At a berry farm, Clayton picks 1 1/4 cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins. If Clayton needs 3/4 of a cup of mixed berries for each batch of muffins, how many batches can he make?

2 batches

Step-by-step explanation:

1. State the given;

Convert to improper fractions;

1 1/4 blackberries

5/4 blackberries

Simplify;

Twice as many blueberries;

5/4 *2

10/4

5/2

2. Find the total amount of berries;

Simplify;

blackberries + blueberries

= 5/4 + 5/2

*note; convert to like denominators

= 5/4 + 10/4

= 15/4

3. Divide by the amount that the recipe calls for;

Total / required

15/4 / 3/4

*note; dividing by a fraction is the same as multiplying by the fraction's reciprocal

15/4 * 3/4

45/16

*note; convert to a mixed number

2 13/16

Remember, for the sake of the problem, one can only make a full recipe, hence the answer is 2.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

35%

step-by-step explanation: