Base case: if n = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for n = k, namely that k ² - k is even. This means that k ² - k = 2m for some integer m.
Induction step: show that the assumption implies (k + 1)² - (k + 1) is also even. We have
(k + 1)² - (k + 1) = k ² + 2k + 1 - k - 1
… = (k ² - k) + 2k
… = 2m + 2k
… = 2 (m + k)
which is clearly even. QED
i need help please and thank you
Answer:
the length of each shape will alternate between even numbers and is numbers.
Step-by-step explanation:
just think !
there are 3 cubes in the basic shape.
now, with every step he adds 1 more cube to the length, and one more cube to the height. that means 2 more cubes.
so, it goes 3, 5, 7, 9, ... cubes
therefore, the first answer is wrong. the shape in every step will always have an uneven (odd) number of boxes. remember, adding an even number to an uneven number will always result in an uneven number. only uneven and uneven or even and even can have even results.
but the length itself - he only adds there one box at a time, will go
2, 3, 4, 5, 6, ...
so, it will alternate between even and uneven numbers.
State the gradient of the line perpendicular to the line y=3x-2
Answer:
-1/3
Step-by-step explanation:
3 is the gradient of the other line
m1×m2=-1 (equation for perpendicular lines)
m1×3= -1
m1= -1/3
Pls confirm if its correct
correct me if wrong
thanks! :)
Use the diagram to the right.
If AD = 17 and AC = 2y - 6, find the value of y. Then find AC
and DC.
Step-by-step explanation:
if AD =17,then Dc is also 17 because from the diagram,it is given that AD=DC.
And because AD and DC are equal,it means AC = AD +DC,therefore AC = 17+17,AC =34
AC=2y-6
therefore
34=2y-6
28=2y and y=14
Answer:
Step-by-step explanation:
Given that f(x) = 2x³-7x²+7ax+ 16 is divisible by x-a, find
(i) the value of the constant a
(ii) the remainder when f(x) is divided by 2x+1.
Answer:
a = - 2, remainder = 21
Step-by-step explanation:
The Remainder theorem states that if f(x) is divided by (x - a) the remainder is f(a)
Since f(x) is divisible by (x - a) then remainder is zero , then
f(a) = 2a³ - 7a² + 7a² + 16 = 0 , that is
2a³ + 16 = 0 ( subtract 16 from both sides )
2a³ = - 16 ( divide both sides by 2 )
a³ = - 8 ( take the cube root of both sides )
a = [tex]\sqrt[3]{-8}[/tex] = - 2
Then
f(x) = 2x³ - 7x² - 14x + 16
Evaluate f(- [tex]\frac{1}{2}[/tex] ) for remainder on division by (2x + 1)
f(- [tex]\frac{1}{2}[/tex] ) = 2(- [tex]\frac{1}{2}[/tex] )³ - 7(- [tex]\frac{1}{2}[/tex] )² - 14(- [tex]\frac{1}{2}[/tex] ) + 16
= 2(- [tex]\frac{1}{8}[/tex] ) - 7([tex]\frac{1}{4}[/tex] ) + 7 + 16
= - [tex]\frac{1}{4}[/tex] - [tex]\frac{7}{4}[/tex] + 23
= - [tex]\frac{8}{4}[/tex] + 23
= - 2 + 23
= 21
Jaya's mother is 5 years more than three times her age. Find Jaya's age if her mother is 44 years old.
Answer:
Jaya is 13 years old.
Step-by-step explanation:
Let's assume Jaya's age to be x years old.
Jaya's mothers age is (3*x)+5.
3x+5=44
3x=39
x=13.
Hi, Can you solve it?
Answer:
57
Step-by-step explanation:
Customer are charged a late fee of 20% of their bill. This person is a week late on a bill of $200.00 What should we charge for the late fee?
Multiply the amount owed by 20% by changing the percent to a decimal.
20% = 0.20
200 x 0.20 = 40
The late fee is $40
Combine Like Terms
5. Which expression is equivalent to 30x-5y-15x+10 ?
20xy
- 15x-5y+10
10xy+10
15x-5y+10
Answer:
(15x -5y + 10)
Step-by-step explanation:
After you combine like terms and factor the expression that's what you get :)
6-(-11) how to solve
Hi ;-)
Calculate
[tex]6-(-11)=6+11=\boxed{17}[/tex]
Answer:
17
Step-by-step explanation:
6-(-11)
Subtracting a negative is like adding
6+11
17
what is the zero turn for the arithmetic sequence 128,96,64,32
You are falling by [tex]32[/tex],
[tex]128, 128 - 32, 128 - 32\cdot2,\dots[/tex]
In general your sequence is defined as,
[tex]a_n=128-32\cdot n[/tex] where [tex]0\leq n \lt\infty[/tex].
The question is at which [tex]n[/tex] does the value [tex]a_n=0[/tex].
If you divide [tex]128[/tex] with [tex]32[/tex] you get the number of steps needed to stuff [tex]128[/tex] with [tex]32[/tex], [tex]4[/tex].
If you plug in [tex]n=4[/tex], you get [tex]a_4=128-32\cdot4[/tex], since [tex]32\cdot4=128[/tex] you get [tex]a_4=0[/tex].
The zero turn of the arithmetic sequence is thus at [tex]n=4[/tex].
Hope this helps :)
Define a variable and write an inequality for each problem. Then solve.
15. Nineteen more than a number is less than 42.
16. The difference of three times a number and 16 is at least 8.
17. One half of a number is more than 6 less than the same number.
18. Five less than the product of 6 and a number is no more than twice that same number.
Answer:
15) n+19<42
16) 3n-16 (less or equal) 8
17) n/2 > n-6
18) 6n-5<2n
Step-by-step explanation:
Let A={5,8}, B={p,q}, C={r,v} How many elements are in A×B?
There are 4 elements in the set A* B
How to determine the number of elements in A * B?The sets are given as:
A={5,8}
B={p,q}
C={r,v}
The expression A * B implies that:
A * B = n(A) * n(B)
Where n( ) implies that the number of elements in......
So, we have
A * B = 2 * 2
This is so because sets A and B have 2 elements each
Evaluate the product
A * B = 4
Hence, there are 4 elements in the set A* B
Read more about sets at
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Find the differential of the function w=x^(4)sin(y^(4)z^3)
Step-by-step explanation:
[tex]w = x^4\sin(y^4z^3)[/tex]
The differential [tex]dw[/tex] is
[tex]dw = 4x^3\sin(y^4z^3)dx [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(4y^3z^3)dy [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(3y^4z^2)dz[/tex]
Find out the area and circumference of a circle of diameter 50cm
Step-by-step explanation:
d=2r.
50=2r
r=50/2
r=25cm.
circumference of circle =2πr
=2×22/7×25
=157cm(approx)
area of circle=πr²
=22/7×(25)²
=704cm
Supplementary angles are pairs of angles whose measures total 180º. Determine the measure of
supplementary to an angle with a measure of 92°
Hi there!
»»————- ★ ————-««
I believe your answer is:
88°
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
As mentioned in the question, supplementary angles add up to 180°.⸻⸻⸻⸻
[tex]\boxed{\text{Setting Up An Equation...}}\\\\a + 92 = 180\\----------\\ a - \text{Unknown angle measure.}\\----------\\\rightarrow a + 92 - 92 = 180 - 92\\\\\rightarrow \boxed{ a = 88}[/tex]
⸻⸻⸻⸻
The unknown angle measurement should be 88°.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Are these answers correct? Thxxx
What is the answer to -(2-k)
Answer:
Step-by-step explanation:
k-2
Answer:
k-2
Step-by-step explanation:
-(2-k) - Expand the brackets
-2+k - Reorder the equation
k-2
find a formula for the arithmetic sequence consisting of the positive multiples of 4
9514 1404 393
Answer:
4n
Step-by-step explanation:
For positive multiple number 'n', the value is 4n.
a[n] = 4n . . . . . where a[n] is the n-th term of the sequence
Answer:
an = 4n
Step-by-step explanation:
got it right on test
Critical Thinking Point M is the midpoint of AB. The coordinates of point A are
(-8, 3) and the coordinates of Mare (–2, 1). What are the coordinates of point B?
Answer:-1,4
Step-by-step explanation:
Your average bi-weekly net pay is $489.00. What is 15% of your average monthly net pay? (1 point)
$146.70
$158.93
$160.13
Bi weekly means you get paid every 2 weeks so you would get two paychecks per month.
Monthly net pay = 489.00 x 2 = $968.00
Multiply monthly by 15%
968 x 0.15 = $146.70
Answer: $146.70
If Your average bi-weekly net pay is $489.00. Your average monthly net pay is:$146.70.
Average monthly net payFirst step
Monthly net pay=$489.00×2
Monthly net pay=$968
Second step
Average monthly net pay:
Average monthly net pay=$968×15%
Average monthly net pay=$146.70
Therefore your average monthly net pay is:$146.70.
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Which of the following is equivalent to?
Answer:
Answer is 1/6
Step-by-step explanation:
[tex] {36}^{ - \frac{1}{2} } \\ = \frac{1}{ {36}^{ \frac{1}{2} } } \\ \\ = \frac{1}{ \sqrt{36} } \\ \\ = \frac{1}{6} [/tex]
Solve for t: 2t/r=d
Step-by-step explanation:
2t/r=d cross multiply
2t=rd
t=rd/2
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I don’t understand this please help.
The width of a rectangle measures (2p - 9q) centimeters, and its length measures
(7p - 10q) centimeters. Which expression represents the perimeter, in centimeters,
of the rectangle?
Given Data : Length = (7p - 10q) and Breadth = (2p - 9q)
Calculation :
⟹ Perimeter = 2(Length + Breadth)
⟹ Perimeter = 2(7p - 10q + 2p - 9q)
⟹ Perimeter = 2(9p - 19q)
⟹ Perimeter = 18p - 38q centimetres
Answer : 18p - 38q centimetresThe required perimeter of the rectangle is 18p - 38q centimeters.
It is required to find the required perimeter of the rectangle.
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
width of a rectangle = (2p - 9q) centimeters,
length measures= (7p - 10q) centimeters.
We know that
⟹ Perimeter = 2(Length + Breadth)
By put the value width and length in perimeter we get,
⟹ Perimeter = 2(7p - 10q + 2p - 9q)
⟹ Perimeter = 2(9p - 19q)
⟹ Perimeter = 18p - 38q centimeters
Therefore, the required perimeter of the rectangle is 18p - 38q centimeters.
Learn more about rectangle here:
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Find the value of x.
9514 1404 393
Answer:
x = 6
Step-by-step explanation:
The angle bisector divides the sides proportionally.
(6x -1)/42 = (10x +5)/78
13(6x -1) = 7(10x +5) . . . . . . . multiply by 546 = LCM(42, 78)
78x -13 = 70x +35 . . . . . . . . eliminate parentheses
8x = 48 . . . . . . . . . . . . . . . . add 13-70x
x = 6 . . . . . . . . . . . . . . . . . divide by 8
What is 12 divided by 2/5?
Answer:30
Step-by-step explanation:
Which of the following is equal to square root of 3 and square root of 6.
Answer:
the answer is the second option which is 6⅓
Answer:
6^1/6
Step-by-step explanation:
Rewriting with the exponents as fractions
(6^1/3) ^1/2
We know a^b^c = a^(b*c)
6^(1/3*1/2)
6^1/6
Find the linear function f if f^-1(2)=-1 and f^-1 (-9)=3
Answer:
[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]
Step-by-step explanation:
We want to find the linear function given that:
[tex]f^{-1}(2) = -1\text{ and } f^{-1} (-9) = 3[/tex]
Recall that by the definition of inverse functions:
[tex]\displaystyle \text{If } f(a) = b\text{ then } f^{-1}(b) = a[/tex]
In other words, f(-1) = 2 and f(3) = -9.
This yields two points: (-1, 2) and (3, -9).
Find the slope of the linear function:
[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(-9) - (2)}{(3) -(-1)} = -\frac{11}{4}[/tex]
From point-slope form:
[tex]\displaystyle y - (2) = -\frac{11}{4}( x- (-1))[/tex]
Hence:
[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]
We can simplify if desired:
[tex]\displaystyle f(x) = -\frac{11}{4}x -\frac{3}{4}[/tex]
9.00391 to the nearest ten-thousandth
Answer:
It is 9.0039
Step-by-step explanation:
9 » ones
.0 » tenths
0 » hundredths
3 » thousandths
[tex]{ \boxed{ \bf{9} \: » \: ten - thousandths}}[/tex]
1 » hundred thousandths
Answer:
9.0039
Step-by-step explanation:
If f(x)= 2|x|+3x, then the value of f(-1) is
Answer:
-1
Step-by-step explanation:
f(-1) = 2|-1| + 3(-1)
|-1| = 1
=> f(-1) = 2(1) - 3
=> f(-1) = 2 - 3
=> f(-1) = -1
