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3 years ago

Find the function p(x) = f(x) × g(x). f(x)=3, g(x)=6x-4

Mathematics

1 answer:

trasher [3.6K]3 years ago

6 0

Answer:

p(x) = 18x - 12

Step-by-step explanation:

given p(x) = f(x) × g(x), then

p(x) = 3(6x - 4 ) ← distribute by 3

p(x) = 18x - 12

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The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?

daser333 [38]

Answer:

$d=\frac{3}{2}=1.5$

Step-by-step explanation:

We have the function:

$y=a(x-2)(x-1)$

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are (x-2) and (x-1).

Therefore, our roots/zeros are x=1, 2.

So, the average of them are:

$d=\frac{1+2}{2}=3/2=1.5$

Therefore, regardless of the value of a, the minimum/maximum value will occur at x=d=1.5.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

$y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a$

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

$x=-\frac{b}{2a}$

So, we will substitute -3a for b and a for a. This yields:

$x=-\frac{-3a}{2a}=\frac{3}{2}=1.5$

Confirming our answer.

4 0

3 years ago

N 2+ 6n - 16 = 0 Solve equation by factoring.

Naily [24]

Answer:

N = -3n+8 Brainlist please :)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Question 3 (open to see pic)

melamori03 [73]

The points (1,-2) and (4,16) are not in the line but the point (-3,-18) is on the line. (Work is shown in the image)

8 0

3 years ago

An object in a simulation accelerates

notsponge [240]

Observe the graph below. This graph represents the scenario.

The question is ill formated, the complete question is

In a simulation, a moving object accelerates from rest to 4 meters per second in 2 seconds. For the following three seconds, it increases linearly until it reaches a speed of 10 meters per second. Following three seconds at that speed (acceleration = 0), the item progressively decelerates until it comes to rest two seconds later. Draw the graph of this scenario for 10 seconds?

I'll describe how the graph may show.

It will move diagonally upward from time 0 to 2 seconds until it reaches the y axis at a speed of 4 m/s.

Then, from 2 to 5, the position will move up diagonally until it reaches the y axis at a speed of 10 m/s.

The next 5 to 8 seconds will be horizontal.

After that, it will descend diagonally.

Observe the graph below. This graph represents the scenario.

Learn more about Acceleration here-

brainly.com/question/21509870

#SPJ10

5 0

2 years ago

Solve for x. Round your answer to the nearest tenth. (one decimal place) X=?? degrees

fredd [130]

Answer:

Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15
x = arctan (8/15)
x = 28.1° (rounded)

4 0

3 years ago