Geometry: CC 2015 > Chapter 2: Chapter 2 Test >
Conjecture: Twice the number of units in the length of any side of a rectangle is equal to the number of square units in the area of the rectangle.
The area of ABDE is 4 and 2 X AB = 4
The area of ABCF is 2 and 2 x BC = 2.
The area of ABCF is 2 and 2 x AB = 4
The area of ABDE is 4 and 2 x BD = 4
The statement proves that the conjecture is
Answers
Answer:
The area of ABCF is 2 and 2 × AB = 4
The statement proves that the conjecture is false
Step-by-step explanation:
A conjecture is a proposition or conclusion that is presumed to be true or correct but which is based on incomplete details or information
Given the length of the sides of rectangle ABDE, we have;
Length AB = 2 units
Length DE = 2 units
The area of ABDE = 2 × 2 = 4 unit²
Therefore, the area of the rectangle ABDE is equal to 2 × the length of either AB or DE
However, the are of rectangle ABCF = 2 × 1 = 2 unit²
While the area of rectangle 2 × the length of side AB = 2 × 2 = 4 unit², which is not equal to the number of square units in the area of the rectangle.
Therefore;
The area of ABCF is 2 and 2 × AB = 4
The statement (above) proves that the conjecture is false.
Related Questions
math - algebra (9th grade) please include work
Answers
Answer:
Step-by-step explanation:
Y) [tex]\frac{x+4}{8}[/tex] = 3
*multiply both sides by 8 - cancels out 8 in denominator*
x + 4 = 24
*subtract 4 from both sides*
x = 20
E) [tex]\frac{x-5}{2}[/tex] = 1
*multiply both sides by 2 - cancels out 2 in denominator*
x - 5 = 2
*add 5 on both sides*
x = 7
N) [tex]\frac{x+2}{4}[/tex] = 2
* multiply both sides by 4 - cancels out 4 in denominator*
x + 2 = 8
*subtract 2 from both sides*
x = 6
Consider the linear function that is represented by the equation y = 2 x + 2 and the linear function that is represented by the graph below.
Which statement is correct regarding their slopes and y-intercepts?
A. The function that is represented by the equation has a steeper slope and a greater y-intercept.
B. The function that is represented by the equation has a steeper slope, and the function that is represented by the graph has a greater y-intercept.
C. The function that is represented by the graph has a steeper slope, and the function that is represented by the equation has a greater y-intercept.
D. The function that is represented by the graph has a steeper slope and a greater y-intercept.
Answers
Answer:
A
Step-by-step explanation:
Answer:
C. The function that is represented by the graph has a steeper slope, and the function that is represented by the equation has a greater y-intercept.Step-by-step explanation:
Given function
y = 2x + 2And a graph. We can see it is
y = 2.5x + 1A. The function that is represented by the equation has a steeper slope and a greater y-intercept.
FalseB. The function that is represented by the equation has a steeper slope, and the function that is represented by the graph has a greater y-intercept.
FalseC. The function that is represented by the graph has a steeper slope, and the function that is represented by the equation has a greater y-intercept.
TrueD. The function that is represented by the graph has a steeper slope and a greater y-intercept.
FalseWhich equation is correctly setup to solve for x?
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The formula for the hypotenuse of a triangle is:
[a squared] plus [b squared] = c squared
a and b represent the two sides of the triangle.
You would have to square 8 and 4, add them, then take the square root of it to find the length of the hypotenuse.
The first equation is correct.HELP ME HELP ME HELP ME HELP ME
Answers
Answer:
i think it's A i hope it is
Answer:
D
Step-by-step explanation:
Pls easy geometry !! Help asp for Brainly, pls !!
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CO=DO
Now,BC-CO=AD-DO
OB=OA
In triangle BOD and AOC
OB=OA(s)
Angle DOB=angle AOC(A)(vertically opposite angle)
DO=CO(s)
Therefore triangle BOD is congruent to triangle AOC
Hence,DB=CA
Marcus is a recent college graduate. He has $18,000 in student loans. He took out a loan to buy a car and owes $16,000. The car is now worth $14,000. He got his first paycheck and has $1400 in his checking account. What is Marcus' net worth? (Enter the positive or negative dollar amount only.)
