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
The sides in each pair of figures are proportional. Find the missing length.
Answer:
41. is c.
42. is d.
Step-by-step explanation:
How do you model a decimal using a fraction?
Answer:
The only reason I can’t type it right now it’s cause I’m doing something important so I’m so sorry if I hade to type this out but I’m a bit busy right now And I’m trying to answer as much questions as possible. Thank you
Step-by-step explanation:
Hope this helps you
Write down the decimal in fractions with the denominator 1.
We multiply the denominator and numerator by 10 for every number after the decimal point.
Simplify the fraction if needed.
5. (09.06 MC)
The graphs of the polar curves r = sin e-2 and r = cos(20 + 3) are shown.
Find the area of R, which is the region inside r = sin 6-2, but outside r = cos(20 + 3). (10 points)
31.416
12.566
15.708
0 25.133
Answer:
12.566
Step-by-step explanation:
A = ∫1/2(r)^2dtheta from a - b = 0 to 2π
∫1/2(sin^2theta-4sintheta+4)dtheta
[9/4theta+2costheta-1/8sin2theta] from 0 to 2π…
when you solve this you get 14.137 without taking out the cos(2theta+3)
how do you put 300,000+10,000+6,000+20+9
Answer:
three hundred thousand plus ten thousand plus six thousand plus twenty plus nine
Step-by-step explanation:
300,000 → three hundred thousand
10,000 → ten thousand
6,000 → six thousand
20 → twenty
9 → nine
+ → plus
Now put everything together.
Best of Luck!
2ja bag has 3 red and 6 green balls. Two
balls are drawn from the bag one after the
other without replacement. What's the
probability of having a green ball drawn
both times
Answer:
5/12
Step-by-step explanation:
Probability of drawing green ball on the first time=6/9=2/3
Probability of drawing green ball on the second time=5/8
Probability of having a green ball drawn
both times=(2/3)*(5/8)=10/24=5/12
(2x+1)(3x+4)=0
2x+1=0 3x+4=0
Solve for both equations. What are the two x-values/answers going to be? Leave your answer in a simplified fraction.
(I don’t know what to do next)
Answer:
2x+1=0.
2x=0-1.
2x=-1.
2x/2=-1/2.
x=-2.
3x+4=0
3x=0-4
3x=-4
3x/3=-4/3
[tex]x = 1 \frac{1 }{3} [/tex]
-8 + 2x + 17 - x + 20
Study the figure and find the effort.
Please help...
Answer:
300
Step-by-step explanation:
I hope it will help you.
For what values of k will the equation 4x² + 8x + k = 0 have two complex solutions?
Answer:
k = -4x² - 8x
Step-by-step explanation:
Subtract 4x² from both sides of the equation.
8x + k = -4x²
Subtract 8x from both sides of the equation.
k = -4x² - 8x
Answer:
k > 4
Step-by-step explanation:
Using the discriminant to determine the nature of the solutions
• If b² - 4ac < 0 then the solutions are not real, that is they are complex
Given
4x² + 8x + k = 0
with a = 4, b = 8, c = k , then
8² - (4 × 4 × k) < 0
64 - 16k < 0 ( subtract 64 from both sides )
- 16k < - 64
Divide both sides by - 16, reversing the symbol as a result of dividing by a negative quantity.
k > 4
Any value of k greater than 4 will mean the equation has 2 complex solutions
ANSWER QUICK 70 POINTS!!!!!!!!!!!!!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1-Line 2-Associative property .
Line 2-Line 3- Distributive property
Solution:-[tex]\\ \rm\longmapsto (9+x)x[/tex]
[tex]\\ \rm\longmapsto x(x+9)[/tex]
[tex]\\ \rm\longmapsto x(9+x)[/tex]
[tex]\\ \rm\longmapsto x^2+9[/tex]
THE STUDENTS ON THE SCHOOL NEWSPAPER ARE CONTRIBUTING MONEY FOR A GIFT FOR THEIR STAFF ADVISOR. THE COST PER STUDENT FOR THE GIFT VAIES INVERSELY AS THE NUMBER OF STUDENTS WHO CONTRIBUTE. iT WILL COST $6 PER STUDENT IF 12 STUDENTS CONTRIBUTE. HOW MUCH WILL IT COST PER PERSON IF 15 STUDENTS CONTRIBUTE
Answer:
ok
Step-by-step explanation:
Is 1 3/4 closer to 1 or 2 ? Explain your answer
Answer:
it's closer to 2
Step-by-step explanation:
In order to get to 1 from that number, you have to subtract 3/4. In order to get to 2 from that number, you only have to add 1/4. Clearly, the jump in adding is smaller than the jump to subtracting, which means it's closer to 2.
The number is closer to 2
What is fraction?A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.
All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.
The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.Given number:
1 3/4 = 7/4
On dividing
7/4 = 1.75
Hence, the number is closer to 2.
Learn more about fraction here:
https://brainly.com/question/10354322
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Pls help will do brainliest answer
Answer:
[tex]f(x) = 15 \csc(x) + 5[/tex] (first option)
Step-by-step explanation:
[tex]f(x) = a \: \csc(x) + b[/tex]
[tex]a + b = 20[/tex]
[tex] - a + b = - 10[/tex]
••••
[tex]2b = 10[/tex]
[tex]b = 5[/tex]
[tex]a = 20 - 6 = 15[/tex]
[tex] = f(x) = 15 \csc(x) + 5[/tex]
See attachment for the question
Answer:
-22
Step-by-step explanation:
f(x) = 3x^2 - 5
let x= 3
f(3) = 3*(3)^2 -5 = 3(9) -5 =27-5 =22
g(x) = -2x+5
Let x = 3
g(3) = -2(3) +5 = -6+5 = -1
f(3) *g(3) = 22(-1) = -22
Find the area.
