Our friend claims that a rectangle with the same perimeter as △QRS will also have the same area. Is your friend correct? Explain. yes; Any rectangle with a perimeter of 12 units will have an area of 6 units. yes; If a rectangle does not have the same perimeter as △QRS, it will not have the same area, so your friend's statement is correct by counterexample. no; A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no; A 1×5 rectangle has a perimeter of 12 units and does not have an area of 6 units, so a counterexample shows that your friend's statement is not correct.

Answers

Answer 1

Answer:

A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no

Step-by-step explanation:

We are given vertices in the attached

To solve this question, we are given vertices, we solve using the formula:

√(x2 - x1)² +(y2 - y1)² when given (x1, y1) and (x2, y2)

We are given Triangle QRS

Where: Q = (-2, 1) , R = (-2, -2), S =(2, -2)

QR : Q = (-2, 1) , R = (-2, -2)

= √(-2 - (-2))² + (-2 - 1)²

= √0² + 3²

= √9

= 3 units

RS : R = (-2, -2), S =(2, -2)

= √(2 -(-2))² + (-2 - (- 2))²

= √4² + (0)2

= √16

= 4 units

QS: Q = (-2, 1), S =(2, -2)

= √(2 -(-2))² + (-2 - 1)²

= √(2 + 2)² + (-3)²

= √4² + 9

= √16 + 9

= √25

= 5 units

The Area of Triangle QRS = 1/2bh

b = base = RS = 4 units

h = height = QR = 3 units

= 1/2 × 4 × 3

= 6 square units

Perimeter of Triangle QRS = QR + RS + QS

=( 3 + 4 + 5)units

= 12 units

Our friend is claiming that a rectangle with the same perimeter as will have the same area as the triangle

The perimeter of a rectangle

= 2L + 2W

12 units = 2L + 2W

12 - 2L = 2W

W = 12 - 2L/2

The Area of a Rectangle = L × W

6 square units = LW

6 = LW

6 = L ×(12 - 2L/2)

6 = 12L - 2L²/2

Cross Multiply

6 × 2 = 12L - 2L²

12 = 12L - 2L²

2L² - 12L + 12

2(L² - 6L + 6)

Therefore, from the calculation above, we can conclude:

A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no.

Our Friend Claims That A Rectangle With The Same Perimeter As QRS Will Also Have The Same Area. Is Your
Answer 2

Answer:

Step-by-step explanation:

Answer:

A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no

Step-by-step explanation:

We are given vertices in the attached

To solve this question, we are given vertices, we solve using the formula:

√(x2 - x1)² +(y2 - y1)² when given (x1, y1) and (x2, y2)

We are given Triangle QRS

Where: Q = (-2, 1) , R = (-2, -2), S =(2, -2)

QR : Q = (-2, 1) , R = (-2, -2)

= √(-2 - (-2))² + (-2 - 1)²

= √0² + 3²

= √9

= 3 units

RS : R = (-2, -2), S =(2, -2)

= √(2 -(-2))² + (-2 - (- 2))²

= √4² + (0)2

= √16

= 4 units

QS: Q = (-2, 1), S =(2, -2)

= √(2 -(-2))² + (-2 - 1)²

= √(2 + 2)² + (-3)²

= √4² + 9

= √16 + 9

= √25

= 5 units

The Area of Triangle QRS = 1/2bh

b = base = RS = 4 units

h = height = QR = 3 units

= 1/2 × 4 × 3

= 6 square units

Perimeter of Triangle QRS = QR + RS + QS

=( 3 + 4 + 5)units

= 12 units

Our friend is claiming that a rectangle with the same perimeter as will have the same area as the triangle

The perimeter of a rectangle

= 2L + 2W

12 units = 2L + 2W

12 - 2L = 2W

W = 12 - 2L/2

The Area of a Rectangle = L × W

6 square units = LW

6 = LW

6 = L ×(12 - 2L/2)

6 = 12L - 2L²/2

Cross Multiply

6 × 2 = 12L - 2L²

12 = 12L - 2L²

2L² - 12L + 12

2(L² - 6L + 6)

Therefore, from the calculation above, we can conclude:

A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no.


Related Questions

Suman monthly income rs 25000 he spend 1/5 of his income for house rent and 3/5 of his income an.other exp enditure how much did he save every month

Answers

Answer:

₹ 5000

Step-by-step explanation:

Income= ₹ 25000

House rent = 1/5 of 25000

                  = [tex]\frac{1}{5}*25000[/tex]

                 = ₹ 5000

Other expenditure = 3/5 of 25000

                              = [tex]\frac{3}{5}*25000[/tex]

                              = 3 * 5000

                              = ₹ 15000

Savings = 25000 - ( 5000 + 15000)

              = 25000 - 20000

              = ₹ 5000

Answer:

I will return to this question in 3 minutes....please wait.