Answers
Given :
Marcus is a recent college graduate. He has $18,000 in student loans. He took out a loan to buy a car and owes $16,000. The car is now worth $14,000. He got his first paycheck and has $1400 in his checking account.
To Find :
Marcus's net worth.
Solution :
We know, net worth is given by :
Net worth = $( Total amount owns - Total loan )
Net worth = $( 16000+1400) - ( 18000+14000)
Net worth = $(17400 - 32000)
Net worth = $-14600
Therefore, Marcus' net worth is $-14600 ( He is in a loan of $14600).
Hence, this is the required solution.
Amanda has four boards that are each 64 inches long. She needs to cut each board into multiple pieces that are each 12 45 inches long. How many pieces will she have after she cuts all four boards?
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Answer:
You need to divide 64 by 12/45. Whenever you divide fractions you keep the first number as it is, change the sign to multiplication and write the reciprocal of the second fraction which is you have to flip the fraction. It is going to be 64 times 45/12. Which is 240/1 which is 240.
Step-by-step explanation:
Using simple algebra, it is found that Amanda will be able to cut 20 pieces of [tex]12\frac{4}{5}[/tex] inches length.
What is algebra?Algebra is the branch of mathematics that deals with mathematical operations and symbols operating on numbers, variables and expressions
Let Amanda cut total x pieces
Given that length of each piece =[tex]12\frac{4}{5}[/tex] inches = 64/5 inches
Total length cut for all the pieces can be found by multiplying the number of pieces with length of each piece
∴ Total length cut for x pieces = x × 64/5 = 64/5 x
Given that Amanda has 4 boards for cutting
Length of each board = 64 inches
Total length offered by 4 fours boards for cutting is calculated by multiplying length of each board by 4 .
Total length offered for cutting by 4 boards = 4 × 64 = 256 inches
Therefore,
Total length cut for x pieces = Total length offered for cutting by 4 boards
⇒ 64/5 x = 256
⇒ x = 256/(64/5) = (256×5)/64 = 4×5 = 20
Therefore, There will be 20 pieces cut from all four boards .
Also, Learn more about algebra from the link below:
https://brainly.com/question/24875240
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132 days to 110.4 days
Answers
382.4 days from 132 days t 110.4 days
A music sharing service has an initial fee of $25 and a monthly fee of $6. When a person joins the service, it costs the company $70 to create the new account. Which inequality can be used to determine how many months, m, it would take for the company to stop losing money on a new customer?
Answers
Answer: [tex]25+6m > 70[/tex]
Step-by-step explanation:
Let m = Number of months
Combined charges for music sharing service = 25+6m
Cost of joining to company = $70
According to the question,
Combined charges > Cost of joining to company (To find number of months it would take for this)
[tex]25+6m > 70[/tex] (required inequality)
A father's age is three times the sum
of the ages of his two children.After 5
years his age will be two times the sum
of their ages.Find the present age of the
father
Answers
After 5 years,
Father's age = (x + 5) years
Sum of ages of his children = (y + 10) years
From the given information, we have:
x = 3y ...(1)
and x + 5 = 2(y + 10)
x - 2y = 15 ...(2)
From (1) and (2), we have,
3y - 2y = 15 y = 15
x = 3y = 45
Father's age = 45 years
help me i'm crying
help me
Answers
Answer:
Get a tissue blow your nose and wipe your tears
Step-by-step explanation:
Tell Mommy
Answer:
See below and learn
Step-by-step explanation:
To solve the figure. You need to split the shape up with the lines shown.
Let's solve the top triangle first.
The formula to find the area of a triangle is y = 1/2(b*h)
So the base is 2+2+6 which equals 10. And the height is 4.
