Mathematics, 27.01.2020 20:31 KillerSteamcar

Abaker has 10 cups of sugar to make cookies. each batch calls for 113 cups of sugar.

how many batches of cookies can he make?

enter your answer, as a mixed number in simplest form, in the box.

Answers: 2

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Answers

Answer from: noodleboy0923

The number of batches of cookies made is $7\frac{1}{2}$

Solution:

Given that, baker has 10 cups of sugar to make cookies

Each batch calls for $1\frac{1}{3}$ cups of sugar

To find: Number of batches of cookies can be made

From given information,

Total number of cups of sugar = 10

Cups of sugar for 1 batch = $1\frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}$

Therefore, number of batches of cookies can be made is found by dividing the total number of cups of sugar by cups of sugar for 1 batch

Thus we get,

$\text{Number of batches of cookies can be made} = \frac{\text{Total number of cups of sugar}}{\text{Cups of sugar for 1 batch}}$

Substituting the values, we get

$\text{Number of batches of cookies can be made} = \frac{10}{\frac{4}{3}}\\\\\text{Number of batches of cookies can be made} = 10 \times \frac{3}{4}\\\\\text{Number of batches of cookies can be made} = \frac{15}{2}\\\\\text{In mixed form, we get }\\\\\rightarrow \frac{15}{2} = 7\frac{1}{2}$

Thus number of batches of cookies made is $7\frac{1}{2}$

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

hard

step-by-step explanation:

Outline the necessary transformations to prove cbf ≅ edf using a paragraph proof. be sure to name

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Abaker has 10 cups of sugar to make cookies. each batch calls for 113 cups of sugar.

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