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3 years ago

If f(x) = 7x + 4 and g(x) = x + 4, what is (fog)(-3)?

Mathematics

1 answer:

PolarNik [594]3 years ago

7 0

Answer:

(fog)(-3)= 11

Step-by-step explanation:

we have from statement:

f(x) = 7x + 4

g(x) = x + 4

so we have:

(fog)(x)= 7(x+4) + 4

(fog)(-3)= 7(-3+4) + 4

(fog)(-3)= 7(1) + 4

(fog)(-3)= 11

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Graph the functions on the same coordinate axis. {f(x)=−2x+1g(x)=x2−2x−3

NikAS [45]

Answer:

(2,-3) and (-2,5)

Step-by-step explanation:

Let us graph the two equations one by one.

1. $f(x)=-2x+1$

If we compare this equation with the slope intercept form of a line which is given as

$y=mx+c$

we see that m = -1 and c =1

Hence the slope of the line is -2 and the y intercept is 1. Hence one point through which it is passing is (0,1) .

Let us find another point by putting x = 1 and solving it for y

$y=-2(1)+1$

$y=-2+1 = -1$

Let us find another point by putting x = 2 and solving it for y

$y=-2(2)+1$

$y=-4+1 = -3$

Hence the another point will be (2,-3)

Let us find another point by putting x = -2 and solving it for y

$y=-2(-2)+1$

$y=+1 = 5$

Hence the another point will be (-2,5)

Now we have two points (0,1) ,(1,-1) , (2,-3) and (-2,5) we joint them on line to obtain our line

$g(x)=y=x^2-2x-3$

$y=x^2-2x+1-1-3$

$y=(x-1)^2-4$

$(y+4)=(x-1)^2$

It represents the parabola opening upward with vertices (1,-4)

Let us mark few coordinates so that we may graph the parabola.

i) x=0 ; $y=y=(0)^2-2(0)-3=0-0-3=-3$ ; (0,-3)

ii)x=-1 ; $y=(-1)^2-2(-1)-3=1+2-3=0$ ; (-1,0)

iii) x=2 ; $y=(2)^2-2(2)-3 = 4-4-3 =-3$ ;(2,-3)

iii) x=1 ; $y=(1)^2-2(1)-3 = 1-2-3 =-4$ ;(1,-4)

iii) x=-2 ; $y=(-2)^2-2(-2)-3 = 4+4-3 =5$ ;(-2,5)

Now we plot them on coordinate axis and line them to form our parabola

When we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.

3 0

3 years ago

A boy's age in ten year time will be four times his age five years ago. Find his present age.

Katyanochek1 [597]

Answer:

He is ten.

Step-by-step explanation:

10 yrs old. Go ahead 10 yrs to make 20. Which is four times as much as five years old. (Which is 5 years before 10)

Hope this helps! :)

8 0

3 years ago

Which statement is true about the potential<br> solution x = -5?

Vlad1618 [11]

Answer:

The answer to this question is d

4 0

3 years ago

Read 2 more answers

An experiment consists of ranomly drawing three cards in succession without replacement from a standard deck of 52 cards. Let A

nadya68 [22]

Answer:

0.0045248 ;

0.1312218 ;

0.0001809 ;

0.1659729

Step-by-step explanation:

Number of Kings in deck = 4

Total number of cards in deck = 52

Picking without replacement :

A = King on first draw :

P(A) = 4 / 52

A = King on 2nd draw :

P(B) = 3 / 51

A = King on 3rd draw :

P(C) = 2 / 50

1.) P(A n B) = P(A) * P(B)

P(A n B) = 4/52 * 3/51 = 12 / 2652 = 0.0045248

2.) P(A u B) = P(A) + P(B) - P(AnB)

P(AuB) = 4/52 + 3/51 - 0.0045248 = 0.1312218

3.) P(A ∩ B ∩ C) = P(A) * P(B) * P(C)

P(A ∩ B ∩ C) = 4/52 * 3/51 * 2/50 = 0.0001809

4.) P(A U B U C) =

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) - P(AnBnC)

P(AnC) = P(A) * P(C) = 4/52 * 2/50 = 0.0030769

P(BnC) = P(B) * P(C) = 3/51 * 2/50 = 0.0023529

4/52 + 3/51 + 2/50 - 0.0045248 - 0.0030769 - 0.0023529 + 0.0001809 = 0.1659729

6 0

3 years ago

When solving a system of equations, how do you determine which method to use?

bazaltina [42]

Substitution is best to use one one or both equations is already solved for one of the variables. Elimitation can be use if all variables have a coefficient other than 1.

5 0

2 years ago