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3 years ago

9. Given f(x) = 7x2 and g(x) = x +1, find f(g(x)). SHOW ALL WORK.

Mathematics

2 answers:

Nezavi [6.7K]3 years ago

8 0

I hope this helps you

f(g(x)) =f(x+1)=7(x+1)^2

f(x+1)=7.(x^2+2x+1)

f(x+1)=7x^2+14x+7

statuscvo [17]3 years ago

5 0

f(g(x)) simply means g(x) is substituted for x in f(x)=7x^2

Since g(x)=x+1, then f(x)=7(x+1)^2

f(x)=7(x^2+2x+1)

f(x)=7x^2+14x+7

So f(g(x))=7x^2+14x+7

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Consider the following division of polynomials.

Bond [772]

$x^4=x^2\cdot x^2$ . Multiplying the denominator by $x^2$ gives

$x^2(x^2+2x+8)=x^4+2x^3+8x^2$

Subtracting this from the numerator gives a remainder of

$(x^4+x^3+7x^2-6x+8)-(x^4+2x^3+8x^2)=-x^3-x^2-6x+8$

$-x^3=-x\cdot x^2$ . Multiplying the denominator by $-x$ gives

$-x(x^2+2x+8)=-x^3-2x^2-8x$

and subtracting this from the previous remainder gives a new remainder of

$(-x^3-x^2-6x+8)-(-x^3-2x^2-8x)=x^2+2x+8$

This last remainder is exactly the same as the denominator, so $x^2+2x+8$ divides through it exactly and leaves us with 1.

What we showed here is that

$\dfrac{x^4+x^3+7x^2-6x+8}{x^2+2x+8}=x^2-\dfrac{x^3+x^2+6x-8}{x^2+2x+8}$

$=x^2-x+\dfrac{x^2+2x+8}{x^2+2x+8}$

$=x^2-x+1$

and this last expression is the quotient.

To verify this solution, we can simply multiply this by the original denominator:

$(x^2+2x+8)(x^2-x+1)=x^2(x^2-x+1)+2x(x^2-x+1)+8(x^2-x+1)$

$=(x^4-x^3+x^2)+(2x^3-2x^2+2x)+(8x^2-8x+8)$

$=x^4+x^3+7x^2-6x+8$

which matches the original numerator.

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2 years ago

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rusak2 [61]

Answer:

The correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean

Explanation:

To calculate how many standard deviations a particular value in a group is from the mean, you can use the z-score:

$z-score=(x-\mu )/\sigma$

Where:

$z-score$ is the number of standard deviations the value of x is from the mean

$\mu$ is the mean

$\sigma$ is the standard deviation

Substitute in the formula:

$z-score=(10-6)/2=4/2=2$

Which means that the number of blue-eyed students in Mr. Garcia's class is 2 standard deviations above the mean.

Above the mean is the same that to the right of the mean, because the in the normal standard probability graph the central value is Z = 0 (the z-score of the mean value is 0), the positive values are to the right of the central value, and the negative values are to the left of the central value.

Therefore, the correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean,

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3 years ago

How to convert 5x^2-60x+200 to vertex form?

Rom4ik [11]

Y=a(x-h)^2+k

is what vertex form look like. (h,k) is your vertex so in this problem your vertex would be (60,200)

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2 years ago

-6y+15= -27 what is y?

stealth61 [152]

Answer:

y=7

Step-by-step explanation:

-6y= -27-15

-6y= -42

y=7

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2 years ago

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The grocery store is located at a point on a coordinate plane with the same y-coordinate as the bank but with the opposite x-coo

Alexxandr [17]

Across the y axis. This question becomes easier if you graph it out in your head. Let's say the bank is at (2,2). Because the grocery store has an opposite x coordinate, the bank would be at (-2,2). If you look at this in your head, they are not even on different sides of the x axis, and therefore must be reflected across the y axis.

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2 years ago

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