Answer:
nth term = 4 + n^2
Step-by-step explanation:
Sorry if the answer is long but I'm hoping my explanation can help.
In order to understand the issue, we should try to find the pattern between the terms given.
The terms given were 5, 8, 13, 20 and 29.
Between the first term and second term, the difference is 3.
Between the second and third term, the difference is 5.
The pattern goes on and we find out that the difference between the (n-1)th term and the nth term is
2n - 1.
Hence, we can determine the pattern of the numbers is
nth term = (n-1) term + 2n - 1
We can use this to find term 0 (before term 1) by plugging in the values for term 1
5 = 0th term + 2 (1) - 1
5 = 0th term + 1
Hence the 0th term = 4
If we expand on the summation,
We can find the nth term
nth term = 4 + 2 (1) - 1 + 2(2) - 1 + ... + 2(n-1) - 1 + 2n - 1
As we can see, the number 1 has been subtracted n times (excluding the -1 in 2(n-1)). Hence, we can split combine all of the subtracted ones into -n.
We can rewrite it as
nth term = 4 + 2 (1) + 2(2) + ... + 2(n-1) + 2n - n
Now, we will move 4 and n to one side.
nth term = 4 - n + 2 (1) + 2(2) + ... + 2(n-1) + 2n
We can factorize 2 out from every term to the right of -n. This would give out
nth term = 4 - n + 2 (1 + 2 + ... + (n-1) + n)
The term (1 + 2 + ... + (n-1) + n) can actually be rewritten by using the triangular formula.
The triangular formula is stated such that
Tn = (n*(n+1))/2
This heavily simplifies the equation into
nth term = 4 - n + 2 [(n*(n+1))/2]
This equation becomes
nth term = 4 - n + n^2 + n.
Now, we can finally simplify into the final equation
nth term = 4 + n^2
Andrew washed 32 car windows in 4 hours. At this rate, how many windows did he wash in 8 hours?
8 hours is twice as many as 4:
Multiply the number of windows in 4 hours by 2:
32 x 2 = 64 windows in 8 hours
Answer:
64
Step-by-step explanation:
32÷4=8 8 car windows per hour. 8×8=64
Plz help me! 25 POINTS!
Answer:
g(x) = 24(2^(x-1)) +16
Step-by-step explanation:
A function is stretched vertically by a factor of 'a' by multiplying by 'a'.
g(x) = 4·f(x) = 4(6(2^(x-1) +4)
g(x) = 24(2^(x-1)) +16
Employee: "We have a promotion that will allow us to beat our competitors' prices and save you money. Did you notice that our competitor is selling that same item for $150.00?
Customer: "Yes"
Employee: "Our price for that item is $120.00, for a savings of __________."10% 15% 20% 30% 40%
Answer:
20%
Step-by-step explanation:
120 / 150 = 0.8 or 80%, so the difference is 20%
The discount percentage is 20%.
Given that the competitor is selling an item for $ 150.00, while the price for that item in the store is $ 120.00, the following calculation must be performed to determine the discount percentage:
150 = 100 120 = X 120 x 100/150 = X 80 = X 100 - 80 = X 20 = X
Therefore, the discount percentage is 20%.
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help please
The serving size for a toddler’s daily vitamin C is 4/5 cup of orange juice. If there are 3 1/4 cups of orange juice, how many servings of vitamin C are there for a toddler? Show your work
Answer:
3
Step-by-step explanation:
First you change 2 1/4 into an improper which is 9/4. Then you do KFC(Keep Change Flip) 9/4 x 4/3=36/12. THEN YOU SIMPLIFY=9/3,that can still be simplified so the final answer is 3.Its 3 because there are 3 wholes in 9/3.
WILL GIVE BRAINLIEST
Select the graph of the solution. Click until the correct graph appears.
| x | = 2
Answer:
It is the second graph, the one with two filled in dots, but no line.
Step-by-step explanation:
The reason it is not the first one is because it has not filled in dots, AND no line, so it's basically saying there is no answer, which is not true.
The reason the third one (the one with a line) is wrong is because, for example, x cannot be 1, because 1 ≠ 2, and if there is a line, it should be true.
