The function f(x)=5(2)^x was replaced with f(x)+k , resulting in the function graphed below. what is the value of k?

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

5 0

Since adding a constant to a function simply moved the graph upwards by that amount, solve f(x) for any value and see how much the graph given is different from that value of y...the simplest way in this case may be to simply find f(0) which is:

5*2^0=5

Clearly the graph at x=0 is at y=-2 so we can see that k is:

5+k=-2 so

k=-7

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A city doubles its size every 56 years. If the population is currently 60,000, what will the population be in 112 years?

Anestetic [448]

Answer:

240,000

Step-by-step explanation:

The population is going to get quadrupled. (56 + 56 = 112)

60,000 x 4 = 240,000

Hope this helped! Please mark as brainliest! Thanks!

7 0

3 years ago

Need help with number 10 please

Naddika [18.5K]

Answer:

Pilar is correct. Both systems have solution (-2, 4).

Step-by-step explanation:

Graphing, or any other means of solving these systems of equations reveals both systems have the same solution: (x, y) = (-2, 4).

_____

By Cramer's rule, the solution to the first set is ...

x = (2(6)-4(2))/(2(5)-4(3)) = 4/-2 = -2

y = (2(5)-6(3))/-2 = -8/-2 = 4

(x, y) = (-2, 4) is the solution to the first system

Since the first equation of the second system is the same as the first equation of the first system, we know the above solution satisfies that equation. We only need to check to see if the same point satisfies the second equation of the second system:

11(-2) +8(4) = -22 +32 = 10 . . . . . yes,

(-2, 4) is the solution of the second system

Pilar is correct that both systems have the same solution.

_____

Cramer's Rule tells you the solution to

ax +by = c
dx +ey = g

is ...

x = (bg -ec)/(bd -ea)
y = (cd -ga)/(bd -ea) . . . . same denominator as for x

I like to use Cramer's Rule when the solution is needed without a lot of steps. Here, we could use the Elimination method to eliminate the y-variable and solve for x. Then more steps are needed to find y. The writing out and explanation are tedious, so it is much simpler just to use a formula that gives the answer.