Answer:
The statement is true is for any [tex]n\in \mathbb{N}[/tex].
Step-by-step explanation:
First, we check the identity for [tex]n = 1[/tex]:
[tex](2\cdot 1 - 1)^{2} = \frac{2\cdot (2\cdot 1 - 1)\cdot (2\cdot 1 + 1)}{3}[/tex]
[tex]1 = \frac{1\cdot 1\cdot 3}{3}[/tex]
[tex]1 = 1[/tex]
The statement is true for [tex]n = 1[/tex].
Then, we have to check that identity is true for [tex]n = k+1[/tex], under the assumption that [tex]n = k[/tex] is true:
[tex](1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}[/tex]
[tex]\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}[/tex]
[tex]\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}[/tex]
[tex]k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot (2\cdot k +1)^{2} = (k+1)\cdot (2\cdot k +1)\cdot (2\cdot k +3)[/tex]
[tex](2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)[/tex]
[tex]k\cdot (2\cdot k - 1)+3\cdot (2\cdot k +1) = (k + 1)\cdot (2\cdot k +3)[/tex]
[tex]2\cdot k^{2}+5\cdot k +3 = (k+1)\cdot (2\cdot k + 3)[/tex]
[tex](k+1)\cdot (2\cdot k + 3) = (k+1)\cdot (2\cdot k + 3)[/tex]
Therefore, the statement is true for any [tex]n\in \mathbb{N}[/tex].
The price of a necklace was reduced from $30 to $21. By what percentage was the price of the necklace reduced
Answer:
= 30% decrease
3 x 8 - 4 divided by 2 + ½
Answer:
8Step-by-step explanation:
24 - 4 / 2 1/2 =
20 / 2 1/2 =
20 / 5/2 =
20 x 2/5 =
4 x 2 = 8
Hope that helps!
Answer:
10 1/2
3 times 8 =24
24-4=20
20/2=10
10+ 1/2 = 10 1/2
16/25 as a percentage
Answer:
64%
Step-by-step explanation:
16/25 = 0.64
0.64*100 = 64
64%
Which expression is equivalent to -2(9y-3)
a) -18y + 6 c) -18y -3
b) -18y - 6 d) 18y + 6
Answer:
a. -18y+6
Step-by-step explanation:
i hope this helps :)
What is the measure of the missing angle?
Answer:
28 degrees
Step-by-step explanation:
85 + 67 = 152
180 - 152 = 28
Answer:
X = 28
Step-by-step explanation:
85
+67
=152
180
-152
=28
the width of a rectangle is 2 in less than its length the area is 24 square inches find the dimensions of the rectangle
Answer:
6,4
Step-by-step explanation:
Create a system of equations
l-2=w
w*l=24
Substitute
l-2*1=24
l=6
6-2=4
w=4
Dimensions of the rectangle are 6inch and 4 inch.
What is rectangle?
"Rectangle is a quadrilateral whose all angles are right angle and opposite sides are parallel and equal in measurement."
What is dimensions?" Dimension is measurement of any object such as length, width and height of any object."
What is area?"Area is a space occupied by an object."
Let 'l' be the length of the rectangle.
According to the question,
Width = l - 2
Area= 24 square inches
Formula used
Area of a rectangle = length x width
[tex]24 = l[/tex] × [tex](l-2)[/tex]
⇒[tex]24[/tex] = [tex]l^{2} -2l[/tex]
⇒ [tex]l^{2} -2l -24=0[/tex]
⇒[tex]l^{2} -6l+4l -24 =0[/tex]
⇒[tex]l(l-6) +4(l-6) =0[/tex]
⇒[tex](l-6)(l+4) =0[/tex]
⇒[tex]l=6[/tex] or [tex]l= -4[/tex]
length cannot be negative.
Therefore, [tex]l=6[/tex]inch
⇒width = [tex]6-2[/tex]
⇒ width = 4 inch
Hence the dimensions of the rectangle are 6inch and 4 inch.
Learn more about dimensions of the rectangle here
https://brainly.com/question/22461630
#SPJ2
HELPP MEE PLEASEEEE!!!
Answer:
1) 2
2) -2
3) -8
4) -2
Hope this helps!
Directions: calculate the rise,run, and slope on the line below
Answer: Rise = 3 Run=1 slope=3/1 or just 3
Step-by-step explanation:
start at the left most point and count up to the line that contains the 2nd point
so rise 3
then count over to that 2nd point
so run is 1
slope is rise/run so 3/1
Which of the following is the value for x?
Answer:
67
Step-by-step explanation:
Figure JKLM is dilated by a scale factor of 1 over 3 with the center of dilation at the origin. What are the coordinates for the vertices of the new image?v
Answer:
It’s A
Step-by-step explanation:
I took the test
If it is dilated by a scale factor of 1/3 with the center of dilation at the origin, The new point is at J'(-1, 2), K'(2, 2), L'(1, 1) and M'(0, 1).
