Determine the value of the first term and write a recursive definition for the following

A square garden plot has an area of 24 ft2.

strojnjashka [21]

The area of a square is equal to the side squared.
$s^2=A$

We can plug in 24 for A and then take the square root of each side to find s.
$s^2=24 \\ s=\sqrt{24}$

We can simplify √24.
The prime factorization of 24 is 2×2×2×3.
Since we have 2×2 inside the radical we can simplify to have 2 outside the radical.
$\sqrt{24}=\sqrt{4\times6}=\boxed{2\sqrt{6}\ ft}$

We can then use a calculator to find an approximate decimal value for 2√6.
(You could technically calculate it by hand using the Babylonian method, I don't think you're expected to do that, though)
$2\sqrt{6}\approx\boxed{4.9\ ft}$

6 0

2 years ago

An amount of $40,000 is borrowed for 11 years at 7 5% interest compounded annually. If the loan is paid in full at the end of th

valina [46]

Amount to be paid back = $ 88,624.36

<u>Step-by-step explanation:</u>

Principal amount = $ 40,000

Rate of interest = 7.5%

Number of years = 11

$A=P\left(1+\frac{r}{n}\right)^{n t}$

Plugin the values as,

$A=40000\left(1+\frac{7.5}{100}\right)^{11}$

$A=40000(1+0.075)^{11}$

$A=40000(1.075)^{11}$

$A=\$ 88,624.36$

6 0

2 years ago

Determine the slope of the line that passes through the points:

miskamm [114]

Answer:

The slope of the line is 4.

Step-by-step explanation:

Recall that slope = rise over run: rise / run.

From the table we see that if x changes from 0 to 4, a run of 4, y changes from -1 to 15, a rise of 16, the slope of this line must be

m = rise / run = 16/4 = 4

The slope of the line is 4.

4 0

3 years ago

Luna's dining room is 19 feet wide and 22 feet long. Luna wants to install wooden trim

Marrrta [24]

9514 1404 393

Answer:

$4.92

Step-by-step explanation:

The cost is found by multiplying the number of feet by the cost per foot. The number of feet is the perimeter of the dining room, the sum of the lengths of all the sides.

There are two sides of the rectangular room that are 19 feet, and two sides that are 22 feet, so the total length of trim is ...

P = 2(L +W) = 2(22 ft + 19 ft) = 2(41 ft) = 82 ft

The cost is then ...

cost = ($0.06/ft)(82 ft) = $4.92

It will cost Luna $4.92 to buy enough trim.

3 0

2 years ago

Ash company reported sales of $580,000 for year 1, $630,000 for year 2, and $680,000 for year 3. Using year 1 as the base year,

Elenna [48]

Answer:

Year 2: 109.4%

Year 3: 118.9%

Step-by-step explanation:

<h3>Given;</h3>

Ash company reported sales of $580,000 for year 1
$630,000 for year 2,
$680,000 for year 3.

Now,

For the revenue trend percent for year 2

Year 2: $580,000 / $530,000 × 100 = 109.4%

For the revenue trend percent for year 3

Year 3: $630,000 / $530,000 × 100 = 118.9%

Thus, The answer is 109.4% and 118.9%.

<u>-TheUnknownScientist 72</u>

3 0

1 year ago