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3 years ago

The Inverse of G(x) is a function. True or False

Mathematics

1 answer:

Paha777 [63]3 years ago

5 0

Answer:

Inverse of G(x) is not a function

Step-by-step explanation:

We have been given with graph and given graph is of the function $y=x^2-4$

We need to tell whether the inverse of given function is function or not.

We need to interchange the variables to find inverse of a function we will get

$x=y^2-4$

Now, after simplifying we will get $y^2=x+4$

Hence, $y=\pm\sqrt{x+4}$

Here for each value of x there will not be different value of y

Therefore inverse of G(x) is not a function.

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Please help me with vivid explanation

Ivanshal [37]

Answer:

864 m²

Step-by-step explanation:

First calculate the total area of the rectangular field

The area of a rectangle is given by the product of the length and the width

let A be the total area

A = 100*120

A = 12000 m²

Calculate the area of the small rectangles

Let A' be the total area of the four small rectangles and A" the area of one small rectangle

A' = 4 A"
A' = 4 [( $\frac{120-4}{2}$ )*( $\frac{100-4}{2}$ )]
A' = 4*58*48
A' = 11136 m²

Substract the A' from A to get the area of the road

Let A"' be the area of the road

A"' =A-A'

A"' = 12000-11136

A"' = 864 m²

3 0

3 years ago

How would I solve 16x^4-41x^2+25=0 ???

sveticcg [70]

$16{ x }^{ 4 }-41{ x }^{ 2 }+25=0$

${ x }^{ 4 }={ ({ x }^{ 2 }) }^{ 2 }\\ \\ 16{ ({ x }^{ 2 }) }^{ 2 }-41{ x }^{ 2 }+25=0$

First of all to make our equation simpler, we'll equal $x^{2}$ to a variable like 'a'.

So,

${ x }^{ 2 }=a$

Now let's plug $x^{2}$ 's value (a) into the equation.

$16{ ({ x }^{ 2 }) }^{ 2 }-41{ x }^{ 2 }+25=0\\ \\ { x }^{ 2 }=a\\ \\ 16{ (a) }^{ 2 }-41{ a }+25=0$

Now we turned our equation into a quadratic equation.

(The variable 'a' will have a solution set of two solutions, but 'x' , which is the variable of our first equation will have a solution set of four solutions since it is a quartic equation (<span>fourth-degree <span>equation) )

Let's solve for a.

The formula used to solve quadratic equations ;

$\frac { -b\pm \sqrt { { b }^{ 2 }-4\cdot t\cdot c } }{ 2\cdot t }$

The formula is used in an equation formed like this :
</span></span>
$t{ x }^{ 2 }+bx+c=0$

In our equation,

t=16 , b=-41 and c=25

Let's plug the values in the formula to solve.

$t=16\quad b=-41\quad c=25\\ \\ \frac { -(-41)\pm \sqrt { -(41)^{ 2 }-4\cdot 16\cdot 25 } }{ 2\cdot 16 } \\ \\ \frac { 41\pm \sqrt { 1681-1600 } }{ 32 } \\ \\ \frac { 41\pm \sqrt { 81 } }{ 32 } \\ \\ \frac { 41\pm 9 }{ 32 }$

So the solution set :

$\frac { 41+9 }{ 32 } =\frac { 50 }{ 32 } \\ \\ \frac { 41-9 }{ 32 } =\frac { 32 }{ 32 } =1\\ \\ a\quad =\quad \left\{ \frac { 50 }{ 32 } ,\quad 1 \right\}$

We found a's value.

Remember,

${ x }^{ 2 }=a$

So after we found a's solution set, that means.

${ x }^{ 2 }=\frac { 50 }{ 32 }$

and

${ x }^{ 2 }=1$

We'll also solve this equations to find x's solution set :)

${ x }^{ 2 }=\frac { 50 }{ 32 } \\ \\ \frac { 50 }{ 32 } =\frac { 25 }{ 16 } \\ \\ { x }^{ 2 }=\frac { 25 }{ 16 } \\ \\ \sqrt { { x }^{ 2 } } =\sqrt { \frac { 25 }{ 16 } } \\ \\ x=\quad \pm \frac { 5 }{ 4 }$

${ x }^{ 2 }=1\\ \\ \sqrt { { x }^{ 2 } } =\sqrt { 1 } \\ \\ x=\quad \pm 1$

So the values x has are :

$\frac { 5 }{ 4 }$ , $-\frac { 5 }{ 4 }$ , $1$ and $-1$

Solution set :

$x=\quad \left\{ \frac { 5 }{ 4 } \quad ,\quad -\frac { 5 }{ 4 } \quad ,\quad 1\quad ,\quad -1 \right\}$

I hope this was clear enough. If not please ask :)

3 0

3 years ago

Read 2 more answers

Sean has worked 66 hours over the last 10 days without a day off. He worked either a 6 hour day or an 8 hour day. During the 10

marysya [2.9K]

He worked an 8 hour day 3 days.

Let x be the number of 8 hour days he works. Then 10-x is the number of 6 hour days he works.

8x + 6(10-x) = 66

Using the distributive property,
8x + 6*10 - 6*x = 66
8x + 60 - 6x = 66

Combining like terms,
2x + 60 = 66

Subtract 60 from both sides:
2x + 60 - 60 = 66 - 60
2x = 6

Divide both sides by 2:
2x/2 = 6/2
x = 3

There were 3 days he worked 8 hours.

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4 years ago

Chapter 11 lesson 1 math homework math in my world

kvv77 [185]

I’m sorry but what???

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3 years ago

PLS HELP ENTIRE TEST DUE IN 10 MIN

Katen [24]

Answer:

(-3, 6)

Step-by-step explanation:

Once turned the original points are to be flipped and since it is counter clockwise it will make the x usually change from positive to negative and vise versa

4 0

3 years ago

Read 2 more answers