I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP .. I need the answers for all of them ASAP
Answers
Problem 61
Refer to this link where I solved the problem earlier
https://brainly.com/question/24517029
===========================================================
Problem 62
T(n) = nth triangular number
T(n) = n(n+1)/2 = 0.5n(n+1)
That squares to (0.5n(n+1))^2 = 0.25n^2(n+1)^2
The next triangular number after T(n) is
T(n+1) = 0.5(n+1)(n+1+1) = 0.5(n+1)(n+2)
That squares to 0.25(n+1)^2(n+2)^2
Notice how each squared result has 0.25 and (n+1)^2 found buried in them.
Let's say A = 0.25(n+1)^2
That would mean the first result 0.25n^2(n+1)^2 becomes An^2
The second result 0.25(n+1)^2(n+2)^2 becomes A(n+2)^2
Let's add those to see what happens
An^2+A(n+2)^2
An^2+A(n^2+4n+4)
A(n^2+n^2+4n+4)
A(2n^2+4n+4)
0.25(n+1)^2*(2(n^2+2n+2))
0.5(n+1)^2(n^2+2n+1+1)
0.5(n+1)^2((n+1)^2+1)
0.5k(k+1)
We see that the result is a triangular number where k = (n+1)^2
This shows that adding the squares of consecutive triangular numbers gets us another triangular number.
A few examples
3^2+6^2 = 9+36 = 45 which is in the form n(n+1)/2 when n = 96^2+10^2 = 36+100 = 136 which is in the form n(n+1)/2 when n = 16Answer: Triangular number===========================================================
Problem 63
I'll borrow some of the ideas from problem 62
We found that after squaring the nth and (n+1)th triangular numbers, we got An^2 and A(n+2)^2 respectively. We let A = 0.5(n+1)^2
Subtract those expressions to get...
A(n+2)^2 - An^2
A(n^2+4n+4)-An^2
A(n^2+4n+4-n^2)
A(4n+4)
4A(n+1)
4*0.5(n+1)^2*(n+1)
(n+1)^3
This proves that the difference between the squares of consecutive triangular numbers is a perfect cube, aka a cube number.
A few examples:
6^2 - 3^2 = 36 - 9 = 27 = 3^310^2 - 6^2 = 100-36 = 64 = 4^3Answer: Cube number===========================================================
Problem 64
Refer to this link where I solved the problem earlier
https://brainly.com/question/24517029
Related Questions
What is the value of f(3) when
f(3) when f(x) = 4x+1
Answers
Answer:
f(3) = 13
Step-by-step explanation:
f(x) = 4x+1
f(3) = 4(3) + 1
f(3) = 12 + 1
f(3) = 13
the perimeter of a rectangular tray is 60in the length of the tray is double the width of a tray determine the dimensions of the rectangular tray
Answers
Answer:
Step-by-step explanation:
Width = w
Length = double the width = 2*w = 2w
Perimeter of rectangular tray = 60 in
2*(length + width) = 60
2*( 2w + w) = 60
2*3w = 60
6w = 60
Divide both sides by 6
w = 60/6
w = 10 in
length =2w = 2*10 = 20
length = 20 in
Width = 10 in
Find the area for all of these numbers
Answers
………………….
Answer:
The Answer is 29cm
Step-by-step explanation:
The area of this shape is made from two shapes.
Shape one is a rectangle with the dimensions 2cm by 4cm
2x4 = 8
So the area of rectangle 1 is 8
The other rectangle has the dimensions 4cm by 7cm
Because you have to account for the other triangle not being there (solved)
4x7 = 21
21+8
29cm
(4x – 6) + (5x + 1).
Answers
Answer:
9x - 5
Step-by-step explanation:
(4x – 6) + (5x + 1).
4x - 6 + 5x +1
9x - 5
Have a good day
Answer:
9x - 5
Step-by-step explanation:
To get the this answer you would combine like terms. 4x and 5x are like terms, so you would combine them and get 9x. -6 and 1 are like terms, so you would combine those and get -5.
*WILL MARK BRAINLIEST*
The line plot below shows the lengths, in yards, of fabrics that are for sale at a craft fair. How many yards of fabric in all are for sale?
*NO SPAM, NO LINKS.*
*PLEASE LOOK AT THE PICTURE OF THE CHART I PROVIDED BELOW*
*ANSWERS ONLY IN FRACTIONS*
Answers
Let y=|x|-2, where the domain is the set of integers from – 4 to 4.
What is the range?
