All categories

2 years ago

Can someone check if this is right or did I solve it wrong?

Mathematics

1 answer:

ICE Princess25 [194]2 years ago

4 0

Answer:

f(3x) - 2g(x+1) = 12x - 5

Step-by-step explanation:

You've got f[g(x)] and g[f(x)] correct

However, f(3x) means substitute 3x for x in f(x):

f(3x) = 2(3x) - 3

⇒ f(3x) = 6x - 3

2g(x+1) = 2[4 - 3(x + 1)]

⇒ 2g(x+1) = 2[4 - 3x -3]

⇒ 2g(x+1) = 2[1 - 3x]

⇒ 2g(x+1) = 2 - 6x

f(3x) - 2g(x+1) = (6x - 3) - (2 - 6x)

⇒ f(3x) - 2g(x+1) = 12x - 5

You might be interested in

What is the domain of the function y equals 2 square root of

Helga [31]

Answer:

Domain: x>=1

Step-by-step explanation:

what values of x make it work (square roots must be greater than or equal to zero)

sqrt (5x-5) >=0

square each side

5x-5 >=0

add 5 to each side

5x>=5

divide by 5 on each side

5x/5 >=5/5

x >=1

6 0

3 years ago

For each day in New England, the probability that it is mostly cloudy is 0.10 . Cindi is planning to go leaf watching, and her f

kolbaska11 [484]

Answer:

0,37

Step-by-step explanation:

It will be easier if we noun the events.

A= Cindi's friend comes to England.

B= New England is mostly cloudly.

We are searching the probability of just A doesn´t happen or just A happens but not B.

The probability of A doesn´t happen is one minus the probability of A:

$=(A^{|} )=1-P(A)=1-0.7=0.3$

The events A and B are independent for this reason the probability than both occurs is the product of the probability of each event. It means:

$P(A \cap B)= P(A)P(B)=0.1*0.7=0.07$

The probability of A doesn´t happen or A and B happen is:

$P(A^{|} \cup (A \cap B))= P(A^{|} )+P (A \cap B)-P(A^{|} \cap A\cap B)=0.3+0.07-0=0.37$

Conclusively we have to rest the probability of A doesn´t happen and A and B happen, but A happens and doesn´t happen and the same time is impossible. For this reason, we have the same result.

$P(A^{|} \cup (A \cap B))-P(A^{|} \cap A\cap B)=0.37-0=0.38$

Then the probability either Cindi's friend does not come to New England, or she does come but it is mostly cloudy is 0.37

8 0

3 years ago

Two boxes are stacked one on top of the other. One box is 6 feet 7 inches tall, and the other is 6 feet 6 inches tall. How high

Orlov [11]

Answer:

7ft 1in.

Step-by-step explanation:

add the two 6 ft together and that gives you 12 ft. then add 7 in + 6 in which gives you 13 in. There are 12 in a foot, so you take 12 away from the 13 giving you 1 in remaining and 1 additional foot to add to the 12.

6 0

2 years ago

The nth term of a sequence is represented by 3n4−10/6n4+7 . What is the limit of the the nth term as n becomes increasingly larg

Cerrena [4.2K]

Answer:

Step-by-step explanation:

Given the limit of the function expressed as;

$\lim_{n \to \infty} \frac{3n^4-10}{6n^4+7} \\$

To take the limit, we nee to divide through by the highest power of n first

$\lim_{n \to \infty} \frac{3n^4/n^4-10/n^2}{6n^4/n^4+7/n^4}\\= \lim_{n \to \infty} \frac{3-10/n^2}{6+7/n^4}\\= \frac{3-10/(\infty)^2}{6+7/(\infty)^4}\\= \frac{3-0}{6-0}\\= \frac{3}{6}\\ = \frac{1}{2}\\$

Hence the limit of the the nth term as n becomes increasingly large is 1/2

3 0

3 years ago

Find the coordinates of the y-intercept and x-intercepts of the following. (image!)

marissa [1.9K]

Answer:

Step-by-step explanation:

We can do this a couple of ways. We can graph it -- see below. Or we can do the math.

Math

y = x^2 - 2x - 15

This trinomial factors into

y = (x - 5)(x + 3)

from which

x - 5= 0

x = 5

and

x + 3 = 0

x = - 3

The y intercept is the value obtained when all the xs on the right = 0

y = 0^2 - 2*0 - 15

y = - 15

<em>Answer</em>

x intercepts: (-3,0),(5,0)
y intercept: (0,-15)

The graph is below.

4 0

2 years ago