the nth term of a sequence is 3n2-1
the nth term of a different sequence is 30-n2
find the only number in both sequences
Answers
Answer: The common number is 26.
Step-by-step explanation:
We know that the n-th term of a sequence is:
aₙ = 3*n^2 - 1
And the n-th term of another sequence is:
bₙ = 30 - n^2
Remember that in a sequence n is always an integer number.
We want to find a number that belongs to both sequences, then we want to find a pair of integers x and n, such that:
aₙ = bₓ
This is:
3*n^2 - 1 = 30 - x^2
Let's isolate one of the variables, i will isolate n.
3*n^2 = 30 - x^2 + 1 = 31 - x^2
n^2 = (31 - x^2)/3
n = √( (31 - x^2)/3)
Now we can try with different integer values of x, and see if n is also an integer.
if x = 1
n = √( (31 - 1^2)/3) = √10
We know that √10 is not an integer, so we need to try with another value of x.
if x = 2:
n = √( (31 - x^2)/3) = √(27/3) = √9 = 3
Then if we have x= 2, n is also an integer, n = 3.
Then we have:
a₃ = b₂
The common number between both sequences is:
a₃ = 3*(3)^2 - 1 = 26
b₂ = 30 - 2^2 = 26
Related Questions
When you are finding a percent increase you do the following
Answers
Answer:
Step-by-step explanation:
Percent increase calculation
To calculate the percentage increase:
First: work out the difference (increase) between the two numbers you are comparing.
Increase = New Number - Original Number.
Then: divide the increase by the original number and multiply the answer by 100.
% increase = Increase ÷ Original Number × 100.
Scott drove 754 miles in 13 hours how many miles would he drive in 8 hours
Answers
You would divide 13 by 754=58
Then 58 times 8= 464
So 464 miles
3. solve - 7 - 6 = k
1
-13
13
-1
Answers
Answer:
k=-13...............
Calculate the length of AC in ABAC to 1 decimal place.
Answers
The length of AC in triangle BAC is equal 10.7 units
Cosine RuleIn trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The formula is given as
AC² = AB² + BC² - 2(AB)(BC) cos AC
AC² = 6² + 7² - 2(6)(7)cos110
AC = 10.7
Using cosine rule, the length of AC is 10.7 unit.
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In 2015 the cost of a complete bathroom package represented_____ of the monthly average household expenditures of the bottom 40% of the poorest population. Group of answer choices 40% 5% 27% 14%
Answers
In 2015, the cost of a complete bathroom package represented D. 14% of the monthly average household expenditures for the bottom 40% of the poorest population.
This means that out of the total monthly expenses of these households, 14% was spent on bathroom packages. This percentage highlights the financial burden that bathroom expenses placed on these families, as they had to allocate a significant portion of their limited resources towards this essential facility.
Among the given answer choices - a. 40%, b. 5%, c. 27%, and d. 14% - the correct answer is d. 14%, as this is the percentage mentioned in the question. The other percentages do not apply to the context of the question and therefore can be disregarded.
In summary, the cost of a complete bathroom package in 2015 accounted for 14% of the monthly average household expenditures of the bottom 40% of the poorest population. This percentage reflects the financial strain on these households to meet their basic needs, including essential facilities like bathrooms. Therefore the correct option is D
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Look carefully at the diagram.
The value of y is ___ °
Answers
The value of y in the triangle is 20°
How to find the value of y in the triangle?Consider the labeling on the image I attached
Since vertically opposite angles are equal. Thus:
x = 50°
Since the sum of angles on a straight line is 180°. Thus:
t + 70° = 180°
t = 180°-70°
t = 110°
Since the sum of angles in a triangle is 180°. Thus:
x + t + y = 180°
50 + 110 + y = 180°
160 + y = 180
y = 180 - 160
y = 20°
Therefore, the value of y is 20°
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Find an expression for a cubic function f if f(2) = 36 and f(−4) = f(0) = f(3) = 0. Step 1 A cubic function generally has the form f(x) = ax3 + bx2 + cx + d. If we know that for some x-value x = p we have f(p) = 0, then it must be true that x − p is a factor of f(x). Since we are told that f(3) = 0, we know that $$ Correct: Your answer is correct. x-3 is a factor.
Answers
A cubic function is a type of polynomial function with degree 3. It has the general form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.
Step 2: Using the factor we found in step 1, we can write the cubic function as:
f(x) = a(x - 3)(x - r)(x - s)
where r and s are the remaining roots (zeros) of the function.
Step 3: We can use the other given values to find the values of r and s. Since f(2) = 36, we have:
36 = a(2 - 3)(2 - r)(2 - s)
-36 = a(1 - r)(1 - s) ... (1)
Since f(-4) = 0, we have:
0 = a(-4 - 3)(-4 - r)(-4 - s)
0 = a(1 + r)(1 + s) ... (2)
Since f(0) = 0, we have:
0 = a(-3)(-r)(-s)
0 = 3asr ... (3)
Step 4: We can use equations (1) and (2) to solve for r and s. Adding equations (1) and (2) gives:
-36 = a[(1 - r)(1 - s) + (1 + r)(1 + s)]
-18 = a(2 - r^2 - s^2) ... (4)
Using equation (3), we can solve for a in terms of r and s:
a = 0 or a = 3rs
If a = 0, then we cannot find a non-trivial solution for r and s. Therefore, we must have a = 3rs. Substituting this into equation (4), we get:
-18 = 3rs(2 - r^2 - s^2)
-6 = rs(2 - r^2 - s^2)
Since r and s are roots of the cubic function, we have:
r + s + 3 = 0
Rearranging this equation gives:
s = -r - 3
Substituting this into the equation above gives:
-6 = r(-r - 3)(2 - r^2 - (-r - 3)^2)
-6 = r(-r - 3)(2 - r^2 - r^2 - 6r - 9)
-6 = r(-r - 3)(-2r^2 - 6r - 7)
-6 = -r(r + 3)(2r^2 + 6r + 7)
Therefore, we have:
r = -3, s = 0.5 + √21/2, or
r = -3, s = 0.5 - √21/2
Step 5: We can now substitute the values of a, r, and s into our original expression for f(x) to get:
f(x) = 3(x - 3)(x + 3)(x - 0.5 - √21/2)
or
f(x) = 3(x - 3)(x + 3)(x - 0.5 + √21/2)
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Is SAA a triangle similarity theorem?
Answers
The SAA (Side-Angle-Angle) criterion is not a triangle similarity theorem.
Triangle similarity theorems are used to determine if two triangles are similar. Similar triangles have corresponding angles that are equal and corresponding sides that are proportional. There are three main triangle similarity theorems: AA (Angle-Angle) Criterion.
SSS (Side-Side-Side) Criterion: If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. SAS (Side-Angle-Side) Criterion.
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Two trains leave a railroad station at noon. The first train travels along a straight track at 90 mph. The second train travels at 75 mph along a straight track that makes an angle of 130 degrees with the first track. At what time are the trains 400 miles apart
Answers
Answer:
Step-by-step explanation:
Answer:
2:36pm
Step-by-step explanation:
Let's say it takes x hours after leaving the station when the trains are 400 miles apart
Let's refer to the two trains using the letters A and B for easier reference
A is the train that travels on a straight track due East
B is the train that travels on a track 130° relative to the path of train A
A travels at a speed of 95 mph
B travels at a speed of 75 mph
Let the distance between the two trains be 400 miles after they have traveled an unknown hours. We have to determine
After hours, train A would be miles from the railroad station and train B would be miles from the station
We can visualize this situation as given in the attached image.
You can see that A = 95x, B = 75x and the longest side is 400 miles
We will use the law of cosines to determine x
The Law of Cosines (also called the Cosine Rule) says:
where is the angle opposite c i.e. the angle bounded by a and b which are the other two sides
Using the diagram as a reference we see
c = 400, a = 95x, b= 75x, 130°
Using this information and plugging values into the cosine rule formula we get
But we know that c = 400 since that's what the question says
So we get
So the two trains will be 400 miles apart 2.6 hours after they have left the station.
2.6 hours = 2 hours and 36 minutes
So the trains will be 400 miles 2 hours and 36 minutes after they have left the station
Since they have left at noon, they are 400 miles apart at 2:36pm
hope this helps ;)
A homeowner bought a homeowner's insurance policy. The homeowner pays an annual $650 premium for property coverage with a deductible is $1,175 for each claim. A windstorm causes $42,500 in damages. If a claim for the full amount of damages is approved, how much will the homeowner's insurance company pay for the damages?
$42,500
$41,325
$41,975
$40,825
Answers
Answer:
The homeowner’s insurance company will pay for the damages after the homeowner pays the deductible of $1,175 for each claim. Therefore, the amount that the homeowner’s insurance company will pay for the damages is $42,500 - $1,175 = $41,325.
