Please help me It’s my birthday!
2. Janyce conjectured that in the visual pattern below, there would be 3n – 1 small
squares in the nth figure
Can you disprove Janyce’s conjecture?
Answers
Step-by-step explanation:
Janyce's rule doesn't work. In the case where n = 3 her rule predicts that there will be 3(3) - 1 = 8 squares but instead, there are 10 squares. Likewise, for n = 4, there are 17 squares instead of 11 that she predicted. Instead, I propose the rule [tex]n^2 + 1.[/tex] It works for all the figures shown and mostly likely, for all other values of n.
2. Part A;
Given that the number of squares obtained using Janyce conjecture for
figures 3 and 4 which are 8 and 11 squares respectively and the number of
squares in the diagram for figures 3 and 4 which are 10 and 17 squares
respectively are not the same, disproves Janyce conjecture
Part B:
The rule for the number of squares in the nth squares is n² + 1
The reasons the above conclusion and rule are correct is as follows:
2. Part A
The given number of squares in each figure are;
[tex]\begin{array}{|c|c|c|}\mathbf{Figure \ number}&\mathbf{Number \ of \ squares} &\mathbf{Janyce \ conjecture \ (3\cdot n - 1)}\\&&\\1&2 \ squares &(3 \times 1 - 1 = 2) \ squares \\2&5 \ squares&(3 \times 2 - 1 = 5) \ squares\\3&10 \ squares &(3 \times 3 - 1 = 8) \ squares\\4&17 \ squares&(3 \times 4 - 1 = 11) \ squares\end{array}[/tex]
Given that the number squares in figure 3, and 4 are;
Figure 3 = 10 squares
Figure 4 = 17 squares
Janyce conjectured number of squares are;
Figure 3 = 8 squares
Figure 4 = 11 squares
The values for the number of squares in the diagram in figures 3 and 4 are different from Janyce conjecture which disproves Janyce's conjecture for the number of squares in the nth figure
Part B
From the diagrams, we have;
The number of squares on the each figure is given by a square shape with a side length equal to the figure number of squares plus one extra square at the top right end corner, we have;
The area of the square part of the shape = n² = The number of squares in the square shape
The number of squares in the nth figure = n² + 1
Verifying, we have;
Figure 1 = (1² + 1) squares = 2 squares (Same as in diagram)
Figure 2 = (2² + 1) squares = 5 squares (Same as in diagram)
Figure 3 = (3² + 1) squares = 10 squares (Same as in diagram)
Figure 4 = (4² + 1) squares = 17 squares (Same as in diagram)
Therefore;
The correct formula for the number of squares in the nth figure = n² + 1
Learn more about the nth term of a sequence here:
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Related Questions
write and solve an equation to find the value of X. please explain in details and show your work!
Answers
Answer:175 degrees
Step-by-step explanation: The shape isn't properly drawn.But,I assumed it is a five sided polygon because of the fifth ange
Find the area of this triangle.
8 m
14 m
A = [?] m2
Answers
Answer:
A = 56 m^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the base and h is the height
A = 12 (14)(8)
A = 56 m^2
Find f(-2) for f(x)=3x^2-8x+7
Answers
Answer:
f(-2) = 35
Step-by-step explanation:
Let x = -2.
[tex]3(-2)^2-8(-2)+7\\\\12+16+7\\\\35[/tex]
Can you conclude that this parallelogram is a rectangle? Explain.
Answers
Answer:
The answer is B.
Step-by-step explanation:
All parallelograms that have congruent diagonals are rectangles.
Find the opposite of: - 4x2 - 4x + 2
Answers
Answer:
4x² + 4x - 2
Step-by-step explanation:
The opposite is the negative value
The opposite of - 4x² - 4x + 2 is
- (- 4x² - 4x + 2) ← distribute parenthesis by - 1
= 4x² + 4x - 2
100000-76585 full formula
Answers
Answer:
Bro it is simple the answer is 23415
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
What is the probability that a normal random variable with mean 6 and standard deviation
3 will fall between 5.7 and 7.5
Answers
Answer:
z-score=7.5-6 1.5
___________=______=0.5
3 3
Step-by-step explanation:
Look up -0.1 on a z-table. The result is 0.4602. The means there is a 0.4602 probability the random variable will be below 5.7.