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is dilated by a scale factor of k, the new point is at A'(kx, ky).
JKLM has vertices at J(-3, 6), K(6, 6), L(3, 3) and M(0, 3). If it is dilated by a scale factor of 1/3 with the center of dilation at the origin, The new point is at J'(-1, 2), K'(2, 2), L'(1, 1) and M'(0, 1).
Find out more on Transformation at: https://brainly.com/question/1462871
Find the measure of angle B. PLZ I NEED HELP ASAP!!!!!
Answer:
1)D 2)A 3)D 4)A 5)A
I hope this help but in question 6 you can report
HELPP MEEE PLEASEE!!!!
Answer:
Remove 4 anchors or add 4 floats
Step-by-step explanation:
You want your submarine to go UP 4...
"Anchors" make sub go DOWN and "Floats" make sub go UP
HELP YALL I DIDNT STUDY
Find sale price of a $4200 television with a 35% markdown (show work)
Answer:
2730$
4200×35/100
=4200×0.35
=1470$
1470$ is reduced so
4200$-1470$
=2730$
which number line represents the solution to the inequality (will make brainliest) pls help
Answer:
C
Step-by-step explanation:
because the solution dors not include -3 but everything less than.
can someone please help
Answer:
They are congruent.
Step-by-step explanation:
They both are the same shape and size. The side with one line is the same on the other. The side with two lines also matches the other triangle. Lastly, they both have an angle in the same place
Thomas runs 1200m with a constant velocity of 8ms-' before jogging for
the next 200 seconds at a constant velocity of 2ms",
Draw accurate displacement/time & velocity/time graphs for this
run. Draw these directly underneath each other,
Step-by-step explanation:
only attached the displacement/time graph
What is the additive inverse of -5/7x?
PLEASE HELP!!!!! Which graph represents the solution to this set of inequalities?
TYSM! :)
(A,B,C,or D??)
Answer:
a is the answer
Step-by-step explanation:
.......................
Write the equation of a line
containing the point (2, 5) and a
slope of 3 in Point-Slope Form.
Answer:
y=3(2)+5
Step-by-step explanation:
Formula: y = mx + b
m is your slope
x is your x
b is your y added onto
Which equation is equal to 4a + 2b = 10?
Answer:
26
Step-by-step explanation:
2 plus 24 is 26
the sum of three consecutive even integers
Answer:
B
Step-by-step explanation:
Li’s family is saving money for their summer vacation. Their vacation savings account currently has a balance of $2,764. The family would like to have at least $5,000. Which inequality can be used to determine the amount of money the family still needs to save? 2764 + x > 5000 2764 + x Greater-than-or-equal-to 5000 2764 + x Less-than-or-equal-to 5000 5000 + x > 2764
Answer:
B. 2764 + x Greater-than-or-equal-to 5000
Step-by-step explanation:
A. 2764 + x > 5000
B. 2764 + x Greater-than-or-equal-to 5000
C. 2764 + x Less-than-or-equal-to 5000
D. 5000 + x > 2764
Current balance of their account = $2,764
They need a balance of at least $5,000
At least in inequality means greater than or equal to
Let x = remaining balance to make at least $5,000
The inequality is
2764 + x greater than or equal to 5,000
The answer is B. 2764 + x Greater-than-or-equal-to 5000
The inequality that can be used to determine the amount of money she still needs to save is x ≥ $5000 - $2,764.
What inequality can be used to represent the amount that still needs to be save?The following are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe inequality sign to be used is ≥.
The amount that still needs to be saved: x ≥ $5000 - $2764
To learn more about inequality, please check: https://brainly.com/question/5031619
GEOMETRY! I will give brainliest
Answer:
538.8 (4th option)
Step-by-step explanation:
Area of Circle= 3.14(pi) x r^2
Area=615.44
Sector Area = 315/360 x 615.44 = 538
**65 POINTS PLEASE ANSWER SOON**
If the fourth term of an Arithmetic sequence is 48 and the third term is 36...
(A) What is the first term?
(B) What is the twelfth term?
Answer:
1st term is 12
12th term is 144
Step-by-step explanation:
48-36=a4-a3=a1 so a1 is equal to 12 now to get from a3 to a4, you must add 12, so d=12.
a12=12+11*12=12+132=144
Solve for r 4/r 5/7
What’s the additive inverse of -7x + 3 ?? ! please help it’s due at 11:59 and I have waaay more !
Answer:
7x-3
Step-by-step explanation:
The additive inverse is when you add the number with the inverse to get 0.
Help pls ASAP
The population of rabbits in a local park reserve can be modeled by the function r(x) = 25250(1.08), where t represents the number of years.
Which statement is true based on the function?
Answer:
Step-by-step explanation:
Answer:D
Step-by-step explanation:
can someone help me plss
Answer:
the third is correct
Step-by-step explanation:
heat can be produced by - two things