Is this the right answer....???????

What is the inverse of the function g(x)=-\dfrac{2}{3}x-5g(x)=− 3 2 x−5g, left parenthesis, x, right parenthesis, equals, minu

Semenov [28]

Answer:

$g^{-1}(x)=-\frac{3}{2}x-\frac{15}{2}$

Step-by-step explanation:

Given function,

$g(x) = -\frac{2}{3}x-5$

Step 1 : Replace g(x) by y:

$y = -\frac{2}{3}x-5$

Step 2 : Swap x and y:

$x = -\frac{2}{3}y-5$

Step 3 : Solve the equation for y ( isolate y in the left side ):

$x +\frac{2}{3}y=-5$

$\frac{2}{3}y=-5-x$

$y=\frac{3}{2}(-5-x)$

$y=-\frac{15}{2}-\frac{3}{2}x$

$y=-\frac{3}{2}x-\frac{15}{2}$

Step 4: Replace y by $g^{-1}(x)$ :

$g^{-1}(x)=-\frac{3}{2}x-\frac{15}{2}$

Hence, the inverse of the function g(x) is $g^{-1}(x)=-\frac{3}{2}x-\frac{15}{2}$ .

8 0

2 years ago

Please answer and help me on this question!

Nady [450]

<h3>Answer: 10.1 cm approximately</h3>

=====================================================

Explanation:

The double tickmarks show that segments DE and EB are the same length.

The diagram shows that DB = 16 cm long

We'll use these facts to find DE

DE+EB = DB

DE+DE = DB

2*DE = DB

DE = DB/2

DE = 16/2

DE = 8

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Now let's focus on triangle DEC. We just found the horizontal leg is 8 units long. The vertical leg is EC which is unknown for now. We'll call it x. The hypotenuse is CD = 9

Use the pythagorean theorem to find x

a^2+b^2 = c^2

8^2+x^2 = 9^2

64+x^2 = 81

x^2 = 81 - 64

x^2 = 17

x = sqrt(17)

That makes EC to be exactly sqrt(17) units long.

If you follow those same steps for triangle ADE, then you'll find the missing length is AE = 6

---------------

So,

AC = AE+EC

AC = 6 + sqrt(17)

AC = 10.1231056256177

AC = 10.1 cm approximately

4 0

2 years ago

Attempted but just couldnt understand (25Points)

Rashid [163]

Answer:

a) Function:Yes

b) Domain: $-5\:$

c) Range: $-5\le y\le 3$

Step-by-step explanation:

The given graph passes vertical line test hence it is a function

The given function has x-intercepts at $x=-4.5, x=-1,x=3.5$

We can therefore write this function in factored form as $y=a(2x+9)(x+1)(2x-7)$

There is a y-intercept at (0,-2)

$-2=a(2*0+9)(0+1)(2*0-7)$

$-2=-63a$

$a=\frac{2}{63}$

The required function is

$y=\frac{2}{63}(2x+9)(x+1)(2x-7)$

b) The domain refers to all values of x for which this function is defined.

The domain from the graph is $-5\:$ because there are holes at the end of the graph.

c) The range is the value of y for which x is defined or the graph exists.

From the graph the range is $-5\le y\le 3$

5 0

2 years ago

The factors of 35, 48, and 60 are listed below. Two of these numbers are relatively prime. Click the two numbers that are

Nostrana [21]

Answer:

35 and 48

Step-by-step explanation:

4 0

3 years ago

Can someone explain HOW to simplify this algebraic fraction, as in tell me why and what I need to do for each step : 1-n/n^2-1

Andreyy89

- I’m assuming the expression implies the following:

(1-n)/(n^2 - 1)

The steps goes as follows:

= -(n-1)/(n^2-1) (factored a negative out)
= -(n-1)/[(n+1)(n-1)] (Factored denominator into a difference of squares, but don’t just blindly accept the fact, expand it and you should get the original denominator)

At this point, the (n-1) terms cancel, as you should know: a real number, besides 0, over itself is 1.

= -1/(n+1) , which is the answer

Note: You could also see it as 1/-(n+1) or 1/(-n-1)

8 0

2 years ago