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
Given the relation y = −4x2 − 8, if the input is 2, what is the output
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SksisjsjsjsssnksisnsbxnxlxodjsbsbdfjfJ
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A sphere has a diameter of 24 units. What is its volume in cubic units?
A.576pi cubic units
B.1,728pi cubic units
C.2,304pi cubic units
D 6,912pi cubic units
Pls help!!
Answers
Answer:
C.2,304pi cubic unitsStep-by-step explanation:
Volume of the sphere:
V = 4/3πr³Since d = 24 units,
r = d/2 = 12 unitsThen
V = 4/3π(12³) = 2304πCorrect option is C
Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
If cat and dog start running away from each other how far away from each other will they be after 30 minutes?
Answers
Answer;
They will be 0.5x miles away from each other
Explanation;
Since the dog runs twice the speed of the cat
Its speed will be 2 * x = 2x mph
Now we want to know how far they will be from each other after 30 minutes
Kindly note that 30 minutes is 1/2 hour
Mathematically;
distance = speed * time
Distance of cat = x * 1/2 = 0.5x miles
Distance of dog = 2x * 0.5 = x miles
The dog is x - 0.5x miles = 0.5x miles away from the cat
They will be 0.5x miles away from each other.
Calculation of the distance:Since Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
So here the speed of the dog should be 2x
Now we know that
[tex]Distance = speed \times time\\\\[/tex]
Here distance of cat should be x of 30 minutes or half hour = 0.5x miles
And, Distance of dog should be 2x of 0.5 = x miles
So, the difference should be
= x - 0.5
= 0.5x miles
hence, They will be 0.5x miles away from each other.
Learn more about speed here: https://brainly.com/question/1825528
You work in a grocery store warehouse recording shipments. A driver delivers 25 crates of strawberries for distribution. A store calls needing seven crates of strawberries. After you fill this order, how many crates of strawberries are available for other stores?
Answers
Answer:
18 crates
Step-by-step explanation:
Data provided in the question
The Number of strawberries for distribution delivered is 25 crated
Now he seven crates is required
So the remaining crates left is
= 25 - 7
= 18 crates
hence, after filling the order the number of order crates of strawberries is 18 crates and the same is to be considered
Help which one is it
Answers
Answer:
addition of property of equation
Step-by-step explanation:
You have to move the -3 by adding it to both sides and since the other number is negative you get 1
Answer:
Addition property of equality
Jane's garden is 3.4 meters by 6.5 meters. If fencing costs $2.25 per meter, how much will it cost to put fence around her garden?
Answers
$49.73
because you would multiply the length and width of the fence then multiply by the price.
3.4 x 6.5 = 22.1
22.1 x 2.25 = 49.725
but you would round because you are dealing with money
Which graph has a rate of change of zero?
Answers
Answer:
graph #x
Step-by-step explanation:
where are the graphs
Peyton recorded her height twice a year. She grew 5 1/4 inches in 3 1/2 years. What was Peyton’s average growth rate per year?
Answers
Height in which Peyton grew in 3 ½ years = 5 ¼ inches
Height Peyton grows each year =
= 5 ¼ ÷ 3 ½
= 21/4 ÷ 7/2
= 21/4 × 2/7 ( division of fractions is the same as multiplication with reciprocal )
= 42/28
Let us simplify this by dividing the numerator and denominator by 2 .
= 42 ÷ 2 / 28 ÷ 2
= 21/14
= 1 7/14 inches
Peyton's average growth rate per year was 1 7/14 per year . Let us simplify it .
= Both 7 and 14 are divisible by 2 .
So , 1 whole 7 ÷ 2 / 14 ÷ 2
= 1 whole 1/2
= 1 1/2
Therefore , Peyton's average growth rate per year was 1 1/2 inches .
The length between the bases on a baseball field is 90 feet. A scale drawing shows the distance between the bases are 2 1/2 inches. one inch on this drawing equals how many feet?
