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
The area
of this figure
is square inches.
20 in
28 in
30 in.
7 in
25 in.
Answers
Answer:
946 square Inches
Step-by-step explanation:
First, you should split up the shape into parts.
1st part 28x7
2nd part 30x25
We are multplying simply because
Area = Length x Width
Now that we have split up the parts lets multply them and add them togeher.
28 x 7 = 196
30 x 25 = 750
196 +750 = 946
So the area of this figure is 946 square inches.
The volume (V) of a rectangular pyramid can be determined by using the following
formula.
Iwi
V
Where l= the length of the rectangle, w = the width of the rectangle, and h = the heigh
of the pyramid, what is the result of solving this equation for w?
Ow=3V-th
O2 - V +3 - th
V3
th
3V
O w=
Answers
Answer:
[tex]{ \rm{V = \frac{lwh}{3} }} \\ \\ { \rm{3V = lwh}} \\ \\ { \boxed{ \rm{ \: w = \frac{3V}{lh } \: }}}[/tex]
The approximate average distances from the sun to Mars and Mercury are listed
below:
Mars: 2.28 x 108 kilometers
Mercury: 5.79 x 107 kilometers
How many times farther from the sun is Mars? Write your answer in standard
notation, rounding to the nearest tenth.
Answers
Answer:
3.9
Step-by-step explanation:
Your calculator will tell you ...
(2.28×10^8)/(5.79×10^7) ≈ 3.9
Mars is about 3.9 times as far from the sun as Mercury.
Mrs.Lavander and Mr.Lavander just got marriade.They want to build a mansion but....it cause 1563$ and food...569$ there money is 3641$.How much will they spend?
Answers
Answer:
$2132
Step-by-step explanation:
They will spend : 1563+569= 2132 (dollars)
By the way did you copy the right question ? Because i see unnecessary information in this question. Anyway, try to check it again !
the title block in a working drawing indicates that the scale is a ratio of 1 and 5. This means that the real measurement of the machine is five times the what?
Answers
A scale of 1:5 indicates that real measurement of the machine is five times one unit in the drawing.
The title block on a working drawing shows some important details that may be relevant in reading the drawing. One of such important details is the scale of the drawing.
The scale tells us how the size of the drawing relates to the actual size in the real world. Hence, a scale of 1:5 indicates that real measurement of the machine is five times one unit in the drawing.
Learn more about scale drawing: https://brainly.com/question/147532
Examine the figure. What is the measure of angle b?
Answers
Answer:
b =146
Step-by-step explanation:
34 and b form a straight line so they add to 180
b+34 = 180
b = 180-34
b =146
Pls help , congruent triangles exercise.
Answers
Step-by-step explanation:
We can prove KK'M and LL'M are congruent by using ASA (Angle side angle). Angle side angle means that if we know two angles and one side, we can prove that they are congruent.
First, we know that ∠KMK' = ∠LML' because they are alternative angles. (That's our fist A)
Next, The problem states that KK' and LL' are equal. (so that gives our S)
Finally, we know that ∠ML'L and ∠KK'M are both 90 degrees, making them both equal. (That's our final A)
Hope this helped :D
Determine the slope from the given graph below:
The slope is−17
The slope is 5
The slope is 7
The slope is -5
Answers
Answer:
The slope is positive 7
Step-by-step explanation:
The y-intercept is -5, and the next point going upwards is positive 2. (Sorry I'm bad at explaining)
Answer:
The slope is 7
Step-by-step explanation:
(1,2)(0,-5)
[tex]m=\frac{-5-2}{0-1} ==\frac{-7}{-1} =7[/tex]
Hope this helps
Figure B is a scale image of Figure A, as shown.
7
2.5
Figure A
Figure B
Enter the scale factor applied to Figure A to produce Figure B.
Enter your answer as a fraction, like this: 42/53
Answers
Explanation:
Divide the side length for B over the corresponding side length for A.
scale factor = B/A = 7/(2.5) = 2.8
Let's now convert this to a fraction
2.8 = 2 + 0.8 = 2 + 8/10 = 20/10 + 8/10 = (20+8)/10 = 28/10
Then reduce that fraction
28/10 = (14*2)/(5*2) = 14/5
Note that 14/5 = 2.8
Find an equation in the form y=ax^2+bx+c for the parabola passing through the points.
(3,25) (1,3) (-5,-15)
Thanks for the help! :)
Answers
Answer: [tex]x^2+7.0x-5.0x[/tex]
Step-by-step explanation:
REI.C.6 Level 1
below.
2. A student is solving the system,
2x + 3y = 12
5x - 2y = 11
algebraically. Their work is shown below but is unfinished.
