Answer:
t(n) = 2n² + n - 3
Step-by-step explanation:
Given sequence:
0, 7, 18, 33, 52Find the formula for nth term t(n)
SolutionSequence is neither arithmetic nor geometric, analyzing:
0, 7, 18, 33, 52First level difference
7, 11, 15, 19Second level difference
4, 4, 4As there are two levels, the formula should be in the form of:
t(n) = an² + bn + cTrying the formula with the known terms:
t(1) = 0 ⇒ a+b + c= 0t(2) = 4a + 2b + c = 7 ⇒ 3a + b = 7t(3) = 9a + 3b + c = 18 ⇒ 3(3a+b) + c = 18 ⇒ 21 + c = 18 ⇒ c = -3Going back to previous equations to find remaining coefficients:
t(1) ⇒ a+ b = 3 ⇒ t(2) = 2a + (a+b) = 7 ⇒2a + 3 = 7 ⇒ a= 2 ⇒ b = 1So the formula becomes:
t(n) = 2n² + n - 3
if ( 3x + 2) (5x + 1) = ax2 + bx + 2
What is the value of a - b ?
a - b= 2
Step-by-step explanation:
expanding the brackets
we have 15x^2+13x+2
a= 15 b= 13
thus, a-b =15-13
=2
The value of a - b if, (3x + 2) (5x + 1) = ax² + bx + 2 is 2 i.e a - b = 2.
What is expression?At least two numbers or variables, one or more arithmetic operations, and a statement are all required components of a mathematical expression. The term "expression" or "mathematical expression" refers to a finite collection of symbols that are well-formed in line with context-dependent criteria.
Given:
(3x + 2) (5x + 1) = ax² + bx + 2
Write the left term of the equation in the format of the right term,
3x (5x + 1) + 2(5x + 1)
15x² + 3x + 10x + 2
15x² + 13x + 2
Compare the above equation to ax² + bx + 2,
a = 15 and b = 13
Calculate the value of a - b as shown below,
a - b = 15 - 13
a - b = 2
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A. Can trace a particular file in a few seconds. B. Help us in many ways by coming up with new information. C. Are more useful in an office setting. D. Are now more costly and compact.
Answer:
A. can trace a particular file in a few seconds.
Step-by-step explanation:
The new locator has now easy access and user friendly. The data saved here is useful when you are locating a file. It will take few seconds to locate a file. This saves time in finding the relevant files. The new locator is user friendly and is not really technical to operate it.
Which equations have the variable term in the equation –6 + 2x = 6x – 9 isolated to one side of the equals sign, and the constant isolated to the other side? Select all that apply.
Answer:
C and D
Step-by-step explanation:
–4x = –3 and 3 = 4x is the answer.
(I did the quiz)
A laser printer prints 200 pages in 4 minutes. How many pages does it print in 25 minutes?
Answer: I think the answer is 1250.
Step-by-step explanation:
I did 200 divided by 4 which is 50. I then multiplied 50 * 25 and got 1250.
Dash offers and unlimited talk and texting plan for $80 per month AB&C charges $0.20 per text message and $55 for 1,000 min of talk time per month Horizon charges $0.10 per text message and $75 for 1,000 minutes of talk time per month what is the equation for each of them and which phone bill should I go with
Answer:
Let's define x as the number of text messages send.
y as the number of 1,000 minutes talk per month.
(so we can write y = N/1000) where N is exactly the number of minutes that you talked that month.
> The equation for Dash is:
C1(x, y) = $80
>The equation for AB&C
C2(x,y) = $0,20*x + $55*y
> Horizon
C3(x,y) = $0.10*x + $75*y.
Now, which company you should go for?
Well, it depends on the values of x and y that you have.
if in your case you have x > y, you may want to go with Horizon, because the price per text is smaller.
if you usually talk, you may want to go with AB&C because the slope for y is smaller.
If you send a lot of texts and talk a lot, then Dash is the best option, because there is no dependence with the variables x, y
If M is the midpoint of XY, XM=2x+5 and YM=25, find XY.
Answer:
50
Step-by-step explanation:
Since M is the midpoint of XY, this means that XM and MY must be equivalent from the definition of midpoint.
So:
[tex]XM=MY[/tex]
The entire length of the segment (XY) is:
[tex]XY=XM+MY[/tex]
We know that XM is equivalent to MY. Substitute MY for XM:
[tex]XY=MY+MY[/tex]
Combine like terms;
[tex]XY=2MY[/tex]
We are told that YM (or MY) is 25. So:
[tex]XY=2(25)[/tex]
Multiply:
[tex]XY=50[/tex]
So, the length of XY is 50.
And we're done!
50?