Answers
Answer:
36
Step-by-step explanation:
Select all the true statements. Group of answer choices The ratio of triangles to squares is 2 to 4. The ratio of squares to smiley faces is 6:4. The ratio of smiley faces to triangles is 6 to 4. There are two squares for every triangle. There are two triangles for every smiley face. There are three smiley faces for every triangle.
Answers
Answer:
The ratio of triangles to squares is 2 to 4
There are two squares for every triangle.
There are three smiley faces for every triangle.
Step-by-step explanation:
The number of triangles, smiley and squares are shown in the diagram attached.
From the diagram, there are 6 smiley faces, 2 triangles and 4 squares.
A ratio compare two or more values, thereby showing how many times one number contains the other.
A) Correct. The ratio of triangles to squares = number of triangle / number of square = 2 / 4 = 2 to 4
B) Incorrect. The ratio of squares to smiley faces = number of square / number of smiley face = 4 / 6 = 4 to 6
C) Incorrect. The ratio of smiley faces to triangles = number of smiley faces / number of triangles = 6 / 2 = 6 to 2
D) Correct. Since the ratio of squares to triangles = number of squares / number of triangle = 4 / 2 = 2 / 1 = 2 to 1, hence there are two squares for every triangle
E) Incorrect. Since the ratio of triangles to smiley faces = number of triangle / number of smiley faces = 2 / 6 = 1 / 3 = 1 to 3, hence there is one triangle for every 3 smiley faces
F) Correct. Since the ratio of smiley faces to triangles = number of smiley faces / number of triangles = 6 / 2 = 3 / 1 = 3 to 1, hence there is 3 smiley faces for every one triangle
Which set of points is a function i will give brainliest if correct♡︎シ☀︎︎
Answers
Answer:
C
Step-by-step explanation:
i think it's C hope this helps you
Answer:
B
Step-by-step explanation:
i think.( am i correct?)
the length of the swimming pool is 8 m longer than its width and the area is 105 m squared write in quadratic equation
Answers
Answer:
Step-by-step explanation:
The length of the swimming pool is 8m longer than it's width.
If we say L = length, W = width
From the information above, we can say
L= 8 + w
We are also told the area is 105 m squared.
Note:
Area of a Rectangle = Length x Width
105 = (8 + w ) x w
[tex]105 = 8w + w^2\\[/tex]
Subtract 105 from both sides:
[tex]w^2 + 8w - 105 = 0[/tex]
An aquarium is being filled at a rate of 2.5 inches per second. The equationLaTeX: y=2.5xy = 2.5 x is used to determine the height of the water after LaTeX: xx seconds. Find the domain and range of the situation if it takes 60 seconds to fill the aquarium.
Answers
Answer:
Step-by-step explanation:
Given the equation y = 2,5x
y is the height of the water
x is the time.
To get the range of values of the height at t = 60s, we will substitute x = 60 into the function
y = 2.5(60)
y = 150 in
Hence the range of the situation is [0, 150].
The domain will be all positive integers i.e xEZ
The cost C, in dollars, for delivered pizza depends on the number p of pizzas ordered. The situation is represented by the function rule C equals 5 plus 9 p. Would the graph be continuous or discrete? Explain your answer.
Answers
Answer: discrete
Step-by-step explanation:
The graph would be discrete, because you can only order a whole number of pizzas. This means you cannot have 0.4 of a pizza or 3/5 of a pizza. Therefore, p can only be whole numbers, so you cannot draw a line through the points, since prices for non-whole pizzas are not possible.
6) The wind blew away 35 of your muffins.
That was 5/6
of all of them! With how
many did you start?
Answers
Answer:
42 muffins
Step-by-step explanation:
In order to find the answer, you would divide 35 by 5/6 which would equal 42. So you started with 42 muffins.
Hope this helps and pls do mark me brainliest if you can:)
f(2) = ? pls helpppppp
Answers
Answer:
-2
Step-by-step explanation:
f(2): take the (2) from the f(2) because that's the x value.
you go to where it's 2 on the x-axis.
f(x)=f(2)
f(x)=y
so you are trying to find the y-axis number when you are at 2 on the x-axis.
whichhh is -2
4. Suppose the the function f(x) = 5x + 7
represents the cost to play x rounds of
golf at the local mini-golf attraction. If you
have $20, how much more money do
you need to play 3 rounds of golf?
