Suzie has made a conjecture that the sum of consecutive odd numbers is always a perfect square. The example she used to show this to Timmy is 1 + 3 + 5 + 7+ 16 = 42. However, Timmy was not convinced and made a Venn diagram to find a counter-example, Do you agree with Suzie's conjecture? Use evidence from the Venn diagram to support your response
Answers
Answer:
Of course you don't agree with Suzie's conjecture - if there is a counterexample (and there is) to a conjecture, that conjecture is false.
Additional note:
Any sum of consecutive odd numbers starting with 1 is a perfect square. It can be proven mathematically, but the pleasant "proof" is to look at actual geometrical squares drawn from unit squares (like in your notebook).
When you have a square of NxN (N^2 unit squares), to go to the next square you need to add N on one side, N on a neighboring side, and 1 to fill the missing unit, for a total of adding 2N+1 squares and ending up with (N+1)x(N+1).
Because you can start from a 1x1 square and then add 2*1+1 = 3 to go to 2x2, then add 2*2+1=5 to go to 3x3 and so on.
Step-by-step explanation:
Timmy is not the brightest person for making this Venn diagram. He just needed to find 1 counterexample.
Related Questions
Solve for x.
9x + 1 = 7x - 8x + 4
Answers
Therefore, the answer is 3/10.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Answer:
9x + 1 = 7x - 8x + 4
9x + 1 = -x + 4
9x + 1 - 1 = -x + 4 - 1
9x = -x + 3
9x + x = -x + 3 + x
10x = 3
x = 3/10
Apollo110Research workshop: Generating Research questions and evaluating sources.
Take notes for two sources
Take notes on your second source
Answers
Based on the information, the best research question that Juan should choose will be "How does playing a team sport affect a child's development?"
A research question simply means a question that a researcher wants to answer. It should be noted that choosing a research question is an important element in research.
From the complete question, it should be noted that since Juan is writing a paper about children who play team sports, and he has different research questions, he should choose the one that conveys the research appropriately.
In this case, the best option will be "How does playing a team sport affect a child's development?"
Learn more about research questions on:
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Help help help help help math math math
Answers
Answer:
∠4 = 135°
Step-by-step explanation:
∠4 = the sum of the two remote angles in the triangle. (remote angles are the angles not next to ∠4
∠4 = 80° + 55°
∠4 = 135°
Answer:
<4 = 135
Step-by-step explanation:
I took this test
In the diagram below of triangle K L M KLM, N N is the midpoint of K M ‾ KM and O O is the midpoint of L M ‾ LM . If m ∠ M L K = 3 x + 75 ∠MLK=3x+75, and m ∠ M O N = 93 − 3 x ∠MON=93−3x, what is the measure of ∠ M L K ∠MLK?
Answers
Applying the Corresponding Angles Theorem, the measure of ∠MLK = 84°
Recall:
Corresponding angles are congruent, that is, their angle measures are equal based on the corresponding angles theorem.
The diagram given, showing triangle KLM is in the image attached below.
m∠MLK and m∠MON are corresponding angles, therefore:
m∠MLK =m∠MON
Substitute3 x + 75 = 93 − 3 x
Solve for x3x + 3x = 93 - 75
6x = 18
x = 3
m∠MLK = 3 x + 75
Plug in the value of xm∠MLK = 3(3) + 75
m∠MLK = 84°
Therefore, applying the Corresponding Angles Theorem, the measure of ∠MLK = 84°
Learn more about the Corresponding Angles Theorem on:
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One leg of a 45°-45°-90° triangle is 9. Find the lengths of the other sides.
Answers
Answer:
9, 9√2
Step-by-step explanation:
The ratios of side lengths in a 45°-45°-90° triangle are ...
1 : 1 : √2
The other leg is the same as the first, and the hypotenuse is √2 times that.
The other sides are 9 and 9√2.
2,983,562 to the nearest hurdreth
Answers
Answer:
2,983,562 if you mean hundredth
if to the nearest hundred then 2,983,600
Step-by-step explanation:
A certain music club charges an annual membership fee of $99, in return, its members will be able to buy and download songs at a very low cost of 10 cents each. If Tyna spent a total of $149.30 including the membership fee, how many songs did she buy?