I hope that helps! (´▽`ʃ♡ƪ)
Step-by-step explanation:
please help me please
Answers
Answer:
F
Step-by-step explanation:
Hopefully this helps
Which of the attributes below are shared by both trapezoid
and parallelograms? Select all that apply.
A) 4 sides
B) 4 right angles
C) All sides are straight lines
D) 2 sets of parallel sides
Answers
The attributes shared by both trapezoids and parallelograms are:
A) 4 sides
C) All sides are straight lines
D) 2 sets of parallel sides
So the correct options are A), C), and D).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
9. The population of a certain animal species increases at a rate of 6.5% per year. There are currently
counted 120 of the animals in the habitat you are studying
Which function will model the expected change in the animal population from this point forward?
Answers
Answer:
FV= PV*(1 + g)^n
Step-by-step explanation:
Giving the following information:
Present Value (PV)= 120
Growth rate (g)= 6.5% per year
To calculate the future value of the population in any given year "n", we need to use the following formula:
FV= PV*(1 + g)^n
For example, in 10 years:
FV= 120*(1.065^10)
FV= 225
Can somebody help me and tell me if i’m right or not because I don’t know how to do this
Find the value of y.
Answers
Answer:
y = 5
Step-by-step explanation:
Since the lines are parallel, same side interior angles are supplementary.
That allows us to solve for x.
7x + 17 + 5x - 5 = 180
12x = 168
x = 14
The angles 23yand 5x - 5 are supplementary, so the sum of the measures equals 180°.
23y + 5x - 5 = 180
We already know that x = 14.
23y + 5(14) - 5 = 180
23y = 115
y = 5
a straight line joins the points A (2,1) and B (8,10) The point (6,y) lies on the line AB Find the y coordinate of c
Answers
Step by step
You can graph the two points and find where x=6 and the line meet (attached)
Offering points for who can help me with this
Answers
Answer:
204 feet^2
Step-by-step explanation:
rectangle area = 18 * 10 = 180 feet^2
triangle width = 18 - 10 = 8 feet
triangle area = 6 * 8 /2 = 24 feet^2
total area = 180 + 24 = 204 feet^2
Will give Brainlest!
What is the direct variation of the table below?
Answers
Answer:
18
Step-by-step explanation:
direct variation = y/x
54 / 3 = 18
Ian says that if x < y then | x | < | y |. Is Ian's statement always true, sometimes true or never true? Use a model to help explain your thinking
Answers
In conclusion, Ian's assertion can be true or false based on the sign of x and y. The claim is accurate when x and y share the same sign, but it is untrue when they have the opposite sign.
What does a mathematic statement look like?In essence, a mathematics assertion is a statement that may or may not be true. Symbols and text both may be present. An example is the mathematical equation "The denominator of 4 equals 5" (which is, of course, false).
Sometimes Ian's assertion is accurate.
Think about the following instances:
In the event that x = 2 and y = 5, x < y and |x|< |y|.
In the case where x = -3 and y = -1, x < y and |x| >|y|.
These illustrations show that Ian's claim can occasionally not be true. If both x and y share the same value, i.e., when both are either positive or negative, it is true. In this situation, the smaller number's absolute value will be lower than the larger number's absolute value.
The lower proportion will have a greater absolute value than the larger number, though, if x and y have the opposite signs, that is, if one is positive while the other is negative. As a result, Ian's claim is untrue in this instance.
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Can someone please explain how functions work? With graphs?
Answers
Answer:
no, yes, no, no, yes, no
there you go!
Step-by-step explanation:
The original price of a video game is $32.99 before tax. When Mario bought the video game it rang up as $26.39 before tax. He then paid 8% sales tax on the discounted price.
Part A: What is the percent discount on the game? Show all work and steps in your solution. (5 points)
Part B: What is the total amount that Mario paid for the video game including tax? Show all work and steps in your solution.
Answers
Answer:
Part A: The percent discount on game is 20%.
Part B: Mario paid a total of $28.50 including sales tax.
Step-by-step explanation:
Given that:
Part A:
Original price of video game = $32.99
Discounted price = $26.39
Amount of discount = 32.99 - 26.39 = $6.60
Discount percent = \(\frac{Amount\ of\ discount}{Original\ price}*100\)
Discount percent = \(\frac{6.60}{32.99}*100 = 0.20*100\)
Discount percent = 20%
Part B:
Sales tax = 8% of discounted price
Amount of sales tax = \(\frac{8}{100}*26.39 = 0.08*26.39\)
Amount of sales tax = $2.11
Total amount = $26.39 + $ 2.11 = $28.50
Hence,
Part A: The percent discount on game is 20%.
