If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?

The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the left three units and up two units.

To vertically compress the parent function f(x) = 5x by a factor of one-half, we multiply the function by the compression factor, which is 1/2. So the compressed function is f(x) = (1/2)(5x) = 2.5x.

To shift the function to the left three units, we subtract the shift amount from the x-variable. So the shifted function is f(x + 3) = 2.5(x + 3) = 2.5x + 7.5.

To shift the function up two units, we add the shift amount to the y-variable. So the final transformed function is f(x + 3) + 2 = 2.5x + 7.5 + 2 = 2.5x + 9.5.

The given equation in this case is:

 y = -16 t^2 + 400

We can see that the slope of the equation is negative (-16) which means that the position of Kay is on the positive y-axis , while the bottom of the river is in the origin. This is supported by taking t = 0, the initial y becomes y = 400. Therefore the position of Kay now is at (0, 400).

So to find for the time when the camera hits the water, then y must be zero (t, 0) so we have to find for t in this case.

When y = 0

0 = -16 t^2 + 400

16 t^2 = 400

t^2 = 25

t = 5 s

Therefore it takes 5 seconds for the camera to hit the water and for Kay to see a splash.

Answer:

5 seconds

Step-by-step explanation:

Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive bird nests in the trees. The height of the camera above the water can be modeled by the equation

y = -16t^2 + 400, where t represents the seconds after the camera is dropped.

When splash from the hits the water then the height becomes 0

height is y so we replace y with 0 and solve for t

0 = -16t^2 + 400

Subtract 400 on both sides

-400 = -16t^2

Divide by 16 on both sides

25= t^2

take square root on both sides

t= 5

It takes 5 seconds

Answer:

[tex]f(x)= 2x[/tex]

Step-by-step explanation:

For which function is f(x) not equal to f^-1(x)

LEts check with each function, we find out inverse for each option

[tex]f(x)= 2-x[/tex]

Replace f(x) by y, then switch the variables and solve for y

[tex]y= 2-x[/tex]

[tex]x= 2-y[/tex], Add y on both sides

[tex]x+y= 2[/tex], Subtract x from both sides

[tex]y= 2-x[/tex], Inverse is equal to f(x)

[tex]-f(x)= \frac{2}{x}[/tex]

Replace f(x) by y, then switch the variables and solve for y

[tex]-y= \frac{2}{x}[/tex]

[tex]-x= \frac{2}{y}[/tex],  cross multiply it

[tex]-xy = 2[/tex], divide by x on both sides

[tex]-y= \frac{2}{x}[/tex], Inverse is equal to f(x)

[tex]f(x)= -x[/tex]

Replace f(x) by y, then switch the variables and solve for y

[tex]y= -x[/tex]

[tex]x=-y[/tex], Add y on both sides

[tex]x+y= 0[/tex], Subtract x from both sides

[tex]y=-x[/tex], Inverse is equal to f(x)

[tex]f(x)= 2x[/tex]

Replace f(x) by y, then switch the variables and solve for y

[tex]y= 2x[/tex]

[tex]x= 2y[/tex], divide by 2 on both sides

[tex]\frac{x}{2}=y[/tex],  Inverse is not equal to f(x)

divide 18 by 0.5

18/0.5 = 36

36 jugs are needed

-1>2W+7

-8>2w

w = -8/2 = -4

w>-4

thy get 55/75 and you want to know x/300

55/75 x X/300

 cross multiply 55 x 300 = 16500

 divide that by 75

16500/75 = 220

 x = 220

 they will get $220

The value of trigonometric function sec A is,

⇒ sec A = 25/24

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC angle c is a right angle.

And, c = 25, a = 7

Now, We can draw the tringle ABC.

And, Find the value of side b by using Pythagoras theorem as;

⇒ c² = a² + b²

⇒ 25² = 7² + b²

⇒ 625 = 49 + b²

⇒ b² = 625 - 49

⇒ b = 24

We know that;

⇒ sec A = Hypotenuse / adjacent

Hence, We get;

⇒ sec A = Hypotenuse / adjacent

⇒ sec A = 25 / 24

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multiply 35 by tan(42)

 this equals 31.5141

rounded to 31.51

4% = 0.04

 divide 6 by 0.04 = 150

6 is 4% of 150

double check 150*0.04 = 6

Answer:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

[tex]\frac{120-60}{2-1}=\frac{180-120}{3-2}=\frac{240-180}{4-3}=\frac{300-240}{5-4}=60[/tex]

⇒  The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.

See the attached graph

The comparison operator includes "or equal to" in each case, so the graph of the boundary line is solid. Each bounary line can be graphed in the usual way. Considering the y-intercept and slope is often easiest when the equations are presented in this form:

Since the solution space includes y-values less than those in the first line, the graph is shaded below that line.

Since the solution space includes y-values greater than those in the second line, the graph is shaded above that line.

Where the graph is doubly-shaded is the solution space for the system of equations.

Answer:

1. Dividing the expressions [tex]ax^2+bx+c[/tex] by a is a different step.

2. Yes, both of these factorization are correct. They are not complete because they can be factored further.

3. The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.

Step-by-step explanation:

1.

To factorize the quadratic expressions [tex]ax^2+bx+c[/tex] first we divide it by a. Then we factorize it same as [tex]x^2+bx+c[/tex].

It means all the steps of factoring a quadratic expressions [tex]ax^2+bx+c[/tex] and [tex]x^2+bx+c[/tex] are same except the first step, i.e., divide the expressions [tex]ax^2+bx+c[/tex] by a.

2.

The given quadratic expression is

[tex]P(x)=2x^2+6x-20[/tex]

[tex](2x-4)(x+5)=2x(x+5)-4(x+5)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)[/tex]

[tex](x-2)(2x+10)=x(2x+10)-2(2x+10)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)[/tex]

The product of factors is equal to the given expression. It means both of these factorization are correct.

They are not complete because they can be factored further.

[tex](2x-4)(x+5)=2(x-2)(x+5)[/tex]

[tex](x-2)(2x+10)=(x-2)2(x+5)[/tex]

3.

If the factored form of a quadratic expression is defined as

[tex](x-a)(x-b)[/tex]

Then the related quadratic equation is

[tex](x-a)(x-b)=0[/tex]

[tex]x=a,b[/tex]

The roots of the quadratic equation are a and b.

The related function is

[tex]f(x)=(x-a)(x-b)[/tex]

The x-intercepts of the function are a and b because at x=a and x=b the value of function is 0.

The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.

It should be noted that in order to factorize the quadratic expression, one will have to divide it by a.

The factorization of the quadratic expression ax² + bx + c is different from factoring x² + bx + c as one has to first divide it by a.

Secondly, the factorization by the students isn't complete because they can be factored further.

Lastly, the relationship between the factors of a quadratic expression, the roots of the related quadratic equation is that the roots are the x-intercept of the related function.

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