How many pairs of Whole numbers have a sum of 40

V = x³ - 6x²y + 12xy² - 8y³

V = (x - 2y)³

   = (x - 2y)(x - 2y)(x - 2y) ( start by expanding the first pair of factors )

   = (x² - 4xy + 4y²)(x - 2y) ( multiply the terms from the first group with those in the second )

   = x³ - 4x²y + 4xy² - 2x²y + 8xy² - 8y³ ( combine similar terms )

  = x³ - 6x²y + 12xy² - 8y³

Answer:

Alright, we can express the baseball's motion with an equation like:

h(x) = a*x^2 + b*x + c

Here, x denotes time, while h(x) indicates height.

Let’s construct this:

The acceleration is:

a(t) = a

For velocity, integrating over time results in:

v(x) = a*x + v0

Where v0 signifies the initial vertical velocity.

Subsequently, we can determine position or height by integrating once more:

h(x) = a*x^2 + v0*x + h0

Here, h0 is the initial height.

<pthus our="" equation="" is:="">

h(x) = a*x^2 + v0*x + h0.

<pexamining the="" table:="">

When x = 0s, h(0s) = 6ft

<pthus:>

h(0s) = a*0s^2 + v0*0s + h0 = 6ft

            h0 = 6ft.

It’s also noted that:

h(2s) = h(4s)

<pthe symmetry="" of="" the="" quadratic="" function="" implies="" that="" axis="" lies="" between="" and="" located="" at="" x="3s.&lt;/p"><pin a="" standard="" quadratic="" function:="">

a*x^2 + b*x + c

The symmetry line is given by:

x = -b/2a

<pin this="" instance:="">

b = v0

a = a

<ptherefore we="" derive:="">

3s  = -v0/(2*a)

v0 = -3s*(2a)

<phaving gathered="" all="" necessary="" data="" for="" our="" equation="" we="" can="" express="" it="" as:="">

h(x) = a*x^2 - 6s*a*x + 6ft

<pnext focusing="" on="" just="" one="" variable="" we="" know="" that="" at="" x="2s," h=""><pso:>

h(2s) = 22ft = a*(2s)^2 - 6s*a*2s + 6ft

<pthus our="" resulting="" equation="" reads:="">

h(x) = (-2ft/s^2)*x^2 + (12ft/s)*x + 6ft

b) The height after 5 seconds is expressed as:

h(5s) =  (-2ft/s^2)*(5s)^2 + (12ft/s)*5s + 6ft = 16ft

</pthus></p></pso:></pnext></phaving></ptherefore></pin></pin></pthe></pthus:></pexamining></pthus>

14 minutes. Step-by-step explanation: First, find the perimeter which can be calculated as P=100+80+100+80 = 360 meters, and then multiply it by 6 for the total distance = 2160 meters. To convert meters to kilometers, note that 1000 m = 1 km, so you would find how many kilometers are in 2160 m by cross-multiplying to get 2.16 km. Lastly, you need to calculate the time required represented by T = D/S = 2.16 km / 9 km/h, which simplifies down and gives you the time.

Simply calculate the cost per pencil by dividing the total dollar amount by the number of units: 2.35/24 = $ ______ per pencil, which equals approximately 0.097917, or 97 cents.

Answer:

5 ft

Step-by-step explanation:

Denote the height of the previous jump as j. Therefore, it follows that 1.1j equals 5.5 ft.

By dividing both sides by 1.1, we derive j = 5 ft. This indicates the height from the prior jump.