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Over [174]
3 years ago
10

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

y originally invested.
f(x) = 5,000(1 + 0.04)x

1
0.04
1.04
5,000
Mathematics
2 answers:
Leni [432]3 years ago
7 0

Answer:

5,000

Step-by-step explanation:

Amanda [17]3 years ago
4 0

Answer:

\boxed{5000}

Step-by-step explanation:

The formula for the amount accrued on an investment earning compound interest is

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

where

P = the amount of money invested

r = the interest rate per payment period expressed as a decimal fraction

t = the number of periods

Your formula is

f(x) = 5000(1 + 0.04)^{x}\\\text{By comparing the formulas, we see that the amount of money invested is $\boxed{\textbf{5000}}$}

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Alex has a block of wood that is in the shape of a prism with the dimensions shown. He cuts a 10-cm square hole through the cent
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3 years ago
Y = 4x+1 y=x^2 + 2x - 2 A.6,2 B. 2,6 C. -6,2 D. -6,-2
natta225 [31]

Answer:

The solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Step-by-step explanation:

Given that

y = 4x + 1  (i)

y = x^2 + 2x -2 (ii)

Now, by susbstituting the value of 'y' from equation i to equation ii, we get

4x+1=x^2 + 2x -2

0=x^2 + 2x -2-4x-1

0=x^2 + (2x -4x) +(-2-1)

0=x^2 + (-2x) +(-3)

0=x^2 -2x -3

x^2 -2x -3 = 0 (iii)

Now by factorization, equation iii can be written as

x^2 -3x +x -3 = 0

x(x -3) + 1(x -3) = 0

(x -3)(x +1) = 0

x = 3 and x = -1

By putting the values of x in equation i, we get

y = 4(3) + 1

y = 12 +1

y = 13

and

y = 4(-1) + 1

y = -4 +1

y = -3

Therefore, the solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

7 0
3 years ago
According to postal regulations, a carton is classified as "oversized" if the sum of its height and girth (the perimeter of its
Amanda [17]

Answer:

V(max) =  8712.07 in³

Dimensions:

x (side of the square base)  = 16.33 in

girth   = 65.32 in

height = 32.67 in

Step-by-step explanation:

Let

x  = side of the square base

h = the height of the postal

Then according to problem statement we have:

girth = 4*x     (perimeter of the base)

and

4* x  +  h  = 98  (at the most)   so   h = 98 - 4x  (1)

Then

V = x²*h

V = x²* ( 98 - 4x)

V(x) = 98*x² - 4x³

Taking dervatives (both menbers of the equation we have:

V´(x)  =  196 x   -  12 x²        ⇒   V´(x) = 0

196x - 12x²  = 0   first root of the equation  x = 0

Then   196 -12x = 0      12x = 196     x = 196/12

x = 16,33 in      ⇒    girth = 4 * (16.33)       ⇒ girth = 65.32 in

and from equation (1)

y = 98 - 4x       ⇒  y = 98 -4 (16,33)

y = 32.67 in

and maximun volume of a carton V is

V(max) = (16,33)²* 32,67

V(max) = 8712.07 in³

3 0
3 years ago
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