1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tester [92]
3 years ago
14

Please help me Show your work 10 points

Mathematics
1 answer:
Svet_ta [14]3 years ago
8 0
<h2>Answer</h2>

After the dilation \frac{5}{3} around the center of dilation (2, -2), our triangle will have coordinates:

R'=(2,3)

S'=(2,-2)

T'=(-3,-2)

<h2>Explanation</h2>

First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:

(x,y)→(x-2, y+2)

Next, we are going to perform our dilation, so we are going to multiply our resulting point by the dilation factor \frac{5}{3}. Therefore our second partial rule will be:

(x,y)→\frac{5}{3} (x-2,y+2)

(x,y)→(\frac{5}{3} x-\frac{10}{3} ,\frac{5}{3} y+\frac{10}{3} )

Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)

(x,y)→(\frac{5}{3} x-\frac{10}{3}+2,\frac{5}{3} y+\frac{10}{3}-2)

(x,y)→(\frac{5}{3} x-\frac{4}{3} ,\frac{5}{3}y+ \frac{4}{3})

Now that we have our rule, we just need to apply it to each point of our triangle to perform the required dilation:

R=(2,1)

R'=(\frac{5}{3} x-\frac{4}{3} ,\frac{5}{3}y+ \frac{4}{3})

R'=(\frac{5}{3} (2)-\frac{4}{3} ,\frac{5}{3}(1)+ \frac{4}{3})

R'=(\frac{10}{3} -\frac{4}{3} ,\frac{5}{3}+ \frac{4}{3})

R'=(2,3)

S=(2,-2)

S'=(\frac{5}{3} (2)-\frac{4}{3} ,\frac{5}{3}(-2)+ \frac{4}{3})

S'=(\frac{10}{3} -\frac{4}{3} ,-\frac{10}{3}+ \frac{4}{3})

S'=(2,-2)

T=(-1,-2)

T'=(\frac{5}{3} (-1)-\frac{4}{3} ,\frac{5}{3}(-2)+ \frac{4}{3})

T'=(-\frac{5}{3} -\frac{4}{3} ,-\frac{10}{3}+ \frac{4}{3})

T'=(-3,-2)

Now we can finally draw our triangle:

You might be interested in
Classwork: Multiply, Add, and Subtract Polyno
V125BC [204]
I hope this was helpful

3 0
1 year ago
There were 442 students at Deerlake Middle School who voted on a theme for the spring carnival. Those who voted represent 76% of
never [62]

Answer:

Option C is correct.

Step-by-step explanation:

Number of students of Deerlake middle school that voted = 442

Percentage of student that voted = 76%

Let x be the total number of student.

According to the Question,

\frac{76}{100}\times x=442

x=442\times\frac{100}{76}

x=582

Therefore, Option C is correct.

7 0
4 years ago
I need help i dont know how to do it and i dont know the answer
Aloiza [94]

Answer:

125 ft²

Step-by-step explanation:

We know that that surface area of the triangular prism that will be covered with insulation is equal to the area of the two triangular faces, plus the two lateral rectangular faces.

So you get:

SA = 2 [\frac{1}{2}\\(15)(15)] + 2 [(30)(15)] = 1,125 ft²

3 0
3 years ago
Identify the slope and y-intercept:<br> y = -1/5x+12<br> Slope:<br><br> y-intercept:
ipn [44]

Answer:

Slope: -1/5  y-intercept: 12

Step-by-step explanation:

y = -1/5x + 12

The equation given is the slope-intercept form, y= mx + b

In this equation, the m, or number in front of the x, is the slope of the line.

The b in the equation represents the y-intercept.

Therefore, according to the given equation, the slope is -1/5 and the y-intercept is 12.

8 0
3 years ago
The scale of a map is 1 cm: 77 km.
laiz [17]

\bf \stackrel{map}{1~cm}\qquad :\qquad \stackrel{actual}{77~km}\qquad \cfrac{map}{actual}=\cfrac{1}{77}~\hfill \cfrac{\stackrel{map}{3}}{\underset{actual}{a}}=\cfrac{1}{77}\implies 231=a

4 0
3 years ago
Other questions:
  • What is the area of the object Below?
    15·2 answers
  • 14. All phone numbers consist of a three-digit area code, a three-digit exchange, and then a four-digit number. A town uses the
    12·1 answer
  • How do you balance this?<br> Al + CuCl2 = AlCl3 + Cu
    10·1 answer
  • Please help me answer this geometry question!
    10·1 answer
  • Angle is in standard position, if sin(0) = -1, and A&lt;$&lt; 3,4, find cos(O).<br> Why?
    13·2 answers
  • Last one question plzzzz make it work plzzzz
    7·1 answer
  • Please help. no links
    5·1 answer
  • I WILL GIVE BRAINLIEST IF ITS CORRECT
    12·1 answer
  • Peter says if you subtract 13 from my number and multiply the difference by -6, the result is -42. What is Peters's number?
    13·2 answers
  • The height of the rectangle and the triangle are the same. The base of the triangle is half the base of the rectangle.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!