An arithmetic sequence can be expressed as explicitly or recursively
The explicit formula of the sequence is [tex]a_n = 11 - 4n[/tex]
How to determine the explicit formulaThe recursive formula is given as:
[tex]a_n = a_{n -1} - 4[/tex]
[tex]a_1 = 7[/tex]
Substitute 2 for n in [tex]a_n = a_{n -1} - 4[/tex]
[tex]a_2 =a_1 - 4[/tex]
This gives
[tex]a_2 =7 - 4[/tex]
[tex]a_2 =3[/tex]
Calculate the common difference (d)
[tex]d = a_2 -a_1[/tex]
[tex]d = 3- 7[/tex]
[tex]d = -4[/tex]
The explicit formula is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 7+ (n - 1)*-4[/tex]
Expand
[tex]a_n = 7+4 - 4n[/tex]
[tex]a_n = 11 - 4n[/tex]
Hence, the explicit formula of the sequence is [tex]a_n = 11 - 4n[/tex]
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Diego invested $6,100 in a 9-month certificate of deposit paying 1.8% interest. How much interest did he earn form this investment?
Answer:
0.018
Step-by-step explanation
6,100,9a-mo,0.018
Find the volume of a pyramid with a square base, where the side length of the base is 16.6m and the height of the pyramid is 9.1 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
Formula for volume of square pyramid:-
V = 1/3 x a^2 x h
Where 'a' is the length of one side of the base, and 'h' is the height.
Plug in our values, given that:
16.6m = side length of base.
9.1m = height of pyramid.
V = 1/3 x a^2 x h
V = 1/3 x 16.6^2 x 9.1
V = 1/3 x 275.56 x 9.1
V = 1/3 x 2507.596
V = 2507.596/3
V = 835.865, which rounds to 835.9 cubic meters.
answer quickly please
The line TU is tangent to the circle whose center is at point S
The measure of angle U is 84 degrees
How to determine angle U?From the question, we understand that:
Angle STV = 84 degreesTU is tangent to circle SThis second highlight means that:
Angle STU = 90 degrees
And:
Angle STU = Angle STV + Angle VTU
This gives
90 = 84 + Angle VTU
Subtract 84 from both sides
Angle VTU = 6
The measure of angle U is then calculated as:
U + Angle VTU + Angle UVT = 180 ------ sum of angles in a triangle
This gives
U + 6 + 90= 180
Evaluate the sum
U + 96 = 180
Subtract 96 from both sides
U = 84
Hence, the measure of angle U is 84 degrees
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Write the expression as a product.
25-(a + 7)^2
pls help
Answer:
-(12+a)(a+2)
Step-by-step explanation:
this is to ez
The expression as a product is (a+12)(-a-2)
What is an expression?An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.
Given that, is an expression, 25-(a+7)², we need to write it in product form, 25-(a+7)²
= 25 - (a²+49+14a)
= 25-a²-49-14a
= -a²-14a-24
Factorizing,
= -a²-12a-2a-24
= -a(a+12)-2(a+12)
= (a+12)(-a-2)
Hence, the expression as a product is (a+12)(-a-2)
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If X and Y are 2 finite sets such that n() = 9, n( XY) - 4 and n( XY) -15, then n() is
(A) 5
(B) 6
(C) 10
(D) 12
Answer:
I think it's a hope this helps
Please help i am confused
Answer: (1)
Step-by-step explanation:
The parts listed in the congruence statement aren't corresponding, meaning they don't have to be congruent.
There are 9 members on a board of directors. if they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? a. 504 c. 729 b. 84 d. 362,880
Answer:
A. 504
Step-by-step explanation:
on edge 2022
Answer:
A.
Step-by-step explanation:
EDG 2022
Felipe just started collecting stamps. he has 36 stamps so far. His uncle Caro has 1,890 stamps in his collection. The number of stamps Carlos has is how many times the number Felipe has?
Answer:
52.5
Step-by-step explanation:
just divide bro it ain't that hard
Let n be a positive integer. z^n is the set of all lists of length n whose
entries are in z. prove that z^n is countable. (hint: find a bijection
between z^(n−1) × zand z^n and then use induction.)
What is the constant term in the expression 8xy − 9x2 y − 5x 6
Answer: 6
Step-by-step explanation:
I assume you meant to write 8xy − 9x2y − 5x + 6. The constant term in an expression is defined as a number by itself that contains no variables. Therefore, the answer is 6.
