If f(x) = (square root of x -12 /)-5, find f(13)

Which rule describes the translation below ? In the picture

rewona [7]

The translation rule which describes the given translation is $\fbox{\begin\\\math{(x,y)}\rightarrow(x+5,y-3)\\\end{minispace}}$ .

Further explanation:

Translation is defined as the shifting of the curve in which each point on the curve is shifted in such a way that the shape and size of the curve remains unchanged but the position of each point is changed by a fixed distance.

In the given figure there are two right angle triangle as $S'T'U'$ and $STU$ .

The coordinates of the right angle triangle $S'T'U'$ are $(-4,2),(-4,-2)$ and $(-1,-2)$ and the coordinates of the right angle triangle $STU$ are $(1,5),(1,1)$ and $(4,1)$ .

Consider that the triangle $STU$ is obtained after the translation of each point on the triangle $S'T'U'$ .

The coordinate of the point $S'$ in triangle $S'T'U'$ is $(-4,2)$ .

Step 1:

Use the translation $(x,y)\rightarrow(x-5,y-3)$ for the point $S'$ .

$\fbox{\begin\\\(-4,2)\rightarrow(-4-5,2-3)=(-9,-1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x-5,y-3)$ the coordinate of the point $S$ is $(-9,-1)$ , but in the given figure the coordinate of the point $S$ is $(1,5)$ .

So, the translation $(x,y)\rightarrow(x-5,y-3)$ is incorrect.

Step 2:

Use the translation $(x,y)\rightarrow(x-3,y-5)$ for the point $S'$ .

$\fbox{\begin\\\(-4,2)\rightarrow(-4-3,2-5)=(-7,-3)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x-3,y-5)$ the coordinate of the point $S$ is $(-7,-3)$ , but in the given figure the coordinate of the point $S$ is $(1,5)$ .

So, the translation $(x,y)\rightarrow(x-3,y-5)$ is incorrect.

Step 3:

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point $S'$ .

$\fbox{\begin\\\(-4,2)\rightarrow(-4+5,2+3)=(1,5)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $S$ is $(1,5)$ which is correct as the coordinate for the point $S$ given in the figure is $(1,5)$ .

Step 4:

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point $T'$ .

$\fbox{\begin\\\(-4,-2)\rightarrow(-4+5,-2+3)=(1,1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $T$ is $(1,1)$ which is correct as the coordinate for the point $T$ given in the figure is $(1,1)$ .

Step 5:

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point U’.

$\fbox{\begin\\\ (-1,-2)\rightarrow(-1+5,-2+3)=(4,1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $T$ is $(4,1)$ which is correct as the coordinate for the point $U$ given in the figure is $(4,1)$ .

As per the above calculation it is concluded that the translation $(x,y)\rightarrow(x+5,y+3)$ is correct for the shifting of each point on the triangle $S'T'U'$ to each point on the triangle $STU$ .

The translation of each point on the triangle $S'T'U'$ is shown in the image attached below.

Therefore, the correct translation rule for the shifting of the triangle $S'T'U'$ to the triangle $STU$ is $\fbox{\begin\\\math{(x,y)}\rightarrow(x+5,y-3)\\\end{minispace}}$

Learn more:

A problem to determine the range of a function brainly.com/question/3852778
A problem to determine the vertex of a curve brainly.com/question/1286775
A problem to convert degree into radians brainly.com/question/3161884

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: Translation, shifting, graph, geometry, coordinate geometry, coordinates, shifting of graph, triangle, right angle triangle, movement of curve, shifting of curve, translation of curve.

7 0

3 years ago

Read 2 more answers

Martha has 8 cubic feet of potting soil and 3 flower pots. She wants to put the same amount of soil in each pot. How many cubic

GrogVix [38]

Answer:

2 2/3 cubic feet

Step-by-step explanation:

Martha will put 1/3 of the 8 cubic feet in each pot. That is ...

(1/3)(8 ft³) = 8/3 ft³ = 2 2/3 ft³

Martha will put 2 2/3 cubic feet of soil in each pot.

3 0

3 years ago

Two trains leave towns 471 miles apart at the same time and travel toward each other. One train travels 21 miles per hour slower

nadya68 [22]

Let the slower train's velocity be x-21

Let the faster train's velocity be x

We know that the approach speed is the sum of both speeds, so x+x -21= 2x-21.

The approach rate is given by Distance/time = 471/3 = 157mpH

x+x-21=157

2x=157+21

2x=178

x=89mph

The slower train is travelling 89-21 = 68mph

The faster train is travelling 89mph.

7 0

1 year ago

PLS HELP I WILL MARK BRAINLIEST

tamaranim1 [39]

The green triangle is the rotated image PQR. Point of rotation is (1,-1).

The red triangle is the reflected image XYZ. It’s reflected on the x axis

3 0

3 years ago

Read 2 more answers

Find the volume of the composite figure. Explain your thought, explain how your arrived at your answer. SHOW YOUR WORK FOR FULL

kobusy [5.1K]

We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.

The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
h = √((15 in)² - (10 in)²) = √115 in

The volume of the conical part of the figure is then
V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³

The volume of the hemispherical part of the figure is given by
V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³

Then the total volume of the figure is
V = (volume of conical part) + (volume of hemispherical part)
V = (100π√115)/3 in³ + 2000π/3 in³
V = (100π/3)(20 + √115) in³
V ≈ 3217.39 in³

4 0

3 years ago