Answer:
its the awnser with the 2 not the -2
Step-by-step explanation:
Suppose f(x) = x. Find the graph of f(x) - 5
Answer:
it's the graph that touches the y-axis in the point (0, -5), and the x-axis in the point (5, 0)
Adam is planning a pool party to celebrate the last day of school. He wants to give out beach towels to his guests as party favors. Adam ordered 14 beach towels from Sunshine Party Supply. Since this was a bulk order, Sunshine Party Supply reduced the price of each towel by $3.25. Adam paid $105 in all. How much does Sunshine Party Supply normally charge for a beach towel?
Answer:
10.75
Step-by-step explanation:
first step is to find how much adam paid for each towel
so, the equation used will be x/y=c
where x is total cost, y is number of products bought, and c equals individual cost (with discount)
we end up with 105/14= 7.5$ per towel.
and to close out, we add the given discount of 3.25 to the discounted price of 7.5
which brings the usual price per towel to 10.25
Answer:
Step-by-step explanation:
34x+24x^2=35+57y
Solve for x
1) Move all terms to one side.
[tex]34x+24x^{2} -35-57y=0[/tex]
2) Use Quadratic Formula.
[tex]x=\frac{-34+2\sqrt{1368y+1129} }{48} ,\frac{-34-2\sqrt{1368y+1129} }{48}[/tex]
3) Simplify solutions.
[tex]x=-\frac{17-\sqrt{1368y+1129} }{24} ,-\frac{17+\sqrt{1368y+1129} }{24}[/tex]
Three children each contributed toward a birthday present for their mother. The oldest contributed three times as much as the youngest, while the second oldest contributed 50 cents more than the youngest. If the present costs $10.50, how much did each contribute?
Answer:
Youngest child: $2
oldest child: $6
Second oldest: $2.50
Step-by-step explanation:
Youngest child= x
oldest child= 3x
Second oldest: .50+x
x+3x+.50+x=10.5
5x+.50=10.5
- .50= - .50
5x=10
divided both numbers by 5 and x is equal to 2. So, the youngest child is $2 and you add .50, which is $2.50, and thats for the second child. Last, you do 2 times 3 equals $6 which is the oldest child.
The youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.
Three children each contributing to their mother's birthday present. The eldest gave three times more than the youngest, while the second oldest contributed 50 cents more. If the gift costs $10.50 which is given in the question.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Let the youngest sibling contribute the amount of x dollars
As per the given information,
3x + 0.50 x + x + x = 10.50
Apply the addition operation,
4.50x = 10.50
x = 10.50 / 6.50
Apply the division operation to get
x = 1.90
So the youngest sibling contributed = $1.90
The oldest contributed 1.90 × 3 = $5.27
And the second oldest contributed (1.50)1.90= $2.85
Therefore, the youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.
Learn more about Arithmetic operations here:
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Which angle is the largest?
Answer:
the 4th choice
Step-by-step explanation:
hope this helps
MAy I get braineist pls????????
Which graph represents the function y= 2x – 4?
GIF
st
4
3
3
-3
...2
2+
2
1
+
-3 -2 -1
2
5 4 -3 -2 -1
2
3
-5 -4 -3 -2 -1
2
-2
-2
O
Answer:
4
Step-by-step explanation:
The graph of the function is attached in the solution.
What is graph?A graph is a diagram or a pictorial representation of data or values that show the relationship between quantities or objects.
Given is an equation, y = 2x-4, we need to determine its graph,
So, for the same, finding the coordinates,
y = 2x-4
Put x = 0
y = -4
(0, -4)
Put x = 1
y = -2
(1, -2)
Put the coordinates on the graph and the join them, the line obtained by this will represent the graph of the function given.
Hence. the graph of the function is a straight line.
Learn more about graphs, click;
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It takes Amy twice as long to deliver papers as it does Nancy. How long would it take each girl to deliver the papers by herself if they can deliver the papers together in 36 minutes?
Answer:
so if it takes twice all long for amy as nacy that means
Amy takes 2/3 or 0.6(aprox)
Nacy takes 1/3 or 0.3(aprox)
Amy=24
Nacy=12
Hope This Helps!!!
