Detailed breakdown: 1/2 + 1/2 = 1    

Since both fractions exceed this amount, it is evident that the sum must as well.

Examples: 2/3+3/4= 1 5/12        4/6+6/9= 1 1/3

Hope this adds clarity