The find the probability the random variable will be between 7.5 and 5.7, simply subtract the two probabilities we found (above) from one another:
0.6915+-+0.4602+=+0.2313
So, there is a 0.2313 probability the random variable will fall between 7.5+and 5.7.
Let U= {1,2,3,4,5,6,7,8,9,10}, A={2,4,6,8} B={1,2,3,4}, C={5,6,9}
Hello! i need help with these questions
Answers
Answer: 13. is c, 14. is yes and 15 is no
Step-by-step explanation: Try your best and you might succeed
A display case of plastic bracelets are marked 13 for $3. If Nate has $60, how many plastic bracelets can Nate get? (assume no other taxes or fees)
Answers
Answer:
$4
Step-by-step explanation:
We can write a ratio to solve
15 stickers 30 stickers
----------------- = -------------
2 dollars x stickers
Using cross products
15x = 2*30
15x = 60
Divide by 15
15x/15 = 60/15
x = 4
A bag contains 8 red marbles, 4 blue marbles and 7 green marbles. If three marbles
are drawn out of the bag, what is the exact probability that all three marbles drawn
will be red?
Answers
Based on the way you stated the questions, I do not assume the red marble that was pulled first would be put back, so there’s only 18 marbles left to choose from and 7 of those are red. So on the second marble, you have 7/18 chance of pulling a red.
Again, since neither of the first two marbles were put back, you now have 17 marbles left and 6 of those are red. So you have a 6/17 chance of pulling a third red marble.
Multiply those together, 8/19 * 7/18 * 6/17 and you’ll have your answer.
Answer:
NO. OF RED =8
NO. OF BLUE=4
NO. OF GREEN=7
THEREFORE,TOTAL MARBLES=19
THEREFORE,PROBABILTY OF RED MARBLES=8/19.
find the measure of angle of ABF
Answers
Answer: m∠ABF = 120°
Concept:
Here, we need to know the idea of the corresponding angle theorem and linear pair postulate.
The corresponding angle theorem states that if a transversal cuts two parallel lines, their corresponding angles are congruent.
The linear pair postulate states that two angles that form a linear pair are supplementary.
Solve:
Given information
m∠ABF = m∠ABF = 2x + 3x
According to the corresponding angle theorem, ∠ABF is congruent to ∠BCI which is 2x + 4x.m∠BCH = 3x
Total angle = 180°
∠ABF and ∠BCH are linear pairs which means they form a supplementary angle.Given equation
m∠ABF + m∠BCH = Total Angle
Substitute values into the equation
2x + 4x + 3x = 180
Combine like terms
9x = 180
Divide 9 on both sides
9x / 9 = 180 / 9
x = 20
m∠ABF = 2x + 4x = 2 (20) + 4 (20) = 40 + 80 = 120°
Hope this helps!! :)
Please let me know if you have any questions
A radio telescope has a parabolic surface, as shown below.
A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 9 meters and its width from left to right is 12 meters.
If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex?
Answers
Because the roots of the equation are 0 and 12, we know the formula is therefore of the form
y = ax(x - 12), for some a
So put in x = 6
-9 = 6a(-6)
9 = 36a
a = 1/4
So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x
The gradient of this is dy/dx = 0.5x - 3
The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8
Gradient of the parabolic mirror at x = 4 is -1
So the gradient of the normal to the mirror at x = 4 is therefore 1.
Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.
So the focal point is at y = -8, i.e. 1 metre above the back of the dish.
A rectangular plastic tub is 70 centimetres long, 30 centimetres wide, and 30 centimetres tall. How many litres of water will it hold?
