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Leokris [45]
3 years ago
7

Consider the two functions:

Mathematics
1 answer:
Alik [6]3 years ago
6 0

Answer:

Step-by-step explanation:

1, Find (g-f)(x)

we know (g-f)(x) = g(x) - f(x) = ( 5x -2) -( 2x^2 +3x +6)

= 5x -2 - 2x^2 - 3x - 6

= -2x^2 + 2x -8

So the function (g-f)(x) = - 2x^2 + 2x - 8

2, Find (fg)(x)

we know that (fg)(x) = f(x) * g(x)

= (2x^2 +3x +6 ) *( 5x -2)

= 5x* (2x^2 +3x +6 ) - 2*(2x^2 +3x +6 )

= 10x^3 + 15x^2 +30x -4x^2 -6x - 12

= 10x^3 + 11x^2 + 24x - 12

The answer is (fg)(x)= = 10x^3 + 11x^2 + 24x - 12

You might be interested in
What's 86/8 in a mixed number
dsp73

Answer:

10 6/8 or 10 3/4

Step-by-step explanation:

Calculate out how many times the denominator goes into the numerator. To do that, divide 86 by 8 and keep only what is to the left of the decimal point:

86 / 8 = 10.7500 = 10

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

86 - (8 x 10) = 6

Keep the original denominator and use the answers from Step 1 and Step 2 to get this:

10 6/8

Minimize the fraction part from Step 3 by dividing the numerator and denominator by 2, which is the greatest common factor, to get the final answer. 86/8 as a Mixed Number is:

10 3/4

3 0
3 years ago
The graph of F(x) shown below has the same shape as the graph of G(x) = x^2 but it is shifted down 5 units and to the left 4 uni
grandymaker [24]

\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}

\bf \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}


with that template in mind, let's see

down by 5 units, D = -5

to the left by 4 units, C = +4


\bf G(x)=x^2\implies G(x)=1(1x+\stackrel{C}{0})^2+\stackrel{D}{0} \\\\\\ \begin{cases} D=-5\\ C=+4 \end{cases}\implies F(x)=1(1x+\stackrel{C}{4})^2\stackrel{D}{-5}\implies F(x)=(x+4)^2-5

5 0
2 years ago
Max has been offered positions by two car companies. The first company pays a salary of $12,500 plus commission of $1500 for eac
adell [148]

Answer:

5 Cars

Step-by-step explanation:

Let the number of cars to be sold to make the total pay equal be x.

The first company pays a salary of $12,500 plus commission of $1500 for each car sold.

  • Algebraically written as: 12500+1500x

The second company pays a salary of $17,500 plus a commission of $500 per car sold.

  • Algebraically written as: 17500+500x

Equating both sides

12500+1500x=17500+500x

Collect like terms

1500x-500x=17500-12500

1000x=5000

Divide both sides by 1000

x=5

Therefore, when 5 cars are sold, the total pay would be the same.

7 0
2 years ago
HARD QUADRATICS!!!! A quadratic of the form $-2x^2 + bx + c$ has roots of $x = 3 + \sqrt{5}$ and $x = 3 - \sqrt{5}.$ The graph o
iren2701 [21]

Answer:

hold up this will take a min to work out

Step-by-step explanation:

5 0
2 years ago
Help don't get any of them. please explain
hammer [34]
You really just have to round the numbers. Its super simple what number would round to the number that they are saying they are?
8 0
3 years ago
Read 2 more answers
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