Calculate the production rate per day.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the legible questions:

2) A soda produces 12 bottles in 3 days. How many bottles are produced in 21 days?

Calculate the production rate per day.
$\text{Rate} = \frac{12 \text{ bottles}}{3 \text{ days}} = 4 \text{ bottles/day}$
Calculate the total bottles produced in 21 days.
$\text{Total bottles} = 4 \text{ bottles/day} \times 21 \text{ days} = 84 \text{ bottles}$
The soda produces $\boxed{\text{84 bottles}}$ in 21 days.

3) Simplify the expressions:
- Expand $5(x+2)^2$
Expand the squared term $(x+2)^2$ .
$(x+2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4$
Multiply the result by 5.
$5(x^2 + 4x + 4) = 5x^2 + 20x + 20$
The expanded expression is $\boxed{5x^2 + 20x + 20}$ .
- Factor $x^2-3x$
Identify the common factor in both terms.
The common factor is $x$ .
Factor out the common factor.
$x^2 - 3x = x(x - 3)$
The factored expression is $\boxed{x(x - 3)}$ .

4) A number is multiplied by 7 and then decreased by 2. The result is 23. Write and solve an equation to find the number.
Let the unknown number be $x$ .
Write the equation based on the problem description.
"A number is multiplied by 7": $7x$
"then decreased by 2": $7x - 2$
"The result is 23": $7x - 2 = 23$
Solve the equation for $x$ .
$7x - 2 = 23$
Add 2 to both sides of the equation:
$7x = 23 + 2$ $7x = 25$
Divide by 7:
$x = \frac{25}{7}$
The number is $\boxed{\frac{25}{7}}$ .

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