A) 99+10x=149.30
B) 99-10x=149.30
C) 99-0.1x=149.30
D) 0.1x+99=149.30
Answers
Answer:
D). 0.1x+99=149.30
How many songs Tyna Bought:
503 songs
Step-by-step explanation:
Since the membership fee is 99 you don't have to pay for it again
(Until next year that is)
Now it states that every download cost 10 cents or $0.1
So we don't know how many she will buy so we can replace that unknown value with x
So the equation is
0.1x+99=149.30
To solve this you first subtract 99 on both sides:
Which will result in
0.1x=50.3
Divide 0.1 on both sides
So Tyna bought 503 songs
(HOLY THAT IS A LOT OF SONGS)
Hope this Helps!
A car traveled 133 miles in 4 3/4 hours. What was the cars average speed in miles per hour?
Answers
4 3/4 = 19/4
133/(19/4) = 133(4/19) = 1197/19 = 63 mph
plz help me to answer
Answers
22/3 sorry I accidentally deleted steps
Out of 250 million cars on the road in US, about 3.5% are diesel. What percentage are not diesel?
Answers
Answer:
96.5%
Step-by-step explanation:
Answer:
241250000 cars aren't diesel (Basically 96.5%)
Step-by-step explanation:
250 million = 250000000
If we are talking about the percentage of cars that aren't diesel, we have two ways of solving this. (I'm gonna solve for not just percentage but for amount too)
1. Find out the percentage that isn't diesel by subtracting 3.5% from 100% and then multiplying the answer to get the result.
or
2. We find out what 3.5% of 250 million is and then subtract that from 250 million
Now to make this short, I will do the first one.
100-3.5 = 96.5
96.5% x 250,000,000 = 241250000
Can someone do it and explain please? I don’t get it
Answers
360 - 220 = 140
One side looks larger than the other tho so I am not sure.
Describe how to find all the points on a baseball field that are equidistant from second base and third base.
In the figure, m∠DBE=50. Find each of the following.
m∠BEDm angle b e d
m∠BEAm angle b e eh
x
y
BE
BC
Answers
From the given diagram, the following statements are true:
AB = BC
3y = 5y - 22
3y - 5y = -22
-2y = -22
y = 11
Similarly, m<DBE = 50 degrees
m<BED = 90 - m<DBE
m<BED = 90 - 50
m<BED = 40 degrees
Since BE = BC = 3y
BE = BC = 3(11) = 33
Also, 7x - 2 = 40
7x = 40 + 2
7x = 42
x = 6
Get the measure of m<BEA
m<BEA = 7x - 2
m<BEA = 7(6) - 2
m<BEA = 40 degrees
Learn more on angles here: https://brainly.com/question/16281260
what is the complete factorization of the polynomial below
[tex] {x}^{3} - {2x}^{2} + x - 2[/tex]
[tex]a. (x - 2)(x + i)(x - i)[/tex]
[tex]b.(x + 2)(x - i)(x - i)[/tex]
[tex]c.(x + 2)(x + i)(x - i)[/tex]
[tex]d.(x - 2)(x - i)(x - i)[/tex]
Answers
Answer:
[tex]a. \ (x-2)(x+i)(x-i)[/tex]
Step-by-step explanation:
First of all let's notice that [tex](x-i)(x-i)=(x-i)^2 = x^2+2xi-1 \in \mathbb{C}[/tex] while our original polynomial is real. So we can rule out the even options B and D. At this point, if the polynomial has a factor of [tex](x-\alpha)[/tex] it means tha [tex]\alpha[/tex] is a zero of the polynomial. Let's check both 2 (for option a) and -2 (for option c)
[tex]p(2)=2^3-2(2)^2+2-2= 8-8+2-2=0[/tex]
[tex]p(-2)= (-2)^3-2(-2)^2+(-2)-2=-8-8-2-2=-20[/tex]
At this point 2 is a zero, and our final factoring is a[tex](x-2)(x+i)(x-i)[/tex]
HELP ASAP I don't understand
Answers
Answer:
No
Step-by-step explanation:
These are the artists of each subject, not the general function of each genre.
Brainliest for
If f(1) = 9 and f(n) = -4f(n-1) + 4 then find the value of f(3).