It is the middle of the night and yeah

Step-by-step explanation:

thougth ri4rng4g 3i45uto34jkmt

700 decreased by 62% is?

Answers

Answer:

The answer I got was 266

Step-by-step explanation:

700 - 62% = 266

62% = 434

700 - 434 (62%) = 266

Slope from two points
What is the slope for a line that passes through (10, 17) and (7, 8)?
Your answer

Answers

Answer:

slope is 3

Step-by-step explanation:

10,17

7,8

8-17=-9

7-10=-3

-9/-3=3

A negatively charged balloon comes close to a positively charged cloth. What will happen​

Answers

Answer:

It will attract and move towards each other

Answer: The balloon will be attracted to the cloth i hope this helps :D

Step-by-step explanation:

Solve the following inequality: 2x^2 + x - 1/x^2-x<1​

Answers

Answer:

−1<x<0 or 0<x<1

Step-by-step explanation:

Answer:

I believe it is : -1 < x < 0 OR 0 < x < 1

Or if you want it in interval notation form:

(-1, 0) ∪ (0, 1)

Step-by-step explanation:

hope this helps, lol! <3

What is the slope of the line shown?

Answers

Answer:
Slope = rise/run = 3/2

Answer:

3

Step-by-step explanation:

Subtract the two points on the graph, i did (2,-6) and (4,0), you then get 6/2, simplify that and you get 3

∠A and \angle B∠B are supplementary angles. If m\angle A=(2x-14)^{\circ}∠A=(2x−14)

and m\angle B=(3x-6)^{\circ}∠B=(3x−6)

, then find the measure of \angle A∠A.

Answers

Answer:

∠ A = 66°

Step-by-step explanation:

Supplementary angles sum to 180° thus

∠ A + ∠ B = 180 , substitute values

2x - 14 + 3x - 6 = 180 , that is

5x - 20 = 180 ( add 20 to both sides )

5x = 200 ( divide both sides by 5 )

x = 40

Thus

∠ A = 2x - 14 = 2(40) - 14 = 80 - 14 = 66°

Plz answer it’s timed

Answers

Answer:

1,5

Step-by-step explanation:

cuz it's part of the green

9x + 3 = 6x - 12 + 3x

Answers

0=−15

Step-by-step explanation:

subtract 3 from both sides

9+3=9−12

9+3−3=9−12−3

simplify

9=9−15

subtract 9x from both sides

9=9−15

Simplify again and combine like terms and you should get  0=−15

Select the parent function and its graph.

Answers

Answer:

The first one

Step-by-step explanation:

Answer:

first function, second graph

Step-by-step explanation:

got it right in plato :DDD

The price of a car decreases by 35% to £13000.
What was the car worth before the decrease?

Help

Answers

Answer:

€20,000

Step-by-step explanation:

% decrease = (original price of the car - new price) ÷ original price × 100

Let "x' represents the original price before the decrease.

New price = €13,000

% decrease = 35%

Plug in the values into the equation

[tex] 35 = \frac{x - 13,000}{x}*100 [/tex]

[tex] 35 = \frac{100x - 1,300,000}{x} [/tex]

Multiply both sides by x

[tex] 35*x = \frac{100x - 1,300,000}{x}*x [/tex]

[tex] 35x = 100x - 1,300,000 [/tex]

Subtract 100x from both sides

[tex] 35x - 100x = 100x - 1,300,000 - 100x [/tex]

[tex] -65x = -1,300,000 [/tex]

Divide both sides by -65

[tex] \frac{-65x}{65} = \frac{-1,300,000}{65} [/tex]

[tex] x = 20,000 [/tex]

The car was worth €20,000 before the decrease.

Find the value of x.

Answers

in this problem x equals 10

Step-by-step explanation:

jd

Answer:

13

Step-by-step explanation:


If Jodi walks 1 hour and 17 minutes, explain how you would convert this to
a decimal AND give how many hours this is.

Answers

Answer:

Step-by-step explanation:

17 minutes is 17/60 hours=0.28333 ≅0.283 rounded to the nearest thousandth

Jodi walked for  1.283 hrs.

See attachment for math work and answer.