So y = 1/2(4*10)
PEMDAS solve parentheses first.
y = 1/2(40)
y = [tex]20cm^{2}[/tex]
Now solve the bottom left one.
y = 1/2(2*2)
y = 1/2(4)
y = [tex]2cm^{2}[/tex]
Now the bottom right triangle.
y = 1/2(6*2)
y = 1/2(12)
y = [tex]6cm^{2}[/tex]
And to solve area of a square is
y = b*h
y = 2*2
y = [tex]4cm^{2}[/tex]
And add all of it up to get
y = [tex]20cm^{2}+2cm^{2} +6cm^{2} +4cm^{2} = 32cm^{2}[/tex]
Area = [tex]32cm^{2}[/tex]
X-5=20 show work pleaseeeeeee
Answers
Answer:
x-5=20
x=20+5 (When bringing -5 to the other side of the equal, it changes to +5)
x=25
equations that are equivalent to 6x-4/2
Answers
Enzo and Beatrice are playing games at their local arcade incredibly ends wins five tickets from every game in the trees wins 11 tickets from every game when they stop playing games Enzo in the trees had won the same number of total tickets what is the minimum number of games that Enzo could have played
Answers
Answer:
22 games
Step-by-step explanation:
In order to find the minimum number of games that Enzo played we need to find the least common multiple of tickets where both Enzo and Beatrice are equal. To do this we simply find all the multiples of the number of games each could have played by the number of tickets per game until we find one in common.
5*1 = 5 11*1 = 11
5*2 = 10 11*2 = 22
5*3 = 15 11*3 = 33
5*4 = 20 11*4 = 44
5*5 = 25 11*5 = 55
... ...
... ...
... ...
5*22 = 110 11*10 = 110
Finally, we can see that the minimum amount of games that Enzo needs to play in order for both Enzo and Beatrice to have the same amount of tickets is 22 games.
Casey is using a recipe that requires 23cups of flour for every 2 cups of milk. If Casey uses 5 cups of milk, how many cups of flour are needed?
Answers
Answer: 57.5
Step-by-step explanation:
To solve this problem, you need to multiply the number of cups of flour per cup of milk times 5.
Step 1: Find how many cups of flour per cup of milk.
23/2 = 11.5 cups of flour per cup of milk
Step 2: Multiply the cups of flour per cup of milk, times the 5 cups of milk.
11.5 * 5 = 57.5 total cups of flour
What is the slope of a line perpendicular to Line AB given A (6,2) and B (-3,2)
Answers
Answer:
slope is undefined
Step-by-step explanation:
Calculate the slope m of AB using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(6, 2) and (x₂, y₂ ) = B(- 3, 2)
m = [tex]\frac{2-2}{-3-6}[/tex] = [tex]\frac{0}{-9}[/tex] = 0
A line with a slope of zero is a horizontal line, parallel to the x- axis.
Thus a line perpendicular to AB is a vertical line parallel to the y- axis.
The slope of a vertical line is undefined
identify the sequence 18,13,8,3,-2 PLZ HELPPPPP
Answers
The common difference between each term is -5. The nth term of the sequence as follows: aₙ = 18 - 5(n-1)
The given sequence is 18, 13, 8, 3, -2.
To identify the pattern in the sequence, we can observe that each term is decreasing by 5. Starting from 18, we subtract 5 to get the next term, and so on. The common difference between each term is -5.
Using this pattern, we can continue the sequence as follows:
-2 - 5 = -7
-7 - 5 = -12
-12 - 5 = -17
-17 - 5 = -22
The extended sequence would be -2, -7, -12, -17, -22.
In terms of the general formula, we can represent the nth term of the sequence as follows:
aₙ = 18 - 5(n-1)
For more such questions on sequence
https://brainly.com/question/7882626
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Chelsea and her friends are making small fruit baskets for their neighbors. They have 90 pears, 45 peaches, and 75 apples. What is the greatest number of baskets they can make if each basket has the same number of pears, the same number of peaches, and same number of apples, with no fruit leftover?
Answers
Answer:
15 baskets
Step-by-step explanation:
This question is a GCF question
The first step would be to find the factors of 45, 75 and 90
The factors of 45 are: 1, 3, 5, 9, 15, 45
The factors of 75 are: 1, 3, 5, 15, 25, 75
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The greatest common factor is 15.
