Which translation maps the vertex of the graph of the function f(x) = x onto the vertex of the function g(x) = x2 + 2x +1?

a street light is at the top of a 18 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a s

shutvik [7]

The most appropriate choice for similarity of triangles will be given by -

Speed of tip of the shadow of woman = 6 ft/s

What are similar triangles?

Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.

Here,

The diagram has been attached here

Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.

Height of street light = 18 ft

Height of woman = 6ft

The two triangles are similar [As height of woman is parallel to the height of pole]

$\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\$

To find the speed, we have to differentiate both sides with respect to time 't'

$\frac{dy}{dt} =\frac{3}{2}\frac{dx}{dt}\\\frac{dy}{dt}=\frac{3}{2} \times 4\\\frac{dy}{dt} = 6$

Speed of tip of her shadow = 6 ft

To learn more about similarity of triangles, refer to the link-

brainly.com/question/14285697

#SPJ4

6 0

11 months ago

Someone please help!!

rewona [7]

Answer:

Option 2: (1,0) is the correct answer

Step-by-step explanation:

Given inequality is:

y>-5x+3

In order to find which point is solution to the given inequality we'll put the point one by one in the inequality. If the point satisfies the inequality, then the point is the solution of the inequality.

Putting (0,3) in inequality

$3 > -5(0)+3\\3>0+3\\3>3$

Putting (1,0) in inequality

$0>-5(1)+3\\0>-5+3\\0>-2$

Putting (-3,1) in inequality

$1 > -5(-3)+1\\1> 15+1\\1>16$

Putting (-1,-2) in inequality

$-2>-5(-1)+3\\-2>5+3\\-2>8$

The inequality is true for (1,0)

Hence,

Option 2: (1,0) is the correct answer

4 0

3 years ago

Please, Answer is needed.

Yuki888 [10]

Answer:

540 mins | 9 hours | 540, 9

420 mins | 7 hours | 420, 7

300 mins | 5 hours | 300, 5

180 mins | 3 hours | 180, 3

Step-by-step explanation:

1 hour = 60 mins

To convert hours into minutes, multiply the number of hours by 60 minutes:

9 hours × 60 mins = 540 mins

7 hours × 60 mins = 420 mins

5 hours × 60 mins = 300 mins

3 hours × 60 mins = 180 mins

5 0

3 years ago

Read 2 more answers

Please help

Firdavs [7]

Answer:

y = -x -3

Step-by-step explanation:

I went to Desmos and kept guessing y intercepts until the line passed through the point (-4, 1). Sorry I can't explain the real way to figure this out.

5 0

2 years ago

Can Someone Answer My Final Answers :) I’d appreciate it so much :)

DaniilM [7]

1. Remember that the perimeter is the sum of the lengths of the sides of a figure.To solve this, we are going to use the distance formula: $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$
where
$(x_{1},y_{1})$ are the coordinates of the first point
$(x_{2},y_{2})$ are the coordinates of the second point
Length of WZ:
We know form our graph that the coordinates of our first point, W, are (1,0) and the coordinates of the second point, Z, are (4,2). Using the distance formula:
$d_{WZ}= \sqrt{(4-1)^2+(2-0)^2}$
$d_{WZ}= \sqrt{(3)^2+(2)^2}$
$d_{WZ}= \sqrt{9+4}$
$d_{WZ}= \sqrt{13}$

We know that all the sides of a rhombus have the same length, so
$d_{YZ}= \sqrt{13}$
$d_{XY}= \sqrt{13}$
$d_{XW}= \sqrt{13}$

Now, we just need to add the four sides to get the perimeter of our rhombus:
$perimeter= \sqrt{13} + \sqrt{13} + \sqrt{13} + \sqrt{13}$
$perimeter=4 \sqrt{13}$
We can conclude that the perimeter of our rhombus is $4 \sqrt{13}$ square units.

2. To solve this, we are going to use the arc length formula: $s=r \alpha$
where
$s$ is the length of the arc.
$r$ is the radius of the circle.
$\alpha$ is the central angle in radians

We know form our problem that the length of arc PQ is $\frac{8}{3} \pi$ inches, so $s=\frac{8}{3} \pi$ , and we can infer from our picture that $r=15$ . Lest replace the values in our formula to find the central angle POQ:
$s=r \alpha$
$\frac{8}{3} \pi=15 \alpha$
$\alpha = \frac{\frac{8}{3} \pi}{15}$
$\alpha = \frac{8}{45} \pi$

Since $\alpha =POQ$ , We can conclude that the measure of the central angle POQ is $\frac{8}{45} \pi$

3. A cross section is the shape you get when you make a cut thought a 3 dimensional figure. A rectangular cross section is a cross section in the shape of a rectangle. To get a rectangular cross section of a particular 3 dimensional figure, you need to cut in an specific way. For example, a rectangular pyramid cut by a plane parallel to its base, will always give us a rectangular cross section.
We can conclude that the draw of our cross section is:

6 0

3 years ago

Read 2 more answers