X_________M__________Y
2x + 5 = 25
x = 10 so 2(10) + 5 = 25
25 + 25 = 50
HELP PLEASE
Use greater than, equal to =, or less than sign to compare
2/3 and 1/6
Answer:
2/3 < 1/6
Step-by-step explanation:
hope this helps
Answer:
2/3 > 1/6
Step-by-step explanation:
someone help me please
This is the answer
Hope this answer is helpful...
Hope this answer is helpful...Make me as brainliest...
What is the perimeter of a square with a side length of 3x?
Answer: 12
Step-by-step explanation: to find perimeter we have to add all the sides of the shape so, for a square you can just simply multiply your given side 3 by 4 because there is 4 sides of a square and this equals to 12.
b) By selling
a watch for Rs. 2400, a
dealer gains 25%.
i) What is the cost price?
in How much percent would be profit by selling it for
Rs. 2040?
Answer:
CP=Rs 1920
profit%=6.25%
The width of a rectangle is 4 cm less than the length. The perimeter is at most 48 cm. What are the restrictions on the dimensions of the rectangle?
Answer: 2w + 2 (w + 4) ≤ 48
I don't know why, or the process tho.
Evaluate -3w -2p for w=7 and p= -3
Answer:
-3
Step-by-step explanation:
-3w-2p=-21+18=-3
What is the order of these numbers? Order the numbers from least to greatest. Please help! Thank you so much! −1.4, −85, 0.6, −0.9, 14
which equation should you solve to find x?
Answer:
B
Step-by-step explanation:
sin26° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] → B
The equation that should be solved in order to find x is [tex]sin\ 26^\circ =\frac{x}{10}[/tex]. The correct option is C. [tex]sin\ 26^\circ =\frac{x}{10}[/tex]
Trigonometry: Solving a right triangleFrom the question, we are to determine which equation should one solve to find x
Considering the right triangle in the diagram,
Opposite = x
Adjacent = 9
Hypotenuse = 10
By SOH CAH TOA
We have that
[tex]sin\theta = \frac{opposite}{hypotenuse}[/tex]
Where θ is the angle
Then, we can write that
[tex]sin\ 26^\circ =\frac{x}{10}[/tex]
This is the equation that should be solved in order to find x
Hence, the equation that should be solved in order to find x is [tex]sin\ 26^\circ =\frac{x}{10}[/tex]. The correct option is C. [tex]sin\ 26^\circ =\frac{x}{10}[/tex]
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In a certain grocery store, strawberries cost $4.96 per pound ( 4.96 dollars/lb d o l l a r s / l b ). What is the cost per ounce?
Cost of the strawberry will be $0.31 per ounce.
Given in the question,
Strawberry cost → $4.96 per poundWe can write the cost as [tex]\frac{4.96\text{ Dollars}}{1\text{Pound}}[/tex].
Since, 1 pound = 16 ounces
To convert the cost of the strawberry in dollars per ounce, multiply the price by the conversion factor [tex]\frac{1\text{ Pound}}{16\text{ Ounces}}[/tex].
So the cost of strawberry = [tex]\frac{4.96\text{ Dollars}}{1\text{Pound}}\times \frac{1\text{ Pound}}{16\text{ Ounces}}=0.31\text{ Dollars per ounce}[/tex]
Therefore, cost of the strawberry will be $0.31 per ounce.
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HELP NEEDED MY TIME LIMIT IS ALMOST OVER ILL GIVE BRAINLIEST
Answer:
c. nrkrkrjjrjrjrkerkekkrr
Answer:
c
Step-by-step explanation:
its c :)))))
A beverage is made by mixing 3 parts of water with 5 parts of fruit juice. How many parts of water are mixed with 1 part of fruit juice? A. 3 over 8 B. 3 over 5 C. 5 over 3 D. 5 over 8
If a beverage is made by mixing 3 parts of water with 5 parts of fruit juice then 3/5 fraction of water is mixed with 1 part of fruit juice.
Given that, a beverage is made by mixing 3 parts of water with 5 parts of fruit juice.
What is fraction?Fraction is a combination of numerator and denominator. The number above the division sign is known as numerator and the numerator below the division side is known as denominator.
We have been given that to make a beverage 3 parts of water with 5 parts of fruit juice and we are required to find the fraction of water mixed with 1 part of fruit juice.
Water mixed with 1 part of fruit juice
= Water mixed with 5 parts of fruit juice/5
= 3/5
Hence, if a beverage is made by mixing 3 parts of water with 5 parts of fruit juice then 3/5 fraction of water is mixed with 1 part of fruit juice.
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Raquel realizó un depósito en su cuenta bancaria, pero al llegar al banco se enteró que tenía un saldo negativo de C$2376,5. Si ella depositó C$3568,5, cuánto es ahora el saldo de su cuenta?
