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Mathematics

1 answer:

Rudiy274 years ago

7 0

Answer:

A. $4,960

B. 8%

C. $120

Step-by-step explanation:

Part A

The amount in the account at the end of 3 years is the original amount ($4000) plus the earned interest ($960). That sum will be ...

$4,000 + 960 = $4,960 . . . account balance

Part B

The amount of interest is computed using the formula ...

I = Prt

where I is the interest earned, P is the principal invested, r is the annual rate, and t is the number of years. Putting the given values into this equation, we can solve for r:

960 = 4000·r·3

960/12000 = r = 0.08 = 8%

The interest rate was 8%.

Part C

The additional interest can be computed using the same formula as for part B.

I = Prt

I = 4000·0.01·3 = 120

The additional interest earned at a 1% higher rate would be $120.

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Find the average rate of change f(x)=x^2−6x+8 when x2=1 and x1=3

sergeinik [125]

Answer:

Average rate of change for given function is: -2

Step-by-step explanation:

Given function is:

$f(x)=x^2-6x+8\\x_12= 1\\x_1 = 3$

In order to find the rate of change, we have to find the value of function on x1 and x2

So,

$f(x_1) = (3)^2-6(3)+8 = 9-18+8 = -1\\f(x_2) = (1)^2-6(1)+8 = 1-6+8 = 3$

The formula for finding the rate of change is:

$Rate\ of\ change = \frac{f(x_2)-f(x_1)}{x_2-x_1}$

Putting the values, we get

$=\frac{3-(-1)}{1-3}\\=\frac{3+1}{-2}\\=\frac{4}{-2}\\= -2$

Hence,

Average rate of change for given function is: -2

3 0

3 years ago

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Quadrilateral BCDE is inscribed inside a circle as shown below. Write a proof showing that angles C and E are supplementary.

erma4kov [3.2K]

Each of those angles are Inscribed angles. A useful fact is that the measure of the intercepted arc of an inscribed angle is twice the measure of the angle.

The intercepted arc of ∠C is arc BED. The intercepted arc of ∠E is arc BCD.

m(arc BED) + m(arc BCD) = 2( m∠C + m∠E)

The two arcs combined make u p the entire circle, so the sum of their measures is 360.

360 = 2(m∠C + m∠E)
180 = m∠C + m∠E

The angles are supplementary.