D
36 m
1
180 m
N
37 m
A. 1100 m
B. 1066 m
C. 555 m
D. 338 m
Answer:
Area of triangle = 1/2×base×height
= 1/2×37×30
= 555m²
The area of the triangle with the given parameters is 555 m².
Given that, NE=37 m and height=30 m.
What is the formula to find the area of a triangle?The formula to find the area of a triangle is 1/2×b×h.
Where, b=base and h=height.
Now, Area=1/2×37×30=555 m².
Therefore, the area of the given triangle is 555 m².
To learn more about the area of a triangle visit:
https://brainly.com/question/22964077.
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Find the missing side, then, round to the nearest tenth.
Looking for help with this problem!
Answer:
4.6 = x the side opposite C would be 6.1
Step-by-step explanation:
you can use law of sine
you know you have a right triangle so the missing angle B = 49
4/sin41=x/sin49
Find the midpoint between each pair of points (-1,-5) and (-5,9)
Answer:
(-3,2) is the midpoint
Step-by-step explanation:
ok
5x-9=2x+12
can somebody answer this and if possible, can you show work?
Answer:
X = 7
Step-by-step explanation:
5x-9=2x+12
5x-2x=12+9
3x=21
X=21/3
X=7
Given the sequence -14, -6, -2, 0, 1, ..., find the recursive formula.
Answer:
C is the answer to your question
5. Tristan wants to build a square garden in his backyard that will cover an area of 75 ft². If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain.
Lets find side
Area=75ft^2[tex]\\ \sf\longmapsto Area=(side)^2[/tex]
[tex]\\ \sf\longmapsto (side)^2=75[/tex]
[tex]\\ \sf\longmapsto side=8.3ft[/tex]
Perimeter
[tex]\\ \sf\longmapsto 4(side)[/tex]
[tex]\\ \sf\longmapsto 4(8.3)[/tex]
[tex]\\ \sf\longmapsto 33.2[/tex]
He has 1.2ft short materialWhat is the area of the rhombus shown below?
Answer:
54
Step-by-step explanation:
12*9/2=108/2=54mm^2
Question 5
1 pts
Find the coordinate of the other endpoint if the midpoint is (5,5) and endpoint is (-1,4).
O (9,6)
(11,6)
(11, 14)
O (9, 14)
Answer:
(11,6)
Step-by-step explanation:
Plsssssssssssssssss help fast
Answer:
yes tht right pls mark me branilest
Classify the following polynomials. Combine like terms first. PLEASE ANSWER I'm really confused. :(
2x-x2+4x+x2
x3-5x2+3-2
x3-x3+x2-x2+3
7x-x2+x3+4x2
-6x-x3+6x-4x
Quadratic monomial
Quadratic binomial
Quadratic trinomial
Cubic monomial
Cubic binomial
Cubic trinomial
Linear monomial
Constant monomial
5−33−32+39+3
Not sure?
6. (09.02 MC)
An object's velocity is defined by the vector-valued function v(t)
= (In(t –2), e^(2t-t^2))
What is the acceleration vector a(t) at t(3)? (10 points)
O
01-14
O
O
Answer:
Hello,
Step-by-step explanation:
[tex]v_x(t)=ln(t-2)\ \Longrightarrow\ a_x(t)=\dfrac{1}{t-2} \\\\v_y(t)=e^{2t-t^2}\ \Longrightarrow\ a_y(t)=e^{2t-t^2}*(2-2t)\\\\t=3\ i\ suppose\ \\\\a_x(3)=\dfrac{1}{3-2}=1\\\\a_y(t)=e^{6-9}*(2-6)=-\dfrac{4}{e^3}[/tex]
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
Answer:
9Step-by-step explanation:
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
[tex] = 1 + 8 - 0[/tex]
= 9 (Ans)
The following image is a piece of tile from a bathroom floor. What does the bolded line represent?
A. a line
B. a line segment
C. a ray
D. a plane
The bolded line represents a line segment rather than a line or a plane.
What is a line?A line refers to an infinite figure that extends to the sides. For example, the railway track is composed of two lines.
What is a line segment?This differs from a line because it is not infinite, instead, it is a section of a line with two endpoints. This concept applies to the bolded section of the tile because the section shows only a section of a line between two corners rather than a complete line.
Learn more about lines in: https://brainly.com/question/2696693
Answer:
The answer is B
Step-by-step explanation:
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! NOT A MULTIPLE CHOICE!!!
The point (-2, 5) is reflected over an axis and the new point is located in Quadrant 3.
a. Describe the reflection that happened. What axis was the point reflected over?
b. What are the coordinates of the new point?
9514 1404 393
Answer:
x-axis(-2, -5)Step-by-step explanation:
a) The original point is in quadrant 2. Reflection into quadrant 3 is a reflection over the x-axis.
__
b) Reflection over the x-axis changes the sign of the y-coordinate. The new point is (-2, -5).
Help, been trying for forever
It's A and C.
A because if you multiply the numbers inside square roots , you will get exactly same ans.
C because √75 is 5√3 and if you multiply it with 2 you get 10√3. √50 is 5√2 and if you multiply it with 3 then you get 15√2.
A single ticket for a journey costs $1.25
25 single tickets can be bought in a book for $27
Lily makes 25 journeys.
How much does Lily save by using a book of tickets?
Show your working.
Answer:
answer i dont know please