Please find the surface area of the
Prism... I will mark you brainliest
Answer:
The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
Step-by-step explanation:
Hope it's help
yeah I didn't pay attention today
PLEASE HELP ASAP OF YOU DO FOD BLESS YOU BECAUSE IT WILL RAISE MY GRADE
Answer:
8
Step-by-step explanation:
The basic form of the equation is y=mx+b. The b stands for the y-intercept. In this equation, 8 is b due to its position in the equation, and -8/7 is m. Since we know that 8 is b and that b is the y-intercept, we know that 8 is the y-intercept.
Hope this helps!
how do you write 100 s a fraction, mixed number, or whole number
help please anybody which too are correct
the 1st and 2nd ones r correct
Step-by-step explanation:
hope this helps
Help Asap I am stuck
suppose the value of an investment increases 12% per year and the investment has a current value of 33,00.00 which equation models the value of this investment after x years?
Answer:
bro pls someone hurry i need help
Step-by-step explanation:
how do you find the height of the base
Answer: the height of a triangle can be determined in many different ways depending on whether it's a right triangle, isosceles triangle (a triangle with two equal sides), or equilateral triangle.
Step-by-step explanation:
Step-by-step explanation:
The formula for the Area of a triangle is A = (1/2)bh where b is the base an h is the height. Since the triangle is a right triangle, the base and height are the two shorter sides
A tree trunk can be thought of as a cylinder with a height of 1.7 M if the tree trunk has a diameter of 60 cm what is its volume in metres cubed give your answer to 2 decimal place.
The formula for the volume of a cylinder is pi * radius squared * height, or πr^2h.
To find the radius of the cylinder, take the given diameter (60 cm) and divide it by 2. 60 / 2 = 30 cm.
Now we need to either find the height in centimeters or find the radius in meters. Because a centimeter is 1/100 of a meter, we multiply the radius by 100 to get the radius in meters.
We also must square the radius. So 30 cm multiplied by itself equals 900 cm.
Radius: 900 / 100 = 9 m
We have to square the radius before plugging it into the equation because it would mess up the numbers if we didn't (0.3 m squared is 0.09 m, which is very small).
Now we can plug these values into the formula for the volume of a cylinder.
π * r^2 * h = π * 9 m * 1.7 m = ~48.066 cubic meters
Rounded to two decimal places is 48.07 cubic meters.
The volume of the tree trunk is about 48.07 cubic meters.
56:32=k:28 what is k?
Therefore, k = 49.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
Does (–2, –2) make the equation y = x true?
Answer:
Yes.
Step-by-step explanation:
According to the given co-ordinate.
(x,y) = (-2,-2)
i.e. x = -2, y = -2
So, We can say that x = y = -2.
Hence, the given co-ordinate makes the equation y = x true.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807A car is 12 feet long. Levi makes a scale model of the car at 1:8 of its actual size. How long is the model
Answer:
1.5 feet
Step-by-step explanation:
Answer:
1.5 feet or 3/2 feet
Step-by-step explanation:
given a1 = -1 and a4 = -8 what is a10
Answer:
The nth term of the sequence is given. Find the first 4 terms, a10, and a15 2 What is the first term? a1 = (Type an integer or a simplified fraction.) What is the second term? a2 = (Type an integer or a simplified fraction.) What is the third term? a,-| (Type an integer or a simplified fraction.) What is the fourth term? a4(Type an integer or a simplified fraction.) What is the tenth term❤
if x+y=10 and x-y =6 what is the answer of x cube - y cube fast
Answer:
x+y=10 which means that x=10-y
Replace 10-y in the other equation which gives you:
10-y-y=6
10-2y=6
-2y=-4
y=2
Replace 2 in any of the 2 equations same answer for both:
x+y=10
x+2=10
x=8
So,
[tex] {x}^{3} - y^{3} [/tex]
[tex] = {8}^{3} - {2}^{3} [/tex]
=512-8
=504
Hope this helps!
will give brainlyist
What is the quotient of 1 and 7 over 8 ÷ 3 over 8?
Answer:
5
Step-by-step explanation:
[tex]1\frac{7}{8}\div\frac{3}{8}[/tex]
[tex]=\frac{15}{8}\div \frac{3}{8}[/tex]
[tex]=\frac{15\times \:8}{8\times \:3}[/tex]
[tex]=\frac{15}{3}[/tex]
[tex]=5[/tex]
The quotient is 5.
