4 more than two thirds of a number is 8

Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three

RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

$f(x)=x^{2}$

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

$g(x)=-5x^{2}+100x-450$

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

$g(x)=-5x^{2}+100x-450$

Complete the square

$g(x)=-5(x^{2}-20x)-450$

$g(x)=-5(x^{2}-20x+100)-450+500$

$g(x)=-5(x^{2}-20x+100)+50$

$g(x)=-5(x-10)^{2}+50$

The vertex is the point (10,50)

so

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

5 0

3 years ago

Read 2 more answers

The circumference of a circle is 60 pi cm. What is the radius of the circle?

Artyom0805 [142]

Answer:

30/pi cm

Step-by-step explanation:

2×pi×r =60

r = 60/2×pi =30/pi

4 0

3 years ago

Evaluate the difference quotient for the given function.

kherson [118]

Assuming you mean f(t) = g(t) × h(t), notice that

f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)

Then the difference quotient of f is

$\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}$

Recall the angle sum identity for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

Then we can write the difference quotient as

$\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}$

or

$\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}$

(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)

7 0

3 years ago

Pls help me i'll give the brainlist or whatever it is to the first correct answer. pls NO LINKS.

Yakvenalex [24]

Answer:

628 hope it helps

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A right rectangular pyramid is sliced parallel to the base, as shown.

ELEN [110]

The answer would be the first choice. $15 cm^{2}$

Explanation: The reason for this is that the question was pretty much just asking what the area of the resulting two-dimensional cross section would be -the shape in gray- (which can be found by using the formula $lw$ . To add on, since the dimensions of the shape are already given (5 and 3) all you've to do is multiply: 3*5=15

That's how you get to the answer.

7 0

3 years ago

Read 2 more answers