Perform the requested operation or operations. f(x) = 4x + 9, g(x) = 4x^2 Find (f + g)(x).

Mathematics

1 answer:

astraxan [27]3 years ago

4 0

F(x) = 4x - 9 and g(x) = 4 - x^2

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Trevor is analyzing a circle, y2 + x2 = 49, and a linear function g(x). Will they intersect?

melomori [17]

We have a circumference that is given by the following equation:

$x^{2}+y^{2}=49$

We can write this equation in its standard form as follows:

$x^{2}+y^{2}=7^{2} \\ where \ the \ radius \ r=7$

On the other hand, the linear function is given as the following table:

$x \ \ \ \ \ \ \ \ g(x) \\ -1 \ \ -9.2 \\ 0 \ \ \ \ \ -9 \\ 1 \ \ \ \ \ -8.8$

To check if the circle and the line intersects, let's substitute the equation of the line into the equation of the circle to see if there is a real solution, so:

$x^{2}+(0.2x-9)^{2}=49 \\ \\ \therefore x^{2}+0.04x^{2}-3.6x+81=49 \\ \\ \therefore 1.04x^{2}-36x+32=0 \\ \\ Solving \ for \ x: \\ x_{1}=33.70 \\ x_{2}=0.91 \\ \\ Solving \ for \ y: \\ y_{1}=0.2(33.70)-9=-2.26 \\ y_{2}=0.2(0.91)-9=-8.18$

Finally the intersects are:

$P_{1}(33.70, -2.26) \ and \ P_{2}(0.91, -8.18)$

7 0

3 years ago

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Is this right? I’m currently taking an assessment and I need to make sure I am right.

Leto [7]

Correct good job that seem correct

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3 years ago

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30 find the length of AB. D 20 C Show your work

vovikov84 [41]

You use Pythagoras theorem for this:
You add 52 and 20 for AC which is 72
So you do
X^2 = 72^2 + 30^2
X^2 =5184 + 900
X^2= 6084
X = 6084 squared root
X= 78

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2 years ago

Please help ASAP 25 pts + brainliest to right/best answer !!!

Trava [24]

Answer:

d. 9.25

Step-by-step explanation:

g(f(3.5)) = g(3.5²) = g(12.25) = 12.25 -3 = 9.25

_____

Creating the composite function first

The composition (g ∘ f)(x) means g(f(x)). That is, the value of f(x) is used as the argument for function g.

g(f(x)) = g(x²) = x² -3