Can the GCF of a pair of numbers ever equal one of the numbers? Explain how you know
Answer:
It can
Step-by-step explanation:
For example, the GCF of 44 and 22 is 22.
Felix’s Feed Mill sells chicken feed for $8. 00 per bag. This price is no longer high enough to create a profit. Felix decides to raise the price. He is considering four different plans. Plan A: Raise the price by $0. 10 each week until the price reaches $12. 0. Plan B: Raise the price by 10 percent each week until the price reaches $12. 0. Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12. 0. Plan D: Raise the price by $0. 25 each week until the price reaches $12. 0. Which plan will result in the price of the feed reaching $12. 00 fastest? plan A plan B plan C plan D.
The plan will result in the price of the feed reaching $12.00 fastest is Plan B because it reaches within 5 weeks.
What is decision-making?The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.
Felix’s Feed Mill sells chicken feed for $8. 00 per bag.
This price is no longer high enough to create a profit.
Felix decides to raise the price. He is considering four different plans.
The plan will result in the price of the feed reaching $12.00 fastest will be
Plan A: Raise the price by $0. 10 each week until the price reaches $12. 0.
⇒ $0.10 × 20 = $2
This plan will take 20 weeks to reach at a price of $12.
Plan B: Raise the price by 10 percent each week until the price reaches $12.0. The price of this plan will be in t weeks is
[tex]12 = 8 *1.1^t\\\\t = 4.25 \approx 5[/tex]
This plan will take less than 5 weeks.
Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.0. The amount will be
Amount = 2/8 = $0.25
Plan D: Raise the price by $0.25 each week until the price reaches $12. 0.
⇒ 0.25 × 8 = $2
This will take 8 weeks.
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Please help me it’s due today.
Step-by-step explanation:
i) linear
ii)2
iii) 1
iv) 1
v) -1/5
First one can u type the options in the comment
what energy changes or causes
Answer: Nearly all thermal energy on Earth originates from the sun and radiates to the surface of our planet, traveling in the form of electromagnetic waves, such as visible light. Materials on Earth then absorb these waves to be used for energy or reflect them back into space. In an energy transformation, energy changes form.
Step-by-step explanation:
A cyclist managed to ride 5 miles against the wind in the same time that it took him to ride 10 miles with the wind. If the wind speed is 4 mph, which equation can be used to calculate the cyclist's average rate of speed in miles per hour
Given that the cyclist rides distances of 5 miles and 10 miles due to the wind, the equation that can be used to calculate the speed is therefore;
[tex]\frac{10}{v + 4} = \frac{5}{v - 4} [/tex]
How can the correct equation be found?The distance the cyclist rides against the wind = 5 miles
The distance the cyclist rides with the wind = 10 miLes
Let t represent the time it took the cyclist in both directions, we have;
[tex]t = \frac{10}{v + 4} = \frac{5}{v - 4} [/tex]
Where;
v = The cyclist's average rate of speed
Which gives;
10 × (v - 4) = 5 × (v - 4)
10v - 40 = 5v - 20
5v = 20
v = 20 ÷ 5 = 5
The equation that can be used to calculate the cyclist's average rate of speed is therefore;
[tex]t = \frac{10}{v + 4} = \frac{5}{v - 4} [/tex]
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19. Which of the following statements about the number line is true?
A. Numbers get smaller as you move to the left on the number line.
B. Number lines can't help you compare numerals.
O C. Numbers get larger as you move to the left on the number line.
D. Number lines end with the number 10.
Answer:
A. Numbers get smaller as you move to the left on the number line.
Step-by-step explanation:
A number line is typically drawn so that smaller, more negative numbers are on the left, and larger, more positive numbers are on the right.
__
Numbers get smaller as you move to the left on the number line.
_____
Additional comment
Number lines can be drawn with any scale and range, depending on what they are intended to represent. For representation of small integers, it is not uncommon for a number line to range from -10 to +10. However, that is not the only possible range that might be used.
Any number line can be used to show number order (least to greatest ≡ left to right). A number line with a linear scale can also be used to show relative differences between numbers: a greater distance on the number line corresponds to a greater difference between numbers.
If angle ABC measures 122, what does angle ADC measure?