Answers
Answer:
132
Step-by-step explanation:
f(1) = 9
f(n) = -4f(n-1) + 4
Let n = 2
f(2) = -4f(2-1) + 4 = -4 f(1) +4 = -4(9) +4 = -36+4 = -32
Let n = 3
f(3) = -4f(2-1) + 4 =-4f(2)+4 = -4 (-32) +4 = 128+4=132
4. The population of a town is modeled by the equation P = 3485e
0.125
, where "P"
represents the population as of the year 2000.
• According to the model, what will the population of the town be in 2010?
In approximately what year will the population reach 50,000 people?
Must answer and show appropriate work for both questions here.
Student's Work
Student's Answer
A. Part A: 11,571 people in 2010
Part B: approx. 22 years
B. Part A: 38,416 people in 2010
Part B: approx. 13 years
C. Part A: 11,571 people in 2010;
Answers
The population of the town be in 2010 will be 121634, and it will take 21 years for the population to get to 50000
The population model is given as:
[tex]P(x) = 3485e^{0.125x}[/tex]
(a) The population in 2010
In 2010, the value of x is 10.
So, we have:
[tex]P(10) = 3485 * e^{(0.125 \times 10)}[/tex]
Evaluate the exponent
[tex]P(10) = 3485 * e^{(1.25)}[/tex]
This gives
[tex]P(10) = 121634[/tex]
(b) Year to reach 50000
This means that P = 50000.
So, we have:
[tex]50000 = 3485e^{0.125x}[/tex]
Divide both sides of the equation by 3485
[tex]14.35 = e^{0.125x}[/tex]
Take natural logarithm of both sides
[tex]\ln(14.35) =0.125x[/tex]
[tex]2.66 =0.125x[/tex]
Divide both sides by 0.125
[tex]21.28 = x[/tex]
Rewrite as:
[tex]x =21.28[/tex]
Approximate
[tex]x =21[/tex]
Hence, the population of the town be in 2010 will be 121634, and it will take 21 years for the population to get to 50000
Read more about population models at:
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Give an expression for f + g.
A. 12x3 + 16x2 - 6x -8
B. 4x2 + 3x + 2
C. 4x2 + 3x - 8
D. 12x3 + 16x2 - 6x
Answers
Answer:
A)62x-8
B)11x+2
C)11x-8
D)62x
Step-by-step explanation:
12×3=36
16×2=32
36+32-6=62x-8
71.841 to the nearest tenth
Answers
71.8
Step-by-step explanation:71.841:
The 4 represents the number that we'll be looking at since 4 is the next position to the right of 8, 8 is in the Tenths place. 4 is in the Hundredths place, and 4 will be the only number that could round up the 8.
How?In order to round, we need to remember how to round numbers:
If the digit is less than 5, the number to the left stays the same.If the digit is greater than, or equal to 5, the number to the left rounds up, or increases by 1. Solve:First, 4<5, meaning that 4 is less than 5.
#1 above is stating that the number to the left of 4 stays the same.
If we use that rule:
71.8 is our answer.
PLS HELP!
For which value of x does each expression make sense:
(square root) -2x^2
(square root) (-2x)^3
(square root) (-2x)^2
Answers
The value of x must be less than zero for the expression to make sense
The value of x must be less than zero for the expression to make sense
The value of x must be greater than zero for the expression to make sense
For each of the expressions to make sense, the values inside the square root must be greater than zero.
For the expression [tex]\sqrt{-2x^2}[/tex]
-2x^2 > 0
x^2 < 0/-2
x^2 < 0
x < 0
The value of x must be less than zero for the expression to make sense
For the expression [tex]\sqrt{(-2x)^3}[/tex]
(-2x)^3 > 0
-8x^3 > 0
x^3 < 0/-8
x^3 < 0
x < 0
The value of x must be less than zero for the expression to make sense
For the expression [tex]\sqrt{(-2x)^2}[/tex]
(-2x)^2 > 0
2x^2 > 0
x^2 > 0
x > 0
The value of x must be greater than zero for the expression to make sense
Learn more on inequality here: https://brainly.com/question/24372553
A book store is hosting a special night in which familles can enjoy a story and craft time. Tickets to the event must be bought ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show or explain how you got your answer.steps please
Answers
Answer:
45
Step-by-step explanation:
just typing this so I'll have 20
Which statement is generally true about retirement?
