Mathematics, 15.11.2020 18:20 alisharodriguez1

Can You guys help me with this asap, please

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Answer from: 970032036

Hey there! Let's answer each part of this question in order.

Part a

If Pedro withdrew $\$35$ per week, his change in balance could be represented as -35x since is the number of weeks. Add this to his initial balance of $\$710$ to get the first

$\huge\boxed{710-35x}$

Part b

The same concepts can be applied to solve the next part. Maria started off with $\$570$ in her account and withdrew $\$25$ each week. Apply the same process from the first part to get the second

$\huge\boxed{570-25x}$

Part cWrite an equation

For the last part, we need to find the value of that makes the expressions we made in the first two parts equal to each other, so start by making them into an equation.

$\huge\boxed{710-35x=570-25x}$

Solve the equation

Now we need to solve this equation. Start by bringing the constants to the right and the variables to the left.

Keep in mind that when you move a term to the other side of the equation, you need to change its sign, as you are adding or subtracting the same number from both sides of the equation.

$\begin{aligned}710-35x&=570-25x\\-35x&=570-25x-710\\-35x+25x&=570-710\end{aligned}$

Now, combine the like terms with addition and subtraction.

$\begin{aligned}-35x+25x&=570-710\\-10x&=-140\end{aligned}$

Finally, divide both sides of the equation by to fully isolate the variable and find the final answer.

$\begin{aligned}-10x&=-140\\x&=14\ \text{(weeks)}\end{aligned}$

$\huge\boxed{14\ \text{weeks}}$

Check your answer

We can also check our answer by substituting the final answer back into each expression, simplifying, and making sure the answers are equal.

$\begin{array}{l|l}710-35x&570-25x\\710-35*14&570-25*14\\710-490&570-350\\220&220\end{array}$

Since the expressions are equivalent, we know that Pedro's balance is the same as Maria's balance after weeks.

Answer from: Quest

i'm not entirely sure

step-by-step explanation:

if you ask home depot or lowe's they might be able to you out

Answer from: Quest

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt