Answers
Answer:
a. f(n) = n(n+1)/2
b. 351
c. 19
d. no; n would not be an integer for f(n) = 17.
Step-by-step explanation:
a. The terms are 1, 3, 6, 10, ...
Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.
When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.
For the polynomial ...
[tex]f(n)=an^2+bn+c[/tex]
We can substitute values for n and f(n) to get 3 equations in 3 unknowns:
[tex]1=a\cdot1^2+b\cdot1+c\\\\3=a\cdot2^2+b\cdot2+c\\\\6=a\cdot3^2+b\cdot3+c[/tex]
Solving these equations by your favorite method gives ...
(a, b, c) = (1/2, 1/2, 0)
That is, the function representing the relationship is ...
f(n) = n(n+1)/2 . . . . the function describing the relationship
__
b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26
__
c. The number of the term having 190 squares can be found by solving ...
n(n +1)/2 = 190
n(n +1) = 380 = 19(20)
The 19th term will have 190 squares.
__
d. Terms 5 and 6 are 15 and 21.
17 is not the value of one of the terms in this sequence.
Related Questions
Organic milk costs $2.52 per half gallon. At this rate, how can the price of 4 gallons of organic milk be determined?
by multiplying $2.52 by 4
by dividing $2.52 by 4
by finding the unit price and multiplying it by 4
by finding the unit price and dividing it by 4
Answers
Answer:
A by multiplying 2.52 by 4
Step-by-step explanation:
Have a great day!
Plzzzz help, I don't understand
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
Those angles are corresponding so they are congruent to each other so you should do....
[tex]4m+15=5m-10\\15=m-10\\25=m[/tex]
Therefore the answer is D.
Answer:
Step-by-step explanation:
5m - 10 = 4m + 15
m - 10 = 15
m = 25
Evaluate the following expression if x = -2, y = -3, and z = 5:
x-y
Answers
Answer:
1
Step-by-step explanation:
x-y
=(-2)-(-3)
=-2+3
=1
HEELPPP PLLEEAAASSEEE Literal equations and formulas
Answers
Answer:
i believe its A
Step-by-step explanation:
(FREE BRAINLIEST) The difference of two numbers is 4 and their sum is 14. What is their product?
Answers
Answer:
8 is the answer
A farmer wants to put a fence around his vegetable garden. Only three sides must be fenced since a rock wall will form the fourth side. If he uses 40 m of fencing, what is the maximum area possible? What dimensions should the farmer use?
Answers
Answer: Maximum area = 200m
Dimensions:
Length = 10m
Width = 20m
Such that there is only one side of 20m fenced because the other side of 20m is against the rock wall.
Step-by-step explanation:
We have the next problem.
Suppose that the vegetable area is a rectangle of length L and width W.
Such that the width side coincides with the rock wall, then we have that:
The perimeter is:
P = 2*L + 2*W
But because one of the width sides coincides with the wall, the amount of fence needed will be:
P = 2*L + W = 40m
And the area can be written as:
A = W*L
We want to find the maximum area that we can have.
First, write our two equations:
40m = 2*L + W
A = W*L
First we must isolate one of the variables in the first equation, and replace it into the second equation:
40m - 2*L = W.
then:
A = (40m - 2*L)*L = 40m*L - 2*L^2
We can write this as a quadratic equation:
A(L) = -2*L^2 + 40m*L
Now, notice that it has a leading coefficient negative, then the maximum of the area function will be at the vertex of the quadratic equation.
For a quadratic equation:
f(x) = a*x^2 + b*x + c
The vertex is at:
x = -b/2a
and the point is (-b/2a, f(-b/2a))
In this case we have:
b = 40m
a = -2
Then:
we must evaluate the area function in:
L = -40m/(-2*2) = 10m
A(L) = -2*L^2 + 40m*L
A(10m) = -2*100m^2 + 400m = 200m
Now we can find the width using one of the above equations:
W = 40m - 2*L = 40m - 2*10m = 20m
Then the dimensions that the farmer should use are:
Two sides of length 10m, and one side of length 20m
While shopping at Target, Cathy sees a tank top that she loves for only $4.75. She decides to buy one in blue, red, and white. She pays the cashier with a $20.00 bill. How much change will Cathy get back from the cashier? (don’t factor in sales tax) *
Answers
Answer:
5.75
Step-by-step explanation:
A mortgage company offers a loan for 30 years at an
annual rate that is equal to the prime rate published by
the Federal Reserve plus 2%. This can be modeled
using the function APR(P) = p + 0.02, where p is the
prime interest rate as a decimal. The annual interest
rate is then converted to a monthly interest rate using
the function (APR) =
APR
The Wilsons want to borrow
12
$128,000. Their monthly payments can be calculated
128,000r
by the function m(r) =
1-(1 + r)-360
Answers
Answer: C
Step-by-step explanation:
The Wilsons' monthly mortgage payment will be approximately $9,485.16.