Answers
a=70
b=30
c=30
V = 70*30*30
V = 63,000 Cm^3
And in litres we will need to divide by 1000,
1 litres = 1000Cm^3
So:
V =63,000/1000
V= 63 litres
Solve equation 3.2x=25.6
Answers
Answer:
x=8
Step-by-step explanation:
3.2x=25.6
Divide each side by 3.2
3.2x/3.2=25.6/3.2
x =8
Answer:
[tex]x = 8[/tex]
Step-by-step explanation:
[tex]3.2x = 25.6 \\ \frac{3.2x}{3.2} = \frac{25.6}{3.2} \\ x = 8[/tex]
Solve the following using the order of operations 15+5x8
Answers
Answer:
55
Step-by-step explanation:
Order of operations lists Multiplication before Addition.
So...
8 x 5 = 40
40 + 15 = 55
Answer:
55
Step-by-step explanation:
you have to do 5x8 first and you get 40 and then you add 15
I have one flat face 1 curved face 1 edge or corner I am aI have 6 equal square faces 12 edges and 8 vertices I am a
Answers
Answer:
A . sphere B. Square
Step-by-step explanation:
........
A trapezoid has one base measuring 12', and the other measuring 13'8". What is the area in square feet if the height of the trapezoid is 9'4"?
(Remember for trapezoids A= (b1 + b2)/2 x h
Answers
Answer:
Step-by-step explanation:
buzhou一=12212+13。8.12+13.8=25.8 25.8x9.4=?242.52242.522
The area of the trapezoid is given by A = 121.26 feet²
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the area of the trapezoid be represented as A
Now , the equation will be
Let the height of the trapezium be H = 9.4 feet
The shorter base of the trapezium a = 12 feet
The longer base of the trapezium b = 13.8 feet
Now , Area of Trapezoid = ( ( a + b ) h ) / 2
On simplifying the equation , we get
Area of Trapezium A = ( ( 13.8 + 12 ) 9.4 ) / 2
Area of Trapezium A = 121.26 feet²
Hence , the area of trapezium is 121.26 feet²
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Is x^3x^3x^3 equivalent to x^3^3^3
Answers
Answer:
No they aren't equivalent.
Step-by-step explanation:
x^3x^3x^3=x^3^3^3
[tex](x)^{3x^{3x^3[/tex]=[tex]x^{3^{3^3[/tex]
[tex]x^{3x^{9x}[/tex]=[tex]x^{3^{9}[/tex]
[tex]x^{27x^{2} }[/tex]=[tex]x^{27}[/tex]
Apply log on both sides
27[tex]x^{2}[/tex]logx=27logx
27[tex]x^{2}[/tex]logx/27logx=1
[tex]x^{2}[/tex]=1
This is true if x=1 , -1.
The values are equivalent if x=1 and -1 , otherwise no they aren't equivalent.
brainiest to whoever right !
Answers
Answer:
m<RST = 32°
m<TSQ = 58°
Step-by-step explanation:
m<RST here, meaning the angle of the whole diagram is 90 degrees as you can see.
m<RSQ + m<TSQ = m<RST
15x — 43 + 8x + 18 = 90
23x — 25 = 90
+25 +25
---------------------------
23x = 115
/23 /23
----------------------------
x = 5
Now, plug this into the equation for m<RSQ and m<TSQ to find their values.
m<RSQ = 15x — 43
= 15x - 43
= 15(5) - 43
= 75 - 43
= 32
m<TSQ = 8x + 18
= 8x + 18
= 8(5) + 18
= 40 + 18
= 58
Now, check to see if our values are right or not.
15x — 43 + 8x + 18 = 90
15(5) — 43 + 8(5) + 18 = 90
75 - 43 + 40 + 18 = 90
32 + 40 + 18 = 90
90 = 90 CORRECT
What is the correct answer I will give brainlist only if correct answer ASAP
Answers
Answer:
4 tickets left
Step-by-step explanation:
Dividing 276 by 8 gives you a remainder of 4.
