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2 years ago

What number should be added to the expression x^2 + 2x to change it into a perfect square trinomial?

1 answer:

6 0

$The\ perfect\ scuare:(a+b)^2=a^2+2ab+b^2\\------------------\\\\x^2+2x\to a=x;\ 2ab=2xb\to b=1\\\\therefore\\\\x^2+2x\cdot1+1^2=x^2+2x+\boxed{1}\leftarrow\boxed{A}$

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3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d

pychu [463]

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
$\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}$

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

To obtain $4000 after two years, let A = 4000 and t = 2.

Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.

Substitute and solve for P:

$\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}$

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

$\displaystyle A = Pe^{rt}$

Where e is Euler's number.

Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:

$\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}$

In conclusion, about $3692.47 should be deposited.

8 0

2 years ago

WILL GIVE BRAINLIEST AND THANKS AND RATING!

Lorico [155]

8 is 6.2
9 is 7
The pattern here is +0.8.
4.6 - 3.8=0.8
5.4-4.6=0.8, and so on

6 0

3 years ago

How much interest is earned on $300 at 6% for 6 years?

miskamm [114]

Answer:

108 dollars

Step-by-step explanation:

First, let's convert 6% to a decimal.

We get 0.06 because we multiplied (or divided by 100) it by 1/100.

Now, let's do 0.06 * 300 to get interest on one year. This equals to 18$

Let's now do 18 * 6 to get

108 dollars

7 0

3 years ago

What is 4 percent of 320

aleksley [76]

Answer:

Alright well simplify the expression

which gives u 12.8 Hope this help's Have a nice day :)

Step-by-step explanation:

If u want i can explain with detail

8 0

3 years ago

The blue lake trail is 11 3/8 miles long. Gemma has hiked 2 1/2 miles each hour for 3 hours. How far is she from the end of the

melomori [17]

In the question it is given that the length of the blue lake trail is 11 3/8 miles. In the question it is also given that Gemma has hiked for a total time of 3 hours and each hour she has hiked 2 1/2 miles.
Now coming to solving the problem we get:
Total length of blue lake trail = 11 3/8 miles
   = 91/8 miles
Distance hiked by Gemma in 1 hour = 2 1/2 miles
   = 5/2 miles
Then the total distance hiked by Gemma in 3 hours = (5/2) * 3
   = 15/2 miles
The distance left to cover the full trail = (91/8) - (15/2) miles
      = (91 - 60)/8 miles
   = 31/8 miles
   = 3 7/8 miles.
So Gemma is 31/8 miles or 3 7/8 miles from the end of the trail.

7 0

2 years ago