Answer:
Saldo bancario= $1,192
Step-by-step explanation:
Dado la siguiente información:
Saldo del banco= -$2,376.5
Depósito= $3,568.5
Ella tenía una cuenta en negativo. El depósito le ayuda a cubrir el sado y pasar a tener un saldo positivo. Ahora calculamos cuánto le queda en la cuenta.
Saldo bancario= -2,376.5 + 3,568.5
Saldo bancario= $1,192
The horizontal distance of E is 9 units to the east of point F. Determine the coordinates of F if the coordinates of E are (3,8).
Answer:
(-6,8)
Step-by-step explanation:
By reading the question you can determine that point E is to the east, or the right, of point F by 9 units. This ultimately means you must subtract 9 units on the horizontal (x-axis) in order to get to point F.
Paisley is working two summer jobs, making $10 per hour babysitting and $22 per hour tutoring. Paisley must earn no less than $190 this week. Write an inequality that would represent the possible values for the number of hours babysitting, bb, and the number of hours tutoring, tt, that Paisley can work in a given week.
Answer:
10bb + 22tt ≥ 190
a piece of lumber is 2 1/4 ft long is cut into 3 equal pieces .How long will each piece of cut wood be ?
Answer: Each piece would be 3/4 feet long
Step-by-step explanation:
If the piece of lumber is 2 1/4 ft long, and it is cut into 3 pieces then divide
2 1/4 by 3 to find out how long each piece of cut wood would be.
2 1/4 is the same as 9/4
[tex]\frac{9}{4} / \frac{3}{1}[/tex] = 9/12 which also simplifies to 3/4
PLEASE ANSWER I NEED HELP
What is the perimeter of the triangle?
The perimeter of the triangle is 36 units.
Distance
The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by:
[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The coordinate of the triangle is A(0, 0), B(10, 0) and C(5, 12). Hence:
AB = 10 units
[tex]BC=AC=\sqrt{(5-0)^2+(12-0)^2}=13\ units[/tex]
Perimeter of triangle = AB + BC + AC = 10 + 13 + 13 = 36 units
The perimeter of the triangle is 36 units.
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Please help!!! It’s Timed!
Answer:
7/25 im pretty sure sure
three times the sum of a number and 15 is 24
Answer:
[tex]\huge\boxed{\sf x = -7}[/tex]
Step-by-step explanation:
Let the number be x
So,
=> The sum of number and 15 is x + 15
=> Three times will be 3(x+15)
Given that it equals 24
So, the given condition is:
3(x+15) = 24
Resolving Parenthesis
3x + 45 = 24
Subtracting 45 to both sides
3x = 24 - 45
3x = -21
Dividing both sides by 3
x = -7
.4r when r=6
someone help
Answer:
24
Step-by-step explanation:
4(6)=24
I need this answer ASAP
The table shows the number of different types of
animals in a pet store.
Pet
Quantity
Cats
10
Which statements are correct? Select all that apply.
The ratio of cats to dogs is greater than the ratio of
birds to dogs.
The ratio of cats to birds is greater than the ratio of
ferrets to birds.
The ratio of birds to ferrets is less than the ratio of
dogs to ferrets.
The ratio of ferrets to cats is less than the ratio of
dogs to cats.
Dogs
8
Birds
12
Ferrets
4.
Answer:
B and D
(The ratio of cats to birds is greater than the ratio of ferrets to birds; The ratio of ferrets to cats is less than the ratio of dogs to cats)
hope this helps :)
Answer:
it is
Step-by-step explanation:
b
d
In the 21st century, people measure length in feet and meters. At various points in history, people measured length in hands, cubits, and paces. There are 9 hands in 2 cubits. Write an equation to express the relationship between hands, LaTeX: hh, and cubits, LaTeX: cc. Explain your reasoning under your equation.
Answer: 1 hand = 0.22... cubits.
Step-by-step explanation:
We want to write the relation between hands and cubits.
We know that there are 9 hands in 2 cubits.
So we can write:
9 hands = 2 cubits.
Now, we want to have an unit in the left side (so we can see how many cubits are equal to exactly one hand).
Then we can divide by 9 in both sides of the equality.
(9 hands)/9 = (2 cubits)/9
1 hand = 0.22... cubits.
Answer:
22.5 hands = 3 paces
Step-by-step explanation:
Nobody answered b yet again.
(-8 ÷ 4) + 5 + 4(3 - 6)=
Answer:
-9
Step-by-step explanation:
(-8/4)+5+4(3-6)
-2+5+12-24
17-26
-9
Answer:
-9
Step-by-step explanation:
(-8 ÷ 4) + 5 + 4(3 - 6]
-2+5+12-24
-9
Adrianne is going to buy dog treats for $2 each, plus a new $5 dog toy. She will not spend more than $30. What’s the equation