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BartSMP [9]
3 years ago
13

Need help with this ASAP! thank you!

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
7 0

Answer:

-4x^3 + 9x^2+35x -45

Step-by-step explanation:

The notation (f*g)(x) actually just means f(x)*g(x)

We just substitute what f(x) is and what g (x) is

(4x-9) * (-x^2 - 3x + 5 )

4x * -x^2 = -4x^3

4x * -3x = -12x

4x*5 = 20x

-4x^3 + -12x+20x

and

-9 * -x^2 = 9x^2

-9*-3x = 27x

-9*5 = -45

-4x^3 + -12x+20x + 9x^2 + 27x +-45

Now to put this in standard form, we have to order it with the terms with the highest exponents to the ones with the lowest exponents

-4x^3 + 9x^2 -12x+20x+27x -45

-12x+20x+27x

-12x+47x

35x

-4x^3 + 9x^2+35x -45

-45 goes last because it is equal to -45x^0

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Find the value of x in the given figure using parallel lines
pantera1 [17]

Answer:

x = 18 degrees

Step-by-step explanation:

because lines n and m are parallel, 3x and 126 are same side interior angles. This means that when added up they equal 180, so make an equation as so:

3x + 126 = 180

Solve for it and x will equal 18.

6 0
3 years ago
A sound engineer is positioning a cardioid microphone for a music concert. Which equation corresponds to a microphone facing the
Flura [38]

Answer:

D r = 4 − 4 cos(θ)

Step-by-step explanation:

Right on edge

5 0
3 years ago
Find the axis of symmetry of the graph of the function. (5 points) f(x) = 3x2 + 12x + 9
Kryger [21]

Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

<h3>Axis of symmetry</h3>

An axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.

In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.

That is, in a quadratic function that has the form:

f(x)= ax² + bx + c

the axis of symmetry is a vertical line and it is defined as x=\frac{-b}{2a}.

<h3>Axis of symmetry of f(x) = 3x² + 12x + 9</h3>

In this case, you know:

  • a= 3
  • b=12
  • c=9

Replacing in the definition of axis of symmetry:

x=\frac{-12}{2x3}

Solving:

x=\frac{-12}{6}

<u><em>x= -2</em></u>

Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

Learn more about axis of symmetry:

brainly.com/question/24737967

brainly.com/question/10473291

#SPJ1

3 0
2 years ago
.
Maksim231197 [3]

Answer:

D. x=1

Step-by-step explanation:

Image can be rewritten as 3x + 6 = 9.

Solve for x.

3x +6 = 9

Isolate x by subtracting 6 from both sides.

3x = 3

Get rid of the 3 by dividing by 3 on both sides.

x = 1

Hope this helped.

8 0
2 years ago
The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formula
Usimov [2.4K]

well, about A and D, I just plugged the values on the slope formula of

\bf \begin{array}{llll} g(x)=x^3-4x+1\\ L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\\ x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}

for A the values are 8.01 and 8.0, so indeed those "slopes" are close. \textit{\huge \checkmark}

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. \textit{\huge \checkmark}

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)?  well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. \textit{\huge \checkmark}

for F, we know the slope of the line L(x) is 8, is g'(2) = 8?  let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. \textit{\huge \checkmark}

6 0
3 years ago
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