Please put your FULL explanation and make sure it's correct, PLEASE.

. A recipe for cookies calls for 2/3 of a cup of sugar per batch of cookies. Elena used 5 and 1/3 cups of sugar to make multiple

Cerrena [4.2K]

Answer: 8 batches
Step-by-step explanation:
To get the number of batches she made, we can just use proportion to solve it. But first, we need to convert 5 1/3 to improper fraction
5 1/3 = 16/3
Then we can now use the proportion to solve
2/3 cups = 1 batch
16/3 cups = x (note:5 1/3=16/3)
cross multiply
2/3 × x = 16 /3
2x/ 3 = 16/3
we need to make x the subject of the formula, to do that we will multiply each side of the equation by 3/2
2/3 × 3/2 x = 16/3 × 3/2
6x /6 = 48 / 6
x = 8
Therefore she made 8 batches of cookies.

4 0

3 years ago

Read 2 more answers

Three consecutive even integers have a sum of 48 . find the integers.

Mandarinka [93]

x+(x+2)+(x+4)=48

3x+6=48

Minus 6 to both sides

3x=42

Divide 3 to both sides

x=14

Get the next two integers

x,x+2,x+4 or 14,16,18 = 48 is you Answer

4 0

4 years ago

If Ann correctly factors an expression that is the difference of two perfect squares, her factors could be

Sphinxa [80]

Answer:

1.) ???

2.) (2x+3y)(2x-3y)=4x²-9y²

3 0

3 years ago

Please help, see attachment for equation!

Alekssandra [29.7K]

Answer:

The answer to your question is the last option

Step-by-step explanation:

Quadratic equation

2 = - x + x² - 4

Order the equation from the highest power to the lowest power. Do not consider 2 because it is not consider in the options given.

x² - x - 4 = 0

Identify a, b and c

(1) x² -(1) x - 4 = 0

a = 1 b = -1 c = - 6

Substitution

$\frac{-(-1) +- \sqrt{(-1)^{2} - 4(1)((-4)}}{2(1)}$

3 0

3 years ago

Solve the following system of linear equations: 3x1+6x2+6x3 = -9 -2x1–3x2-3x3 = 3 If the system has infinitely many solutions, y

choli [55]

Answer:

The set of solutions is $\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}$

Step-by-step explanation:

The augmented matrix of the system is $\left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right]$ .

We will use rows operations for find the echelon form of the matrix.

In row 2 we subtract $\frac{2}{3}$ from row 1. (R2- 2/3R1) and we obtain the matrix $\left[\begin{array}{cccc}3&6&6&-9\\0&1&1&-7\end{array}\right]$
We multiply the row 1 by $\frac{1}{3}$ .

Now we solve for the unknown variables:

$x_2+x_3=-7$ , $x_2=-7-x_3$
$x_1+2x_2+2x_3=-2$ , $x_1+2(-7-x_3)+2x_3=-2$ then $x_1=12$

The system has a free variable, the the system has infinite solutions and the set of solutions is $\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}$

6 0

3 years ago