How to get the Monthly Mortgage Payment?To calculate the monthly payments for the Wilsons' mortgage, we need to follow these steps:
Convert the annual interest rate to a monthly interest rate using the formula APR(P) = P + 0.02.
Plug the monthly interest rate into the formula m(r) = 128,000 * (r / (1 - (1 + r)⁽⁻³⁶⁰⁾)).
Let's perform the calculations:
Step 1: Convert the annual interest rate to a monthly interest rate
Let's assume the prime interest rate (P) published by the Federal Reserve is 4.5% (0.045 as a decimal).
APR(P) = P + 0.02
APR(0.045) = 0.045 + 0.02
APR(0.045) = 0.065 (monthly interest rate as a decimal)
Step 2: Calculate the monthly payments (m(r)) for a loan of $128,000 with the monthly interest rate (r) obtained from Step 1.
m(r) = 128,000 * (r / (1 - (1 + r)⁽⁻³⁶⁰⁾))
m(0.065) = 128,000 * (0.065 / (1 - (1 + 0.065)⁽⁻³⁶⁰⁾))
Now, let's calculate the monthly payments (m(r)):
m(0.065) = 128,000 * (0.065 / (1 - (1 + 0.065)⁽⁻³⁶⁰⁾))
m(0.065) = 128,000 * (0.065 / (1 - (1.065)⁽⁻³⁶⁰⁾))
m(0.065) = 128,000 * (0.065 / (1 - 0.124823)) (Approximately, (1.065)⁽⁻³⁶⁰⁾ ≈ 0.124823)
m(0.065) = 128,000 * (0.065 / 0.875177)
m(0.065) = 128,000 * 0.074285 (Approximately, 0.065 / 0.875177 ≈ 0.074285)
m(0.065) = 9,485.16
The Wilsons' monthly mortgage payment will be approximately $9,485.16.
Learn more about mortgage here: https://brainly.com/question/1318711
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The art club spent $45 on supplies for valentines to sell during lunches. They made 60 valentines. What selling price for a valentine would result in a profit of zero if all the valentines are sold?
$0.60
$0.75
$1.00
$1.33
Answers
Answer:
Answer is $0.75
Step-by-step explanation:
$0.75x60=$45
Answer:
0.75 :)
Step-by-step explanation:
Divide 45 by 60 which gives you 0.75. To check your answer, multiply 0.75 by 60 then add that answer to -45. So, the answer is 0.75
How is the idea of asymptote applied in real life situations
Answers
Answer: The idea of asymptote applied in real life situations are often used used in designing. Like for example in designing airplanes an asymptote for speed of an airplane use to be the speed of sound.
Step-by-step explanation:
Which is an x-intercept of the continuous function in the
table?
0 (-1,0)
(0, 6)
o(-6, 0)
0 (0, -1)
Answers
Answer:
(-1, 0), (2, 0), (3, 0)
Step-by-step explanation:
x-intercept of a line is defined by a point where y = 0.
So the point in the form of (x, 0) will be the x-intercept of the given continuous function.
From the table attached,
For x = -1, f(-1) = 0
For x = 2, f(2) = 0
For x = 3, f(3) = 0
Points (-1, 0), (2, 0) and (3, 0) are the x-intercepts of the continuous function f(x).
Is this relation a function?
Answers
Answer:
Yes, this is a function
Step-by-step explanation:
ok
Simplify the square root of -72
Answers
Answer:
6i[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex] and [tex]\sqrt{-1}[/tex] = i
Given
[tex]\sqrt{-72}[/tex]
= [tex]\sqrt{36(2)(-1)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex] × [tex]\sqrt{-1}[/tex]
= 6[tex]\sqrt{2}[/tex] × i
= 6i[tex]\sqrt{2}[/tex]
1 = 1/3(10x - 3)
Need help finding the answer to this equation.
Answers
Answer:
x = 3/5Step-by-step explanation:
1 = 1/3(10x - 3)
3 = 10x - 3
6 = 10x
x = 6/10
x = 3/5
Which of the following represents 8 square root x5
Answers
Answer:
[tex]5 \sqrt{8}[/tex]
6 = 3(3x-6) - 3(3x - 8)
Answers
Answer:
Pull out like factors
3x - 6 = 3 • (x - 2)
Pull out 6
6 • ( 1 +( (-1) ))
This equations is a tautology or an Identity which means it's always true.
Step-by-step explanation:
Answer: All real numbers
Step-by-step explanation:
Distribute the 3 into (3x - 6) and - 3 into (3x -8). 6 = 9x - 18 - 9x + 24.Combine the like terms. 6 = 6will give brainlisest plzzzzzzz What is the purpose of a signal phrase? To point out an internal citation to the reader To call attention to plagiarism in informational text To show the need for a reference within an article To indicate the end of the text and the start of citations
Answers
Answer:
To point out an internal citation to the reader
Step-by-step explanation:
A signal phrase is a phrase, clause, or even sentence which leads into a quotation or statistic. These generally include the speaker/author's name and some justification for using him or her as an expert in this context; it may also help establish the context for the quotation...
Simplify Negative 15.6 divided by negative 4
Answers
Answer:
3.9
Step-by-step explanation:
Helena was curious if quadrilaterals QRSTQRSTQ, R, S, T and XYZWXYZWX, Y, Z, W were congruent, so she tried to map one figure onto the other using transformations:
Helena concluded:
"It's not possible to map QRSTQRSTQ, R, S, T onto XYZWXYZWX, Y, Z, W using a sequence of rigid transformations, so the quadrilaterals are not congruent."
What error did Helena make in her conclusion?
Choose 1 answer:
Answers
Answer:
B. Their is no error. This is a conclusion.
Step-by-step explanation I got it right on khan
Helena didn't make any error in her conclusion as the transformation is illustrated accurately.
How to explain the information?From the information given, it was stated that Helena was curious if the quadrilaterals were congruent.
In this case, it is not possible to map the quadrilaterals onto each other using a sequence of rigid transformations, so the quadrilaterals are not congruent.
Therefore, no error is made.
Learn more about transformation on:
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URGENT HELP PLEASE! Write the equation of the line fully simplified in slope-intercept form.
Answers
Answer:
y=-1/2x-3
Step-by-step explanation:
Answer:
y = -1/2x -3
Step-by-step explanation:
so I got the slope of these two points: (-8,1) and (-6,0) which is:
y₂ - y₁ / x₂ - x₁ = (0-1)/(-6+8) = -1/2
then from the graph it is visible that the y-intercept is -3
so with both of this information:
y = -1/2x - 3
plz help em with thsis
Answers
Answer:
0.76
Step-by-step explanation:
0.26 + 0.5
= 0.76
I need help with this math problem
Answers
Answer:
The radius of the hole is 0.42 feet
Step-by-step explanation:
Let us revise the rule of the volume of a cylinder
→ V = πr²h, where
→ V is the volume of the cylinder in a cubic unit
→ r is the radius of the base of the cylinder
→ h is the height of the cylinder
Let us solve our question
→ The volume of the cylinder is 3800 cubic feet
→ The height of the cylinder is 1.3 miles
Very Important Note: dimensions must have the same unit
→ Change the mile to feet
→ There are 5280 feet in 1 mile
→ Multiply 1.3 miles by 5280 to change it to feet
→ The height = 1.3 × 5280 = 6864 feet
Let us substitute the values of V and h in the rule above
∵ V = πr²h
∵ V = 3800 ft³
∵ h = 6864 ft
∴ 3800 = πr²(6864)
→ Divide both sides by 6864π to find r²
∴ r² = 0.1762205081
→ take √ for both sides to find r
∴ r = 0.4197862648
→ Round it to the nearest hundredth
∴ r = 0.42 ft
The radius of the hole is 0.42 feet
If you have unlike (different) denominators, find the ____________ fractions that have the same denominator.
Answers
Which statement best describes how to determine whether f(x) =9-4x IS an odd function ?
O Detemine whether 9-4(-x) is equivalent to 9-4x
O Determine whether 9-4(-)is equivalent to 9+4x
O Determine whether 9- 4(-x) is equivalent to -(9 4x
O Detemine whether 9-4(-)is equivalent to (9 +4x)
Answers
Answer: it’s on quizlet
Step-by-step explanation:
Look ok quizlet most of the answers are there
What value should go in the empty box to complete the calculation for finding the product of 62.834 × 0.45?
Answers
Answer:28.2753
Step-by-step explanation:
9 is added to a number and multiplied by 7. The result is 84.
Answers
Answer:
11
Step-by-step explanation:
you do 9 x 7 = 63 84 -63 = 11
HOPE THIS HELPS :3
Answer:
3
Step-by-step explanation
84/ 7 = 12
12-9=3
3+9= 12
12*7=84
The sum of the interior angles S of a polygon with n sides is given by the formula S = 180(n-2).
a) (3 pts) Find the sum of the interior angles of a pentagon (5-sided polygon).
b) (3 pts) Set up an equation for x and solve it.
158
112
100
Answers
Answer:
,
Step-by-step explanation:
3 x [ 32 = ( 4 + 4 ) x 6 Pls HELP ME ITS ALMOST DONE
Answers
Answer:
-192
Step-by-step explanation:
3×[32-(4×4)×6]
3×[32-(16)×6]
3×[32-(96)]
3×(-64)
-192
2 1/4 divided by 1/8
Answers
Answer:
18
Step-by-step explanation:
50 POINTS! Answer the question step by step please
Answers
Answer:
8x+12=180
8x=168
x=21
3(21)+20= 83 degrees
5(21)-8= 97 degrees
Step-by-step explanation:
5x-8 and 3x+20 are supplementary angles meaning that when added together they equal to 180 degrees. Solve for x and then use to find angle