Jose takes 120 minutes to weed 6 equal rows of vegetable plants in his garden. What is his unit rate
per hour for weeding these rows of his garden?
The unit rate is
rows per hour or
1.

Answers

Answer:

3 rows/hour

Step-by-step explanation:

It is given that, Jose takes 120 minutes to weed 6 equal rows of vegetable plants in his garden.

120 minutes = 2 hours

We need to find the unit rate per hour for weeding these rows of his garden. It can be calculated as follows :

[tex]R=\dfrac{6}{2}\\\\R=3\ \text{rows/hour}[/tex]

So, the rate for weeding these rows of his garden is 3 rows per hour.

10. Which of the following rational numbers is the smallest?Required to answer. Single choice.

(1 Point)

4/7

-26/7

0

-1.6​

Answers

Step-by-step explanation:

-26/7 = -3 5/7

Because that is the smallest

'Hope it would help'

Answer:

0

Step-by-step explanation:

0 is the smallest rational number.

can somebody help me pleaseee ?? it’s due soon & im stuck .

Answers

Answer:

a. lenqth=32 , width=2

b. m∠p=100  m∠Q=50  m∠R=30

c. XY=20  YZ=12

d.m∠1=90    m∠2=90

Step-by-step explanation:

a. the area of a rectangle is length×width so to find the possible sizes for L and W we need to list the factors (multiplication of two numbers to get 64) of 64, which are,

1  AND  64   (this answer is suitable but it's better to choose another

one if available for more accuracy)

2  AND  32  (this is a good answer to use)

4  AND 16   (this one already used in the question)

8   AND  8   (this answer will be wrong as the sizes need to be different because it's a rectangle but it will be good for square)

SO we will choose 2 AND 32 for the answer and we can put them in any order we want.

b. first of all acute angles are angles measured less than 90 degrees. so to have at least one angle not acute we use measures up to 90 degrees.

I will put one answer as 100 degrees (note you can use any number above 90 to not be an acute angle) and the other answers will be two numbers add up to be 80 degrees (and again you can choose any numbers for that).

c. the two answers should add up to be 32 so for this counterexample we can choose any two numbers to have the sum of 32 (remember that 16+16 already chosen in the question.

d. two supplementary angles are two angles add up to be 180 degrees so for this question we need to find two angles sum to 180 and not obtuse (that mean 90 degrees or less) and the only answer can appear is 90+90=180.  

please please pleaseee

Answers

Answer:

a. C= 5/9(F-32)

Step-by-step explanation:

you have to subtract 32 from both sides so that leaves you with f-32=9/5c and so then you need to multipy each side my 5/9 and that leaves yoh with 5/9(f-32)=c

find the coordinates of the midpoint of a segment with the given endpoints 3.)P(-12 -9) Q(2,10) help plz ​

Answers

Answer:

(-5, 0.5)

Step-by-step explanation:

-12+2/2= -5

-9+10/2= 0.5

(-5, 0.5)

Tomas and Kyle each bought a shirt at the school store. Tomas gave the cashier a $20 bill and received $6.15 in change. Kyle gave the cashier a $10 bill and received $1.06 in change. Which statement about the cost of the shirts is true? Tomas's shirt costs $5.09 more than Kyle's shirt. Kyle's shirt costs $5.09 more than Tomas's shirt. Tomas's shirt costs $4.91 more than Kyle's shirt. Kyle's shirt costs $4.91 more than Tomas's shirt.

Answers

Answer:

The answer is C

Step-by-step explanation:

I took the test

Answer:

It is C

Step-by-step explanation:

Part A: A keypad lock asks you to input a four-digit code. If you can choose any digit, 0 through 9, for each of the four digits, how many possible combinations are there? Part B: Suppose the similar keypad lock asks for a four-digit code but does not allow you to repeat a digit. How many possible combinations are there for this lock?

Answers

Answer:

A. 10,000 combinations

B. 5,040 combinations

Step-by-step explanation:

A. four-digit code from 0-9 without restriction

1st digit - 10 options

2nd digit - 10 options

3rd digit - 10 options

4th digit - 10 options

Number of possible options = 10 * 10 * 10 * 10 = 10^4 = 10,000 combinations

b. No repetition of digits

1st digit = 10 options

2nd digit = 9 options

3rd digit = 8 options

4th digit = 7 options

Number of possible choices = 10 * 9 * 8 * 7 = 5,040 combinations

Given the function g(x)= -3x+2, find the following:
f(1)=
f(-1)=
Write your answers as ordered pairs.
Hurry please help!