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\textsf{Given that:}\\[/tex]
[tex] \sf1 \dfrac{7}{8} \div \dfrac{3}{8} \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{7 \times 8}{8} \div \frac{3}{8} \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{15}{8} \div \dfrac{3}{8} \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{ \dfrac{15}{8} }{ \dfrac{3}{8} } \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{ \dfrac{15}{8} \times \frac{8}{3} }{ \dfrac{ \cancel \green3}{ \cancel \red8} \times \frac{ \cancel \red8}{ \cancel \green3} } \\ [/tex]
[tex]\sf \longmapsto \dfrac{ \dfrac{15}{8} \times \frac{8}{3} }{1} \\ [/tex]
[tex]\sf \longmapsto \: \dfrac{15}{ \cancel \red8} \times \dfrac{ \cancel \red8}{3} \\ [/tex]
[tex]\sf \longmapsto \: \dfrac{15}{3} \\ [/tex]
[tex]\sf\longmapsto \:\dfrac{15÷3}{3÷3}\\[/tex]
[tex]\sf\longmapsto \:\dfrac{5}{1}\\[/tex]
[tex]\sf\longmapsto \:\boxed{5} \: Answer.\\[/tex]
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A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?
Step-by-step explanation:
In 8 gallons of gas the car can go = 400 miles
In 1 gallon of gas the car can go = 400/8
In 1 gallon of gas the car can go = 50 miles
How far can the car take you with 1 gallon of gas? With 1 gallon of gas, the car can go 50 miles.
Step by Step calculations:
We know that
With 8 gallons of gas, the car can go 400 miles
Then,
With 1 gallon of gas, the car can go
= 400 / 8
= 50 miles
Therefore, with 1 gallon of gas, the car can go 50 miles.
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The school purchased 35 tickets for the ballet. Adult tickets were $10, and student tickets were $7. The total cost was $266.
If x represents the number of adult tickets purchased, and y represents the number of student tickets purchased, which system of equations represents this situation?
Answer:
Not too sure, but maybe this is what you need.
(Students = S, Adults = A) So, Ax + Sy = 266?
Or
x10 + y7 = $266
Step-by-step explanation:
I think the second one is the most accurate one, ignore the first equation. T^T
Could someone answer this in y=mx+b form please i cannot figure this out 2x-y=4
Answer:
y = 2x - 4.
Step-by-step explanation:
2x - y = 4
Subtract 2x from both sides
- y = -2x + 4
Multiply both sides by -1:
y = 2x - 4.
Answer:
y=-2x+4
Step-by-step explanation:
2x-y=4 - move the 2x to the right side by subtracting 2x from both sides
2x - y = 4
-2x -2x =
-y=-2x+4 - negative variable turns into y, since the negative isn't relevant
y=-2x+4
Im so confused of what to do?
if you're good at maths please help
with steps
Answer:
you need to show the number is prime
Step-by-step explanation:
To show 2^7 -1 is prime, you have to show it is not divisible by any prime less than its square root. That root is approximately 2^(7/2) = 2^3×√2 ≈ 11.3.
The primes of in that range are 2, 3, 5, 7, 11. The prime we're testing is ...
2^7 -1 = 128 -1 = 127
The sum of digits is 10, which is not a multiple of 3: not divisible by 3.
The units digit is 7, not 0 or 5: not divisible by 5.
The test for divisibility by 7 is to subtract twice the units digit from the rest of the number: 12 -2(7) = -2. This is not 0 or a multiple of 7, so 127 is not divisible by 7.
We know that 11² = 121, so 127 is not divisible by 11.
All of the tests for primality pass, so 2^7 -1 is a Mersenne prime.
_____
Additional comment
It is known that 2^n -1 being prime requires n to be prime. (The converse is not true: 2^11 -1 = 2047 = 23×89 is not prime.) The discovery of Mersenne primes is an ongoing process involving thousands of computers around the world. Only about 50 such primes are known.
You will notice that we have made use of some divisibility rules in order to simplify the process of dividing by small numbers. These can be helpful in many situations, so can be useful to learn.