2/3 divided by 3/10
Thanks
Answers
Answer:
[tex] \frac{20}{9} [/tex]
Step-by-step explanation:
[tex] \frac{2}{3} \div \frac{3}{10} [/tex]
➡️ [tex] \frac{2}{3} \times \frac{10}{3} [/tex]
➡️ [tex] = \frac{20}{9} [/tex] ✅
Which equation does not have the same solution as the others
×/3 =3
X + 9 = 12
11 x= 33
X - 2 = 1
Answers
Answer:
the first cuz in
x/3 = 3
x = 9
and in others x = 3
...............
Answer:
x/3=3
Step-by-step explanation:
because is undiferned because x can not be x/3=3
Solve the inequality and enter your solution as an inequality in the box below,
using "<=" for sor">=' for if necessary.
-2(5x + 1) > 48
Answers
Answer:
x < -5
Step-by-step explanation:
-2(5x+1) >48
-10x-2 > 48
-10x-2+2 > 48+2
-10x > 50
p.s : when dividing by a negative number with inequalities, change the sign, i.e. < would then be >....
therefore:
x < -5
Give the equation of a line that passes
through (9,2) and is parallel to:
y = 3x - 6
Answers
Answer:
y = 3x - 25
Step-by-step explanation:
If the line is parallel, it will have the same slope. So, the line will also have a slope of 3.
Plug in the slope and given point into y = mx + b, and solve for b:
y = mx + b
2 = 3(9) + b
2 = 27 + b
-25 = b
Plug in the slope and y intercept into y = mx + b:
y = mx + b
y = 3x - 25
So, the equation of the line is y = 3x - 25
how many inches is in 140 feet?
Answers
Hey there!
The formula for feet to inches is to simply multiply the length value by 12.
So, multiply 140 by 12.
I believe your answer would be 1680 inches.
Hope this helps!
Have a great day!
Answer:
140 feet is 1680 inches. Don't forget to put your units in; your teacher may dock off points for forgetting to put in the unit.
Step-by-step explanation:
A foot is 12 inches, so you must multiply 140 by 12.
[tex]140\times12=1680[/tex]
a rectangular garden is 3 times as long as it is wide .the perimeter is 32m . find the dimensions of the garden
Answers
Answer:
Width= 4
length= 12
perimeter= (16+4)×2
3x+3x+x+x=32, let x be the dimensions
8x=32
x=4
so 3(4)=12
Given MP with M(-12, -5) and P(9, -12), if N lies on MP such that the ratio of MN to NP is 3:4, find the coordinates of N.
Answers
Answer:
(-3,-8)
Step-by-step explanation:
MN:Np=3:4 Let m:n=3:4
Use the formula
xN=(xM*n+xP*m)/(m+n)
yN=(yM*n+yP*m)/ (m+n)
xN= ((-12)*4+9*3)/ (4+3)=-3.
yN=((-5)*4+(-12)*3)/(4+3)=-8.
Which set of ordered pairs represents a function?
{(9,–7), (1, -3), (6, 7), (6, -6)}
{(-7,7), (5,3), (-7, -7),(1, -9)}
{(8,-6), (-9,2), (-9, -8), (-3,4)}
{(-5, -5),(-9,0),(-8,5), (-6,5)}
Answers
Answer:
{(-5, -5),(-9,0),(-8,5), (-6,5)}
Step-by-step explanation:
A function cannot have a domain that is assigned to multiple values (range).
The first set has 6 assigned to both 7 and -6.
The second set has -7 assigned to both 7 and -7.
The third set has -9 assigned to both 2 and -8.
for the following geometric sequence find the explicit formula. {12, -6, 3, ...}
Answers
Answer:
It's geometric sequence where a_1=12, q=-\dfrac{1}{2}a
1
=12,q=−
2
1
So a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}a
n
=12⋅(−
2
1
)
n−1
Answer:
[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex]
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 12 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then
[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex] ← explicit formula
1 A recipe for sugar cookies requires 2 cups of
flour for every 2/3 cups of sugar.
At this rate, how many cups of sugar should be used if 5 cups of flour is included?
Answers
Answer:
3 cups of sugar should be used if 5 cups of floue is included