What type of number is shown below? 0.313311333111...

The function below represents the interest Kristina earns on an investment. Identify the term that represents the amount of mone

Elena-2011 [213]

Answer:

The amount of money originally invested which is the principal P = 5,000

Step-by-step explanation:

Using the compound interest formula, the return on investment can be represented on the interest function as;

f(x) = P(1+r)^x

Where

P is the principal which is the initial investment.

r = rate Proportion

x = time (number of years)

Comparing to the given function;

f(x) = 5,000(1 + 0.04)^x

We can see that;

Principal P = 5,000

Rate r = 0.04

time = x

The amount of money originally invested which is the principal P = 5,000

4 0

2 years ago

A rectangular portrait measures 50cm by 70cm. It is surrounded by a rectangular frame of uniform width. If the area of the frame

snow_tiger [21]

Let us assume uniform width = x cm wide.

Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.

Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.

And width of rectangle made by frame = 70+x+x = (2x+70) cm.

We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.

Total area of the rectangle made by frame would be = (2x+50) * (2x+70)

We know,

Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.

We also given "the area of the frame is the same as the area of the portrait."

We can setup an equation now,

3500 = (2x+50) * (2x+70) - 3500.

Subtracting 3500 from both sides, we get

3500-3500 = (2x+50) * (2x+70) - 3500-3500.

0 = (2x+50) * (2x+70) -7000.

FOIL (2x+50) * (2x+70), we get

0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.

0 = 4x^2 +140x +100x +3500 -7000.

4x^2 +240x -3500 = 0.

Dividing whole equation by 4, we get

x^2 +60x - 875 =0

Applying quadratic formula $=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , we get

$=\frac{-60\pm \sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}$

$x=\frac{-60+\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}=5\left(\sqrt{71}-6\right)$

$x=\frac{-60-\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}:\quad -5\left(6+\sqrt{71}\right)$

We cant take negative value.

So, $x=5\left(\sqrt{71}-6\right)=12.13$

We could take approximately 12 cm.

7 0

2 years ago

Jose and Maris work for different car dealerships. Jose earns a monthly salary of $3,500 plus a 6% commision on his sales, x. Ma

patriot [66]

Answer:

x>$25000

Step-by-step explanation:

4 0

2 years ago

Which graph represents the piecewise-defined function?

chubhunter [2.5K]

Answer: The correct option is 1.

Explanation:

The given piecewise function is,

$y=\begin{cases}-\frac{4}{5}x-3 & \text{ if } x$

It means if x<0, then

$f(x)=-\frac{4}{5}x-3$

If $x\geq2$ , then

$f(x)=3x-10$

Since the f(x) is defined for x<0 and $x\geq2$ , therefore the function f(x) is not defined for $0\leq x$ .

From the graph 2, 3 and 4 we can easily noticed that for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.

Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for $0\leq x$ , hence the first option is correct.

6 0

2 years ago

21. Randy owns a computer store. In 1990, he sold 150 monitors. In 2000, he sold 900

lutik1710 [3]

Answer:

$y=75x+150$