A. Your income will increase, while your expense will stay the same.
B. Your income will decrease, while your expenses will increase.
C. Your income will increase, while your expenses will decrease.
D. Your income will decrease, while your expenses will stay the same.
Answers
The general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
Retirement is the leaving of one's of occupation. This means you cease to be involved in active service in a job or occupation especially when one is considered old and of retirement age.
During retirement, retirement benefits and pension are usually made available to retirees. However, one's income will come to a decline which makes most people scared of retirement. Keeping up with the standard of living they are used to becomes difficult as income to sustain such may not be available.
Therefore, the general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
Learn more about retirement on:
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Answer:
It's B
Step-by-step explanation:
Just took it
Do not round the answer
Answers
Answer:
75.36
Step-by-step explanation:
Using the formula C = 2πr, we can calculate circumference.
Since we are using 3.14 for π, we plug that and the radius in.
C = 2(3.14)(12).
When you multiply all that you get 75.36
What is the constant term -6+x4-x2
Answers
Answer:
-6
Step-by-step explanation:
A constant term is a term that does not have a variable attached, x4 and x2 are both terms that include a variable, so -6 is the constant term.
which of the following is NOT a rational number, -n its like on top of it, -4/7, 3/5 or 2/3
Answers
Step-by-step explanation:
i am very sorry but I don't know the answer
A mailing carton in the shape of a cube has a volume of 684 cubic inches. What is the length of one side of the carton to the nearest tenth of an inch?
Answers
Check the picture below.
help me please please
Answers
Answer:
i think its D or 14/16
Step-by-step explanation:
Answer:
[tex]\frac{14}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] + [tex]\frac{10}{16}[/tex]
Before adding we require the denominators of both fractions to be common
Multiply numerator/ denominator of first fraction by 4
= [tex]\frac{1(4)}{4(4)}[/tex] + [tex]\frac{10}{16}[/tex]
= [tex]\frac{4}{16}[/tex] + [tex]\frac{10}{16}[/tex] ( now add the numerators leaving the common denominator )
= [tex]\frac{4+10}{16}[/tex]
= [tex]\frac{14}{16}[/tex]
The fraction can be simplified by dividing the numerator/ denominator by 2 to
[tex]\frac{7}{8}[/tex]
I hate to ask for help but I know that’s what you guys are here for. I’ve been stuck on this sample work for over 2 weeks simply cause I don’t understand it. Can any of you tell me the answers or help with it?
Answers
Answer:
Step-by-step explanation:
I am not sure what the first question is asking but yes y does very direction with x.
Lemme know if i can help with anything else
:)
Every week Jim runs 8 miles and bikes 12 miles. Write an ordered pair to represent how many miles Jim runs and bikes in 5 weeks. Use the drop-down menus to complete the sentence. Jim runs Choose... miles and bikes Choose... miles in 5 weeks. The ordered pair would be Choose... .
Answers
The ordered pair to represent how many miles Jim runs and bikes in 5 weeks is (3.33, 5)
Writing an ordered pair to represent how many miles Jim runs and bikes in 5 weeks.From the question, we have the following parameters that can be used in our computation:
Every week Jim runs 8 miles and bikes 12 miles.
This means that we have the ratio
Run : Bike = 8 miles : 12 miles
When he bikes for 5 weeks, we have
Run : 5 weeks = 8 miles : 12 miles
This gives
Run/5 weeks = 8/12
So, we have
Run = 5 weeks * 8/12
Evaluate the products
Run = 3.33 weeks
Hence, the number of weeks is 3.33 and the ordered pair is (3.33, 5)
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Yuan wrote 17 letters to friends each month for x months in a row. Write an expression to show how many total letters Yuan wrote.
Answers
This is because you’re not adding or subtracting months from your 17 letters. So cross A and C out. And you’re not dividing the number of letters by months. So cross B out. You’re left with D and this is correct because 17 letters EACH month. EACH is telling us that you multiply 17 and x.
50 mm = how many cm?
Answers
Answer:
5cm
Step-by-step explanation:
50mm ÷ 10 = 5cm