Answers
i dont know i wish I could help.
Answer:
-2 to 2
Step-by-step explanation:
see there's the sign of absolute value around x
so even if we put a negative number in place of x we'll get a positive outcome.
for example,
if x = -4|x| = 4
if x = -3|x| = 3
and so on
so the actual domain of |x| reduces to => 0 to 4.
as you'll get the values of |x| in between 0 and 4 throughout -4 to 4.
where the smallest value is 0 and largest is 4.
for range,
I'll just put these smallest and largest values in place of x and solve for domain
at x = 0y= |0| - 2
y = -2
at x = 4y = |4| - 2
y= 4 - 2
y = 2
so, the range of the function becomes -2 to 2.
What is the simplest form of 56\92?
28/46
16/27
9/16
14/23
Answers
can u guys help 100pts
Answers
Answer:
1 line
Step-by-step explanation:
1 line
Answer:
1 line
Step-by-step explanation:
for the equation Y= 2(x+4)-3 what ordered pair what are used to start a graphing PLEASEEEE HELP
Answers
Answer:
(4,-3)
Step-by-step explanation:
Last year, there were b pies baked for the bake sale. This year, there were 211 pies baked. Using b, write an expression for the total number of pies baked in the two years.
Answers
Answer:
211+b=x
Step-by-step explanation:
How do you solve this?
Answers
Answer:
f(- 10) = 74
Step-by-step explanation:
To find f(- 10) , substitute n = - 10 into f(n) , that is
f(- 10) = - 7(- 10) + 4 = 70 + 4 = 74
Hello there!
We are given a function below:
[tex] \displaystyle \large{f(n) = - 7n + 4}[/tex]
To find f(-10), substitute n = -10.
[tex] \displaystyle \large{f( - 10) = - 7( - 10) + 4}[/tex]
Evaluate the f(-10)
[tex] \displaystyle \large{f( - 10) = 70 + 4}[/tex]
Recall
Negative × Negative = PositiveTherefore,
[tex] \displaystyle \large{f( - 10) = 74}[/tex]
f(-10) = 74
Let me know if you have any questions!
Topic: Functions
Is -15/6 a real number?
Answers
Real numbers are numbers that you can put or find on the number line. -15/6 = -2.5 and that is on the number line.
When the fraction below is written as a decimal, how many digits are in the smallest sequence of repeating digits?
A. 0
B. 1
C. 2
D. 3
Answers
Answer:
2 repeating digits
[tex]f(x)=x^{4} -x^{3} -7x^{2} +10+5x[/tex]
1. write in standard form
2. use Descartes rule of sign
3. possible roots
4. first synthetic division
5. reconsider possible roots
6. second synthetic division
7. quadratic equation
8. solution set
Answers
A regular square-based pyramid has a surface area of 33 m2. If its triangular faces have an area of 6 m2, what is the length of the base of the pyramid?
Answers
Answer:
First we can do 33 time 6
Step-by-step explanation:
The length of the base of the pyramid is 3 meters.
What is a square pyramid?A pyramid is a polyhedron that has a base and 3 or greater triangular faces that meet at a point above the base. A square pyramid is a pyramid with a square base, four triangular sides, five vertices, and eight edges.
For the given situation,
The surface area of the pyramid = 33 m^2
Area of triangular faces = 6 m^2
Let the base of the pyramid be b and the height be h.
The formula of area of triangle is
[tex]A = \frac{1}{2}(b)(h)[/tex]
⇒ [tex]6 = \frac{1}{2}(b)(h)[/tex]
⇒ [tex]6(2) = (b)(h)[/tex]
⇒ [tex]12 = (b)(h)[/tex]
The formula of surface area of square pyramid is
[tex]SA = b^{2}+2bh[/tex]
⇒ [tex]33=b^{2} +2(12)[/tex]
⇒ [tex]33-24=b^{2}[/tex]
⇒ [tex]b=\sqrt{9}[/tex]
⇒ [tex]b=3[/tex]
Hence we can conclude that the length of the base of the pyramid is 3 meters.
Learn more about square pyramid here
https://brainly.com/question/22645991
#SPJ2
a^15/a^5=a^10 true or false
Answers
Answer:
true
Step-by-step explanation:
a^15 ÷ a^5 = a^10
a÷a = a
15- 5 =10
give brainliest please I need it to level up
Answer:
True
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{a^{15} }{a^{5} }[/tex]
= [tex]a^{(15-5)}[/tex]
= [tex]a^{10}[/tex]
WORTH 20 POINTS
Write an algebraic expression
Eight less than x, times the sum of x and four
Answers
Can someone help me it’s due today!
Answers
Answer:
Y is less than or equal to -1, or negative infinity to -1
Step-by-step explanation:
The range is which y values are included. The line extends forever getting lower in y values, and the highest y value is -1. You can either write it as { y | y[tex]\leq[/tex] -1 } or ( -∞, -1]
what are variables???????
Answers
Answer:
a quantity which during a calculation is assumed to be capable of varying in value.
example: 4x-7=5
the variable is x
Step-by-step explanation:
hope that helps>3
Angel got a job at in-n-out burger. He works 20 hours a week and makes $15.75 an hour. How much will his
paycheck be after 2 weeks of work (before uncle sam takes away taxes
Answers
Multiply hours per week by hourly pay rate:
20 x $15.75 = $315.00 per week
Multiply by 2 weeks:
$315 x 2 = $630
After 2 weeks paycheck is $630
Answer:
630
Step-by-step explanation:
15.75 x 20 = 315
315 is how much Angel makes in one week
315 x 2 = 630
630 is how much he will make in two weeks
The 2 signifies how many weeks have been worked
which of the following situations describes a postive number
Answers
Answer:
B. Going up the elevator 14 floors
Step-by-step explanation:
Choice A can't be right because you are going below sea level (negative).
Choice C can't be correct either because the word "losing" let's you know that it's negative.
Choice D isn't right because if you are taking $20 from your checking account, it would be a negative number.
Hope this helps!
A line includes the points (1, 1) and (2, 9). What is its equation in slope-intercept form?
Answers
Answer:
[tex]y=\frac{8x}{1}-7\\[/tex]
Step-by-step explanation:
(1,1) and (2,9)
[tex]\frac{9-1}{2-1}[/tex] =[tex]\frac{8}{1\\}[/tex]
(2,9) and (x,y)
[tex]\frac{y-9}{x-2} =\frac{8}{1} \\\\1(y-9)=8(x-2)\\\\\frac{1y}{1}-\frac{9}{1}=\frac{8x}{1}-\frac{16}{1}\\\\y=\frac{8x}{1}-16+9\\y=\frac{8x}{1}-7[/tex]
Read the sentence from section "The Tetractys" The Greeks made mathematics rigorous- everything had to be proved logically. Which of the following words, if it replaced the word "rigorous" in the sentence above, would CHANGE the meaning of the sentence? A exact B precise C thorough D appealing
Answers
Help me plzzzz
(x+1)^2 -3(x+2)
If you could give an explanation that would be great!
Answers
Answer:
x^2-x-5
Step-by-step explanation:
1. expand the square
(+1)(+1)−3(+2)
2. distribute
(+1)+1(+1)−3(+2)
3. distribute
^2++1(+1)−3(+2)
4. multiply by 1
^2+++1−3(+2)
5. combine like terms
^2+2+1−3(+2)
6. distribute
^2+2+1−3−6
7. subtract the numbers
^2+2−5−3
8. combine like terms
^2−−5
9. gg you are done
^2−−5
Evaluate.
8 x 8 = 5
+ 3 eights
<
= 40 +
h
RE
=
Answers
Answer:
[tex]8 \times 8 = 5 \: ( \:8 \: ) + 3 \: eights \\ = 40 + 24 \\ = 64[/tex]
I hope I helped you^_^
Simplify: 3y^3 • y^2
Answers
Answer:
3y5
Step-by-step explanation:
five friends by a package of 12 cookies and want to share them equally each friend will get 1/5 of the cookies how much will each friend get
Answers
Answer:
2.4 cookies
Step-by-step explanation:
Just divide
g(x)=x^2-5
g(9)
help!
Answers
When asked to find g(9), you’re being told that x=9, since the x in the g(x) was replaced by 9.
So that’s telling you to put 9 in for all x’s:
g(9) = (9)^2 - 5
You then just need to clear up the right hand side.
9^2 - 5 = 81 - 5
= 76
So, g(9) = 76
three times the sum of a number and six
3(x=6)
3(x-6)
3(x+6)
3x+6
Answers
Answer:
3(x+6)
Step-by-step explanation:
Parenthesis after a number typically means multiply, so 3 times the sum of an unspecified number (x), plus 6 would be 3 (x+6)
Simplify: X + x =
5y + y =
Answers
Answer:
[tex]x + x = 2x \\ 5y + y = 6y \\ thank \: ou[/tex]