Therefore, the greatest number of baskets they can make if each basket has the same number of pears, the same number of peaches, and same number of apples, with no fruit leftover is 15 baskets
The temperature fell from 0 degrees farenheight to 6 3/5 in 2 1/5 hours. What was the temperature change per hour?
A. -3
B. -4 2/5
C. 3
D. 4 2/5
Answers
Answer with step-by-step explanation:
C: 3
This is because 6 3/5 is a positive number, and 6 3/5 ÷ 2 1/5 = 3
Hope this was helpful! (brainliest please)
1/3 of 12 = 2/3 of ?
Answers
Answer:
I think it's 6
Dhdneoemd
Answer:
6
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] of 12 = [tex]\frac{12}{3}[/tex] = 4
let the number required be n , then
[tex]\frac{2}{3}[/tex] n = 4 ( multiply both sides by 3 to clear the fraction
2n = 12 ( divide both sides by 2 )
n = 6
Thus
[tex]\frac{1}{3}[/tex] of 12 = [tex]\frac{2}{3}[/tex] of 6
Using Oliver’s table, how can you find the unit rate?
Answers
Answer:
Is there a table I can see if I'll be able to help
Answer:
Oliver’s table indicates that for every increase of 2 strides, the distance he travels increases by 7 feet. So, the change in distance divided by the change in stride gives the unit rate.
Step-by-step explanation:
This Is The Sample AnswerReal quick question. need help plz
Answers
All figures with 4 sides have a total of 360 inside it.
ANY HELP IS GREATLY APPRECIATED What is the sign of the product (−4)(6)(9)(3)?
A. Positive, because the products (−4)(6) and (9)(3) are negative and the product of two negative numbers is positive
B. Positive, because the products (−4)(6) and (9)(3) are positive and the product of two positive numbers is positive
C. Negative, because the product (−4)(6) is negative and the product (9)(3) is positive, and the product of a negative number and a positive number is negative
D. Negative, because the product (−4)(6) is negative and the product (9)(3) is negative, and the product of two negative numbers is a negative number
Answers
Answer:
c
Step-by-step explanation:
there's only one negative in the whole equation making it all negative. if there were two negatives it would become a positive
Name a pair of numbers which would represent the slopes of perpendicular lines.
Answers
The graph of a line in the xy-plane passes through the point (1, 4) and crosses the x-axis at the point (2.0). The
line crosses the y-axis at the point (0, b). What is the value of b?
Answers
Answer with step-by-step explanation:
The graph passes through both (1,4) and (2,0)
Thus it's slope is the difference of ordinates over difference of abscissae or -4
Thus the equation becomes y = -4x + b
This b is the required b
At x=2 ; y=0
Thus 0= -8 + b
b=8
graph the solution to the inequality on the number line 3b + 17 _< 4b +23 + 2b
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Answer:
b_>-2 so the circle is going to be on top of -2 and it is going to be closed, going to the right
Convert 65.000.000 to scientific notation.
Answers
Answer:
6.5 x 10^4
Step-by-step explanation:
Answer:0*10^0
Step-by-step explanation:
what is the area of tile 10 in.6 in.and 8 in
Answers
Answer:
480
Step-by-step explanation:
u multiply 10x6x8=480
so the area is 480 inches
someone please help!!
Answers
8x=3
X=3/8
2)3-8•0=3 g(x)=3
3)-5=3-8x
8x=3+5
8x=8
x=1
4)3-8•3=3-24=-19 g(x)=-19
Hope it helps
x + y = -7
-x+ 4y = 17
X=
y =
Answers
Answer:
x= -9, y= 2
Step-by-step explanation:
5y=10
y=2
x+2=-7
x=-9
Answer:
x=-9y=2Step-by-step explanation:
[tex]x + y = - 7[/tex]
[tex] - x + 4y = 17[/tex]
[tex]y = - 7 - x[/tex]
[tex]x = 4y - 17[/tex]
[tex]y = - 7 - 4y + 17[/tex]
[tex]5y = 10 \\ y = 2[/tex]
[tex]x = 4y - 17 = 4 \times 2 - 17 = 8 - 17 = -9 \\ x = -9[/tex]
