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
exis [7]
2 years ago
10

Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k

> 0. Are Rectangle 1 and Rectangle 2 similar? Why or why not? Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1. Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1. Answer:
Mathematics
1 answer:
Alika [10]2 years ago
8 0

Yes, the two rectangles are similar, because rectangle 2 is a dilation of rectangle 1.

<h3>Are the two rectangles similar?</h3>

We know that rectangle 1 has dimensions L and W.

And rectangle 2 is made by multiplying the dimensions of rectangle 1 by a factor k > 0.

Then, rectangle 2 is just a dilation of rectangle 1, this means that in fact, the two rectangles are similar by definition.

Then:

Dimensions of rectangle 1:

  • Length = L
  • Width = W.
  • Perimeter = 2*(W + L)
  • Area = W*L

For rectangle 2:

  • Length = k*L
  • Width = k*W
  • Perimeter = 2*(k*L + k*W) = k*(2*(L + W))
  • Area = (k*L)*(k*W) = k²(L*W)

Above we can see that the perimeter of rectangle 2 is k times the perimeter of rectangle 1, and the area of rectangle 2 is k squared times the area of the rectangle 1.

If you want to learn more about similar figures:

brainly.com/question/14285697

#SPJ1

You might be interested in
Suppose you take the Medical College Admission Test (MCAT) and your score is the 32nd percentile. How do you interpret this resu
ExtremeBDS [4]

In Statistics, percentiles are a representation of the relative position of a particular value within a data set. For example, if your exam score is better than k% of the rest of the class. That means your exam score is at the kth percentile.

If your test score is at the 32nd percentile it can be interpreted as follows:

-Your test score is better than only 32 percent of the other scores recorded for the test.

-32 percent of the people who took the admission test have scores which are lower than yours.

7 0
2 years ago
A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.
Vlada [557]

Answer:

a)  y=12000(2)^{\frac{t}{50}}

b)  Approx. 27,569 bacteria

c)  About 103 minutes

Step-by-step explanation:

a)

This will follow exponential modelling with form of equation shown below:

y=Ab^{\frac{t}{n}}

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}

b)

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76

The number of bacteria after 1 hour would approximate be <u>27,569 bacteria</u>

<u></u>

c)

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103

After about 103 minutes, there will be 50,000 bacteria

4 0
3 years ago
Solve for j.<br> 3 + 4<br> 2<br> -3
xeze [42]

Answer:

Hello!

Step-by-step explanation:

How do we solve for j when there is no equation with j in it to solve for j. <em><u>Hope we can help you with this when we get a equation! </u></em>

3 0
3 years ago
Saturday, nola bowled 3 games in her bowling league. she had a mean score of 115. the score of her first game was 110. the score
Elina [12.6K]
110+90+145=345
345 divided by 3=115

so the score of her third game was 145 points.
hope i helped! :)
please rate brainliest!
7 0
3 years ago
Read 2 more answers
A van can travel 18 miles on each gallon of gasoline. at that rate how many miles can the van travel on 15 gallons of gasoline
tensa zangetsu [6.8K]
18 / 1 = x / 15......18 miles to 1 gallon = x miles to 15 gallon
cross multiply
(1)(x) = (18)(15)
x = 270 miles
7 0
3 years ago
Read 2 more answers
Other questions:
  • The area of a rectangle is X queered minus 2X -15 and the length of the rectangle is X +3 find the width of the rectangle The ar
    12·1 answer
  • (20a - 1) ÷ b when a= 2 and b= 13​
    15·2 answers
  • How to write a linear equation for this problem
    6·1 answer
  • Is 9.777..... a whole number, integer,rational number, irrational number, real number.
    6·1 answer
  • A jar contains n nickels and d dimes. There is a total of 234 coins in the jar. The value of the coins is $16.10. How many nicke
    6·2 answers
  • Plzzz help its due by 12
    7·2 answers
  • 4x+5=17-2x systematic method solve the equation and check result​
    13·1 answer
  • 6 eggs in 7 dауs what would be the answer?
    11·2 answers
  • Find the equation of the normal to the circle, whose equation is given below, at the point (1,2).( x − 3 ) 2 + ( y + 2 ) 2 = 20
    12·1 answer
  • The fraction 24/5 lies between which 2 whole numbers?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!