Find the sum. Enter your answer in simplest form. 1/6+3/4

Eduardwww [97]

Answer:

It is (x - 3)³ - 9x(3 - x)

Step-by-step explanation:

Express 27 in terms of cubes, 27 = 3³:

$= {x}^{3} - {3}^{3}$

From trinomial expansion:

${(x - y)}^{3} = (x - y)(x - y)(x - y) \\$

open first two brackets to get a quadratic equation:

${(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)$

expand further:

${(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}$

take y to be 3, then substitute:

$( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)$

5 0

3 years ago

How much money should be invested in an account that earns 8% interest compounded quarterly to yield $10,000 in 4 years? (Round

sweet [91]

Answer:

757,576cents

Step-by-step explanation:

Given

Amount = $10000

Time = 4years

Rate = 8%

n = 1/4 year (compounded quarterly

Using the formula to get the principal

A = P(1+r/n)^nt

10000 = P(1+0.08/0.25)^4(1/4)

10000 = P(1+0.32)

10000= 1.32P

P = 10000/1.32

P = 7575.76

Hence he suppose to invest $7575.76 which is equivalent to 7575.76×100 cents i.e 757,576cents

4 0

3 years ago

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.

mamaluj [8]

Answer:

Option c. Reflection across the x-axis and vertical stretch by a factor of 7

Step-by-step explanation:

If the graph of the function $y = cf(x)$ represents the transformations made to the graph of $y = f(x)$ then, by definition:

If $0$ then the graph is compressed vertically by a factor a.

If $|c| > 1$ then the graph is stretched vertically by a factor a.

If $c$ then the graph is reflected on the x axis.

In this problem we have the function $y = -7secx$ and our paretn function is $y = secx$

therefore it is true that

$c = -7\\\\|-7|> 1\\\\-7$ .

Therefore the graph of $y = secx$ is stretched vertically by a factor of 7 and is reflected on the x-axis

Finally the answer is Option c

6 0

3 years ago

Plzzz guys help I'm so confused

GalinKa [24]

Answer:

y = 320,000 ( 1.048 ) ^x

x = number of years

(the ^ before the x symbolizes "to the power of," but I can't do that on my keyboard)

Step-by-step explanation:

formula i used:

A = amount that you start with

t = amount of years / time

%increase: you must convert your percent (4.8%) to a decimal (0.048)

A ( 1 + %increase ) ^t

4 0

3 years ago

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One of Newton’s laws of motion states that objects in motion tend to stay in motion. What is the reason that this law may not al

Nastasia [14]

The answer is D.

The full specification of Newton's First Law is (from Wikipedia)

In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

On earth we're generally in slightly a non-inertial frame, with rotation and revolution around the sun. It's also impossible to turn of gravity, so objects are being acted upon by an outside force. Typically there's also the outside force of friction, which makes things tend to stop.

4 0

3 years ago

Read 2 more answers