A. $22
C. $2
B. $15
D. $5
Answers
Answer:
c
Step-by-step explanation:
c
X+7
——-=9
3
Can you explain step by step on how to solve this problem?
Answers
Answer:
w=−7
Step-by-step explanation:
34+21=−11(w+2)
55=−11(w+2)
-55/11 =w+2
−5=w+2
−5−2=w
−7=w
i need some math help
Answers
Answer:
n = 15
Step-by-step explanation:
Step 1: Write equation
n/3 = 5
Step 2: Solve for n
Multiply both sides by 3: n = 15Answer:
n = 15
Step-by-step explanation:
Step 1: Write equation
n/3 = 5
Step 2: Solve for n
Multiply both sides by 3: n = 15
19. A package of 12 confetti eggs costs $2.88.
At this rate, what is the cost of 1 confetti egg?
Answers
Answer:
0.24$
Step-by-step explanation:
Each egg costs 1/12 of 2.88.
So either you multiply 2.88 by 1/12
or you divde 2.88 by 12
Answer:
0.24
Step-by-step explanation:
you would divide 2.88 by 12 hope this helps.
Alg I Trad Bench 1 Laurel MS 2020-2021 Section 1 8 of 308 of 30 Items Item 8 A taxi service charges a flat rate for the first 3 miles of service. For any additional mileage, the taxi service charges an additional rate per mile, x. The expression 10+2.50(x−3) represents the scenario.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
First 3 miles = flat rate
Subsequent miles = additional rate per mile x
Equation which represents the scenario :
10 + 2.50(x - 3)
If the amount charged by the taxi service for a certain trip is
10 + 2.50(x - 3)
Then. ;
10 = the flat rate charged for the first 3 seconds
2.50 = additional mile charge
x = total trip distance
Hence, (x - 3) = (total trip distance - first 3 miles) = additional miles traveled
A local mechanic charges customers a flat fee of $60 before any work is done in the rate of 85 per hour for labor which equation represents the relationship between the total charge for labor L in dollars and the number of hours worked h?
Answers
Answer:
im not sure but here u go 85x+60
Solve for n
(40-2n)divided by 4=8?
Answers
Answer:
n = 4
Step-by-step explanation:
(40 - 2n) ÷ 4 = 8
10 - 0.5n = 8
-0.5n = 8 - 10
-0.5n = -2
n = 4
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
Answer:
the correct answer is n=4
14. Using 1 inch = 15 feet as the scale factor, what are the blueprint dimensions of a room in a model house that is actually 30 feet x 45 feet?
O2 in x 3 in.
O 3 in 2 in
O2 in x 2 in
O 3 in x 2 in
Answers
0.067318 to 2 significant figures
Answers
In two significant figures it is 0.067.
Need help ASAP Tysm
Answers
Answer:
16.81
Step-by-step explanation:
4.1x4.1=16.81
Candace is a salesperson at the local boat store. She receives a 14% commission on every sale that she makes. How much commission does Candace
make on a boat that sells for $1,995?
Answers
Answer: 00000
Step-by-step explanation:
For The 10% Of People That See This, Hope You Have The Best Day!
Answers
Answer:
Ah thank you, you too from me.
Jose and his mother decide to bake a cake for his Father's birthday. Jose notices that after mixing the cake batter and placing it in the oven he says bubbles forming in the cake as it begins to rise. What explains this Phenomenon? A. Physical Change B. Chemical Change C. Neither physical nor chemical change D. Both physical and chemical change
Answers
Answer:
B) Chemical Change
Step-by-step explanation:
Physical change only changes the physical appearance of good, their chemical properties remaining same. These are usually reversible. Eg : Cutting a cake
Chemical change changes the physical composition of the product(s) involved. These are usually not irreversible. Eg : Baking of a cake, getting bubbles during bake process meanwhile