Answer:
61
Step-by-step explanation:
angle at centre equals twice that at circumference
Need help with this pls
Answer:
Answer:
SORRY
Step-by-step explanation:
ANSWER
Step-by-step explanation:
Answer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWER
2-y^2=-14 solve for y express answer as an integer or in simplest radical form
Answer:
8
Step-by-step explanation:
y^2=-16
y= -16/1 % 2/1
y=-16/1 % 1/2
y = 8
Answer:
y=4
Step-by-step explanation:
its -y^2=-16. square root both sides to get rid of the exponent and it gives you -y=-4 which is the same as y=4
An electrician has an income of $41,500. The income tax the electrician has to pay is 12%. What is the amount of income tax that the electrician has to pay? A) $3,840 B) $4,164 C) $4,980 D) $5,210
Answer:
he has to pay 4980$ in tax
Step-by-step explanation:
Answer:
This question was on my test and I got a 100 so its right
Step-by-step explanation:
1. Which of the following is an example of a system of equations?
x^2 + 5y + 10 = 14
x - y = 12
x+y=12
x – 3y > 23
3x^1/3+ 2y < 100
x+y=12
3x^1/3 + 5y = -19
x + 5y < 55
Answer: (1)
Step-by-step explanation:
A system of equations must have two equations. The first option is the only one that satisfies this.
Do number 17 please.
Answer:
667.2
Step-by-step explanation:
aP/2 apothem is 13.9, perimeter is 16(6)= 96
multiply apothem and perimeter then divide by 2.
Miko and Raj get the same salary. Every month Miko saves
9/11 of her salary while Raj saves
7/9 of his salary. Every year Miko saves $1584 more than Raj. Find the monthly salary of Miko.
Answer:
Step-by-step explanation:
The salaries are the same. Only the fraction of how much is saved is quite different.
Equation
x ( 9/11 - 7/9) = 1584
Explanation: The salary amount is x. The fractional amounts saved are also given. You have to take the difference because one of the people saves more than the other.
The amount that is more is 1584.
Solution
9/11 = 0.8182
7/9 = 0.7778
9/11 - 7/9 = 0.8182 - 0.7778 = 0.0404
Put that into the equation.
x(0.0404) = 1584 Divide by 0.0404)
x(0.0404) = 1584/0.0404
answer:x = 39204
Michelle's keeping track of how much time she spends playing video games. She knows she gamed for a total of 60 hours during the past 3 weeks. She played 4 hours more during the 2nd week than the 1st week. Also, she played 2 hours less during the 3rd week than the 2nd week. How many hours did she spend playing video games during the 3rd week?
Answer:
I have no clue.
Step-by-step explanation:
Answer:
What is a appropriately
What is a Procedure
What is a Enthusiasm
What is a Conflict
What is a Technique
What is a Obtain
What is a conflict management
Factoring
Need help pls
Answer:
2x(2²+3³)
I HOPE THIS HELP, THANKS ME LATER
Answer:
Factor by using the AC method-
1. (x+1) (x+4)
Factor by grouping-
2. (4x-3) (x+2)
y = x + 2
5x - 4y = -3
Solving systems by equations
Answer: x = 5, y = 7
Step-by-step explanation:
1. First, put the variables together/rearrange:
y - x = 2 & 5x - 4y = -3
2. Cancel out variable x by multiply the first equation by 5:
5y - 5x = 10 & 5x - 4y = -3
3. Add equations:
y = 7
4. Then determine x by plugging y back into the first equation y = x + 2:
x = 5
Find the area of the figure below. Use 3.14 to approximate .
Round your answer to the nearest tenth.
Answer:
145.1 m^2
Step-by-step explanation:
(8x15)+(3.14x8)
120+25.12
145.12
round
145.1
What is the measure of the missing angle?
39 faren height plus 33 plus an unknown number to equal 180
Answer:
108
Step-by-step explanation:
39 + 33 + x = 180
To find the missing angle, we have to add together the two angles that are given and then subtract that from 180.
39 + 33 = 72
180 - 72 = 108
Therefore, our answer is 108 degrees.
I hope this helps! Have a lovely day!! :)
Solve for area and perimeter in each of the following problems.
Answer:
1. perimeter =2(l+w)
=2(17+10)
= 54 yards
Are of the perimeter=l times b
=17 x 10
=170 yd square
Just follow this concept for all of them. It the same thing. Good Luck!!
Step-by-step explanation:
A carpenter is making a circular tabletop with a circumference of 4.5 yards.
What is the radius of the tabletop in to the nearest centimetre?