Answers

Answer:

(-1,5)

Step-by-step explanation:

Find ‘k’ if 2 k- 1, 7, 11are in A.P.

Answers

Given:

• 2k -1 , 7 and 11 are in AP .

To find :

• The value of k .

Solution :

• As we know that , In AP common difference is same .

• b - a = c - b

=> 2b = a + c

Here :

• a = 2k-1

• b = 7

• c = 11

=> 2 (7) = 2k-1+11

=> 14 = 2k+10

=> 2k = 14-10

=> 2k = 4

=> k = 4/2

=> k = 2 .

Hence ,the value of k is 2 .

Hope it will help you.

Regards.

m.c.m (3, 16, 2) ?? please help

Answers

B I got it on edg 2020 in may last year

[tex]\bf \colorbox{black} {\bf {\textcolor{blue}{topic = }{ \bf { \textcolor{orange}{mathematics = }{ \bf{ \textcolor{cyan}{answer = }}}}}}}[/tex]

M.C.M=

[tex] \bf \textcolor{red}{ \huge{48}}[/tex]

3-16-2|2

3-8-1 |2

3-4-1 |2

3-2-1 |2

3-1-1 |3

1-1-1

2⁴•3

M.C.M=

2•2=4

2•2=4

4•4=16

16•3=48

[tex] \bf \textcolor{green}{ \underbrace{48}}[/tex]

xLasersx✨

Worth all my points plus brainliest!!! Due in 4 hrs 1-11

Answers

Answer:

1. 15

2. -8/9

3. 5

4. 7

5. a = 20

6. n = 100

7. 3.6 x 10^1

8. 3

9. 4

10. 8.37 x 10^5

11. 6.67 x 10^3

Denise buys a $100,000 condo using a $20,000
down payment on a 30-year fixed-rate loan.
After 5 years of payments, she's made
approximately $24,000 in payments and still
owes approximately $75,000. How much
equity does Denise have in her house? *

Answers

$25,000 because she still owes $75,000.

Find the solution set of the inequality
52−3x<−14.

Answers

Step-by-step explanation:

52 + 14 < 3x

66 < 3x

66/3 < x

22 < x

Answer:

x > 22

Step-by-step explanation:

52- 3x<-14

-3x < -14 -52

-3x < -66

x > 22

Write an expression for: The sum of 5 times a number and twice a number is 42.

Answers

Answer:

42

Step-by-step explanation:

5x5=40  ---->  40+2=42

6 times a number is 27 less than the square of that number. Find the positive solution

Answers

Answer:

6n = 27 - n^2

n = 3

Step-by-step explanation:

This is the answer because:

1) Solve for  n  by simplifying both sides of the equation, then isolating the variable.

Hope this helps!

George filled 10 mugs with coffee. Each mug had 240 mL

Answers

Answer: 2400 mL is the answer.

Answer:

I don't know what you're asking but if the question is how many mL was there all together the answer would be 2,400 mL

Step-by-step explanation:

10 x 240

What is the value of cos(15°)?

Answers

Answer:

The answer is C. [tex]\frac{\sqrt{6} + \sqrt{2} }{4}[/tex]

Step-by-step explanation:

The value of cos(15°) is (√(6) + √(2))/4.

The correct option is C.

What is half-angle formula?

The half-angle formula is a trigonometric identity that relates the trigonometric functions of half of an angle to the trigonometric functions of the original angle.

Using half-angle formula for cosine

cos(x/2) = √((1 + cos(x))/2)

In this case, x = 30°, so we have:

cos(15°/2) = √((1 + cos(30°))/2)

cos(15°/2) = √((1 + √(3)/2)/2)

Now, rationalize the denominator:

cos(15°/2) = √((2 + √(3))/4)

cos(15°/2) = √((1/2 + √(3)/4))

Finally, we factor the numerator by multiplying it by (√(2) + √(6))/(√(2) + √(6)):

cos(15°/2) = (√(2) + √(6))/(2√(2))

cos(15°) = (√(2) + sqrt(6))/(2√(2))

By rationalizing the denominator further, we get:

cos(15°) = (√(2) + √(6))/(2√(2))  (√(2)/sqrt(2))

cos(15°) = (√(2)√(2) + √(6)√(2))/(2√(2)√(2))

cos(15°) = (2 + √(12))/(2 x 2)

cos(15°) = (2 + 2√(3))/(4)

cos(15°) = (√(6) + √(2))/4

Therefore, the value of cos(15°) is (√(6) + √(2))/4.

Learn more about Half angle Formula here:

https://brainly.com/question/30400810

#SPJ2

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