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:
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.
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
What is the slope of the line shown?
Answers
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
Find ‘k’ if 2 k- 1, 7, 11are in A.P.
Answers
• 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.
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
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.
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.
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
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
Find the value of x.
Answers
in this problem x equals 10
Step-by-step explanation:
jd
Answer:
13
Step-by-step explanation:
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:
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
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:
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)
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
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
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
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
∠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°
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!
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
m.c.m (3, 16, 2) ?? please help
Answers
[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✨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.
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
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.
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.
Plz answer it’s timed
Answers
Answer:
1,5
Step-by-step explanation:
cuz it's part of the green
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
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:
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
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
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