Part B: Mario paid a total of $28.50 including sales tax.
–14d+12d+11d+18=–18 solve d
Answers
By solving the given equation, d = -4
To find d in the equation -14d + 12d + 11d + 18 = -18, we need to combine similar terms on the left side of the equation and isolate the variable.
Combining similar terms, we get:
(-14 + 12 + 11)d + 18 = -18
9d + 18 = -18
We can then extract the variable by shifting the constant term to the other side of the equation:
9d = -18 - 18
9d = -36
Finally, we can find d by dividing both sides of the equation by 9:
d = -36/9
d = -4
Therefore, the solution of the equation is d = -4. When d equals -4, the equation is balanced and both sides of the equation are equal.
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Rita wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are 44 feet. Suppose
each can of paint will cover 242 square feet. How many cans will she need to paint the ceiling?
Answers
work:
44x44=1,936
1,936/242=8
Solve for g. If you can please add an explanation
Answers
Answer:
g=7
Step-by-step explanation:
your goal is to isolate the g
times g/-4 by -4/1 the -4 cancels out the other one so you are just left with g
move the g to the other side of the equation then move the 3 and it to the -5 and then multiply the whole thing but -1 to make the equation positive
A new community sports complex is being build in Madison. The perimeter of the rectangular playing field is 466 yards. The length of the field is 7 years less than quadruple the width. What are the dimensions of the playing field?
Answers
Answer:
The dimensions of the field is 185 yards by 48 yards
Step-by-step explanation:
Here, we are interested in calculating the dimensions of the field.
Let the width of the field be x yards
From the question, we are made to know that the length of the field is 7 yards less than quadruple ( 4 times) the width
So mathematically, the length of the field will be ;
(4x -7) yards
The perimeter of the field mathematically is:
2(l + b)
Thus;
2(x + 4x- 7) = 466
2(5x -7) = 466
divide both side by 2
5x - 7 = 466/2
5x - 7 = 233
5x = 233 + 7
5x = 240
x = 240/5
x = 48 yards
Length of field is; 4x -7 = 4(48) -7 = 192 - 7 = 185 yards
Brent took out a 48-month loan for $16,000 to buy a car. The simple interest rate was 8%.
Answers
Answer:
61440
Step-by-step explanation:
S.I=P×R×T÷100
=16000×8×48÷100
=160×8×48
=61440
The graph above shows Jack's mass over a five-month period. Based on the trend in the data, what do you predict will happen to Jack's mass the subsequent month?
A. Jack's mass will increase.
B. Jack's mass will decrease.
C. It is important to predict because there is no trend in Jack's mass.
D. The next month's data will be Anomalous.
Answers
Answer:A
Step-by-step explanation:
Triangle ABC is shown with its inscribed circle drawn. The measure of angle ECF is 72 degrees. What is the measure of angle EGF? Explain or show your reasoning.
Answers
Answer:
108°
Step-by-step explanation:
CB and CA are tangents to the circle at points E and F respectively. GE and GF are radii of the circle with center G.
Since, radii of a circle are perpendicular to the tangents at the point of contacts.
\( \therefore GE \perp CB\\\\
\& \:GF \perp CA\\\\
m\angle GEC =m\angle GFC = 90\degree \\\\\)
In quadrilateral GECF, by interior angle sum property:
\( m\angle C + m\angle E + m\angle F + m\angle EGF = 360\degree \\\\
\therefore 72\degree + 90\degree + 90\degree + m\angle EGF = 360\degree \\\\
\therefore 252\degree + m\angle EGF = 360\degree \\\\
\therefore m\angle EGF = 360\degree - 252\degree \\\\
\therefore m\angle EGF = 108\degree \\\)
Answer:
108°Step-by-step explanation:
Since GE ⊥ BC and GF ⊥ AC,∠GEC = ∠GFC = 90°Sum of 4 angles is 360°, therefore:
∠ECF + ∠EGF = 360° - 180°∠EGF = 180° - 72° ∠EGF = 108°answer this correctly for brainlist
A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
Answers
Answer:
45.5
Step-by-step explanation:
i passed
i took the test
A 30 pound bag of dog food is $45.
Sales tax is 7.25%.
How much is the tax?
Answers
Answer:
tax was $3.26
HELPPPPPPPPPP!!!!!!!!!!!!!!! plss help meh Please and Thank you for your time
Simplify the expression.
3/2(4f - 10)