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3 years ago

I want to know how to solve this equation

Mathematics

1 answer:

andre [41]3 years ago

8 0

9514 1404 393

Answer:

Step-by-step explanation:

To find the inverse of y = f(x), solve the equation x = f(y) for y. For these functions, that's about the easiest way to do it.

A. x = ∛(3y) ⇒ x³ = 3y ⇒ x³/3 = y . . . . . does not match g(x)

B. x = 11y -4 ⇒ x +4 = 11y ⇒ (x +4)/11 = y . . . . matches g(x)

C. x = 3/y -10 ⇒ x +10 = 3/y ⇒ 3/(x+10) = y . . . . does not match g(x)

D. x = y/12 +15 ⇒ x -15 = y/12 ⇒ 12(x -15) = y . . . . does not match g(x)

_____

Additional comment

This is repeated application of the "solve for ..." process. In general, that process "undoes" what is "done" to the variable. The order of operations can tell you the order of the things that are done. The undoing is in the reverse order.

You need to be completely comfortable with the properties of equality (addition, subtraction, multiplication, division), and you need to understand the inverse functions of the functions we usually use: (powers, roots), (exponentials, logarithms), (trig functions, inverse trig functions). Of course, the inverse of addition is subtraction; the inverse of multiplication is division.

Above, we used a "shortcut" a couple of times:

a = b/c ⇒ c = b/a . . . . . equivalent to multiplying both sides by c/a.

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(a) How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers?

Olegator [25]

Answer:

a) 67600000 possible plates

b) 19656000 possible plates where neither digit or letter are repeated

Step-by-step explanation:

The easiest way to solve this problem is seeing how many possibilities and there for each place in the license plate:

We have the following 7 places:

P1 - P2 - P3 - P4 - P5 - P6 - P7

The alphabet has 26 letters and there are 10 digits. So,

a) For each position there are the following possibilites

26 - 26 - 10 - 10 - 10 - 10 - 10

So in all, there are, 26*26*10*10*10*10*10 = 67600000 possible plates

b) Let's do the possibilites for each position again. Now, no letter or number can be repeated, so.

P1 is still 26. Now for P2, the letter in position P1 cannot be repeated, so there are only 25 possibilies. As for the digits, for P3, the first digit, there are still 10 possibilities. For P4, there are 9, since the digit in P3 cannot be repeated. For P5 there are 8, since P3 and P4 cannot be repeated... So there are the following number of possibilities:

26-25-10-9-8-7-6

In all, there are 26*25*10*9*8*7*6 = 19656000 possible plates where neither digit or letter are repeated.

5 0

3 years ago

Question 1 of 10 10 Points AB¯¯¯¯¯¯¯¯ is the diameter of circle T. Point A is located at (-4,2) and point B is located at (2,-8)

wariber [46]

Answer:

The coordinates of the center of this circle is (-1, -3).

Step-by-step explanation:

As we know that $A = (-4,2)$ and $B = (2,-8)$ are points lying on circle T, the center is the midpoint of the segment AB, whose location can be obtained from Midpoint formula:

$C = \frac{1}{2}\cdot A + \frac{1}{2}\cdot B$

$C = \frac{1}{2}\cdot (-4,2)+\frac{1}{2}\cdot (2,-8)$

$C = (-2, 1)+(1,-4)$

$C=(-2+1,1-4)$

$C=(-1,-3)$

The coordinates of the center of this circle is (-1, -3).

6 0

4 years ago

1. Which is greater than 4? (a) 5, (b) -5, (c) -1/2, (d) -25.

Gala2k [10]

Answer:

(a) 5

5 is greater than 4

5 0

3 years ago

Read 2 more answers

For which two beverages is the difference between the prices the greatest? what is the difference?

Anton [14]

Answer:

The biggest difference is between fruit juice and lemonade ($0.6).

Step-by-step explanation:

Giving the following information:

items:

fruit juice. $0.89

iced tea. $1.29

lemonade. $1.49

pretzel. $2.50

popcorn. $1.25

First, popcorn and pretzel are not beverages.

Now, we need to find the differences in prices between each beverage and determine the greatest:

Fruit juice to ice tea= 0.89 - $0.4

Fruit juice to lemonade= 0.89 - 1.49= $0.6

Ice tea to lemonade= 1.29 - 1.49= $0.2

The biggest difference is between fruit juice and lemonade ($0.6).

6 0

3 years ago

Determine whether the set of vectors <img src="https://tex.z-dn.net/?f=%20v_%7B1%3D%283%2C2%2C1%29%2C%20v_%7B2%7D%20%3D%28-1%2C-

Korolek [52]

Since each vector is a member of $\mathbb R^3$ , the vectors will span $\mathbb R^3$ if they form a basis for $\mathbb R^3$ , which requires that they be linearly independent of one another.

To show this, you have to establish that the only linear combination of the three vectors $c_1\mathbf v_1+c_2\mathbf v_2+c_3\mathbf v_3$ that gives the zero vector $\mathbf0$ occurs for scalars $c_1=c_2=c_3=0$ .

$c_1\begin{bmatrix}3\\2\\1\end{bmatrix}+c_2\begin{bmatrix}-1\\-2\\-4\end{bmatrix}+c_3\begin{bmatrix}1\\1\\-1\end{bmatrix}=(0,0,0)\iff\begin{bmatrix}3&-1&1\\2&-2&1\\1&-4&-1\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\end{bmatrix}=\begin{bmatrix}0\\0\\0\end{bmatrix}$

Solving this, you'll find that $c_1=c_2=c_3=0$ , so the vectors are indeed linearly independent, thus forming a basis for $\mathbb R^3$ and therefore they must span $\mathbb R^3$ .

4 0

3 years ago