Continue where the student left off and solve the system.
2x + 3y = 12
5x - 2y = 11
=
2 (2x + 3y = 12)
3 (5x - 2y = 11)
4x + 6y = 24
15x – 6y = 33
-
Answers
Answer:
The solution is x = 3, y = 2.
Step-by-step explanation:
4x + 6y = 24
15x – 6y = 33 Add these 2 equations:
19x = 57
x = 57/19
x = 3. Now Substitute for x in the original equation:
2(3) + 3y = 12
3y = 12 - 6
2y = 6
y = 2.
How do we graph y+6=45(x+3)?
Answers
Answer:
.....,....................
Please look for the question in the picture.
Answers
Answer:
two negitives equals a positive so C none of the above
Hope This Helps!!!
Answer:
A and B
Step-by-step explanation:
Which is equivalent to the following expression? (2x - 1)(x + 3)
Answers
Answer:
2x2+5x−3
Step-by-step explanation:
Expand the polynomial using the FOIL method.
Which expression is equivalent to -8(10x – 3)?
A) -80x + 24
B) -80x - 24
C) - 80x - 3
D) -80x + 3
Answers
Answer:
-8(10x-3) = -80x+24 = A
Step-by-step explanation:
yr welcome
Simplify:
(8)214+(8)(−12)
plz help :(
Answers
1712-96
Your welcome
From a sample size of 169, it was determined that the 68% confidence interval for the population mean is (505, 517). Therefore, the sample mean was ___. and the margin of error was ___.
A. 511; 6
B. 511; 12
C. 513; 6
D. 513; 12
Answers
Answer:
A. 511; 6
Step-by-step explanation:
The margin of error would be [tex]\pm\frac{517-505}{2}=\pm\frac{12}{2}=\pm 6[/tex]
The sample mean would be [tex]505+6=511[/tex] (or [tex]517-6=511[/tex])
y-5=2(x-3) slope intercept.
Answers
Answer:
y=2x-1
Step-by-step explanation:
Because this equation is in point-slope form and we need it in slope-intercept form, all we need to do is simplify y-5=2(x-3).
y-5=2x-6 Distribute.
+5 +5 Add 5 to both sides of the equation.
y=2x-1
Hope this helped! Have a great day ♥
3 2/3 + 2 3/5 + x = 8
Answers
Answer: x= [tex]-\frac {109}{15}[/tex]
1 A community group is painting classrooms. One 20 litre can of costs R1 699,00. It is then reduced by 6%. Determine the new cost of a 20 litre can
Answers
6.99 = 1%
41.94 = 6%
699,00 - 41,94 = 657.06
Translate the sentence into an inequality.
Six times the sum of a number and 20 is greater than 16.
Use the variable c for the unknown number.
Answers
Answer:
6 (20 + c) > 16
Step-by-step explanation:
the sum of the number and 20 is 20 + c. so you multiply that equation by 6 giving you 6 (20 + c)
PLEASE HELP ME:))
what’s the value of x?
Answers
\[tex]\angle B +\angle C + x = 180^{\circ}\\\\\implies x = 180^{\circ} -\angle B -\angle C\\\\\implies x = 180^{\circ} - 75^{\circ} - 50^{\circ}\\\\\implies x = 55^{\circ}[/tex]
write an equation for the line in standard form that passes through the following points (-2,-3) (-3,-6)
Answers
ANSWER: y = 3x + 3
Ok done. Thank to me :>
Which of the following is equivalent to [picture]
A) a0 + a1 + a2 + a3 + a4 + a5
B) a1 + a2 + a3 + a4 + a5
C) a0 + a1 + a2 + . . .
D) a1 + a2 + a3 + . . . + a∞
Answers
Answer:
A) a0 + a1 + a2 + a3 + a4 + a5
Step-by-step explanation:
Answer:
A) a0 + a1 + a2 + a3 + a4 + a5
Step-by-step explanation:
?/5 =8/10 type the missing number that makes this fraction equal
Answers
look at the picture please also be quick bec
Answers
Don’t know how to do this
Answers
Answer:
[tex]horizontal : 76 \\ \\ \\ vertical : 33 \\ \\ pls \: check \: this \: answer \\[/tex]
A rectangle is 8 feet long. Its width is represented by “seven plus x feet.” Which expression represents the area, in square feet, of the rectangle?
Answers
56 + 8x
Area of Rectangle = Length x Width
Area of Rectangle = 8(7 + x)
solve systems of equations 6x+2y=1 y=-3x+3 using substition??? Need answers quickly!!!!!
Answers
Heheh... uhm, yeah, I don't do best with algebraic questions-
Answers
Answer:it's a for sure I think