Evaluate (8 x 10-3) +0.45 – (7 X 10-2). Write your answer in scientific notation.

Which equation is the inverse of y = 9x2 - 4?

m_a_m_a [10]

Answer:

The inverse will be:

$y' = \frac{\sqrt{x+4}}{3}$

Step-by-step explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

$f(x) = 9x^{2} - 4$

$y = 9x^{2} - 4$

$x = 9y' ^{2} - 4$

Now solve for y'.

First add 4 in both sides of the equation and change to the left y'.

$x + 4= 9y'^{2} - 4+4$

$9y'^{2}$ = x + 4

Second divide by 9

$9y'^{2}$ /9 = (x + 4)/9

$y'^{2}$ = (x + 4)/9

Now you will have to clear y, with the square root.

$[tex]y'^{\frac{2}{2}} = \sqrt{x + 4} / \sqrt{9}$ [/tex] =

Simplifying terms

$y' = \frac{\sqrt{x+4}}{3}$

$f^{-1}(x) = \frac{\sqrt{x+4}}{3}$

You can check the answer by doing the evaluation of the following equation:

(f o $f^{-1}$ ) (x)

substitute the equation for y' or inverse function $f^{-1}$

f( $\frac{\sqrt{x+4} }{3}$ )

Now substitue the value into f(x)

You will have

$= 9(\frac{\sqrt{x+4} }{3}} )^{2} - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} ) - 4$

=x

5 0

3 years ago

9x - 3y = -2 -3x + y = -3

morpeh [17]

Multiply 2nd equation by 3 and add to first
9x-3y=-2
-9x+3y=-9 +
0x+0y=-7

0=-7
false
no solution
these lines aer paraalell so no solution

6 0

3 years ago

A painter works 37.5 hours one week. If she worked 5 days, how many hours did she work on average per day? At $15.75 per hour, h

Lyrx [107]

She worked 7.5 hours a day on average. You can get this by dividing the 37.5 by 5.

And the average she made was 118.13 when rounded. You can get this by multiplying the 7.5 by the rate

8 0

3 years ago

Integrate 1 - x / x(x2 + 1) d x by partial fractions.

solniwko [45]

Answer:

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

Step-by-step explanation:

step 1:- by using partial fractions

$[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }$ ......(1)

step 2:-

solving on both sides

$1-x=A(x^{2} +1)+(Bx+C)x......(2)$

substitute x =0 value in equation (2)

1=A(1)+0

A=1

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

-1 = C

step 3:-

substitute A,B,C values in equation (1)

now

$\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 } d x -\int\limits \frac{1}{x^{2}+1 } d x$

by using integration formulas

i) by using $\int\limits \frac{1}{x} d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\$ .....(b)

$\int\limits tan^{-1}x dx =\frac{1}{1+x^{2} } +C$ .....(c)

step 4:-

by using above integration formulas (a,b,and c)

we get answer is

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

6 0

3 years ago

REALLY EASY NEED ANSWER BY 10:00 P. M. AND WILL GIVE BRAINLEIST. PLS HURRY IF YOU HAVE TIME PLEASE ANSWER OTHER QUESTIONS PLS TH

tiny-mole [99]

5) which types have less than 10?
Stand up and suspended.
6) which types have more than 15? Everything except thriller.
7) which months are more than 55? January and February.
January exceeds 55 by 1 and Feb exceeds 55 by 2. $0.25 for each excess. Total charge: $0.75

6 0

3 years ago