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stiks02 [169]
3 years ago
7

If p(x)=2x^2-4x and q(x)=x-3 what is (p*q)(x)

Mathematics
1 answer:
Tanya [424]3 years ago
4 0

Answer: 2x³-10x²+12x or 2x(x²-5x+6)

Step-by-step explanation:

(p*q)(x) means p(x) and q(x) multiplied together.

(2x²-4x)(x-3)

2x³-6x²-4x²+12x

2x³-10x²+12x

You can also factor this by taking out a 2x.

2x(x²-5x+6)

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Determine the number of real solutions of the following system of equations.
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2. Ariana has created a paper airplane for her physics class at school where all the students will be testing their planes by se
sergiy2304 [10]

Answer:

2. The airplane will crash into the ground after 5 seconds.

3. The domain of the function is [0,30] and range of the function is [-\infty,900].

Step-by-step explanation:

2.

Ariana initial attempt is modeled by the function,

h(x)=x^2-12x+35

where, h is the height in feet and x is the time in seconds of the paper airplanes path.

If airplane crash into the ground, then h(x)=0,

0=x^2-12x+35

0=x^2-7x-5x+35

0=x(x-7)-5(x-7)

0=(x-7)(x-5)

Equate each factor equal to 0.

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Therefore the airplane will crash into the ground after 5 seconds.

3.

The height of the rocket in meters is modeled by the function shown below, where t is time in seconds.


h(t)=-4t^2+120t

The value of t must be positive because time can not be negative.

Find the zeros of the function.

0=-4t(t-30)

t=0,30

The leading coefficient is negative, so the it is a downward parabola. Since the zeros of the function are 0 and 30, therefore the function is negative before 0 and after 30.

The height can not be negative, so the domain of the function is

0\leq t\leq 30

The vertex of a downward parabola is the maximum point.

Vertex of a parabola,

(\frac{-b}{2a},h(\frac{-b}{2a}))

(\frac{-120}{2(-4)},h(\frac{-120}{2(-4)}))

(15,h(15))

Put t=15 it in the equation.

h(15)=-4(15)^2+120(15)=900

(15,900)

The range of the function is

[-\infty,900]

Therefore the domain of the function is [0,30] and range of the function is [-\infty,900].

8 0
3 years ago
Sum of the geometric series 20-10+5-5/2
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There are 25,400,000 nanometers in an inch. What is this number written in scientific notation?
Ann [662]

Answer:

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Step-by-step explanation:

Hope this helps :)

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7 0
3 years ago
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