The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].
What is the arithmetic sequence?"Arithmetic means" refers to repeatedly adding a fixed number to produce a series. Let n be "the number." Because the numbers in the sequence are becoming progressively negative, we might conclude that n is negative.We can locate a particular term in an arithmetic series using the method for locating the nth term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.The Arithmetic Mean or Mean of the Group is the sum of all the numbers in a group divided by the total number of items in the list. For instance, since 5 + 7 + 9 = 21 and 21 divided by 3 [there are three numbers] is 7, the mean of the digits 5, 7, and 9 is 4.The difference between each succeeding pair of terms in an arithmetic series is always the same. The following is the explicit guideline for formulating any arithmetic sequence: a = a1 + d (n - 1)The explicit rule for this sequence:
The obvious rule for an arithmetic sequence is given as follows:
[tex]a_{n}=a_{1} +(n-1)d[/tex]
The first term = [tex]a_{1}[/tex].
The number of terms = n.
The common difference for two consecutive terms = d.
A recursive rule for an arithmetic sequence: [tex]a_{1} =4[/tex].
[tex]a_{n} =a_{n-1}-3[/tex]
The arithmetic sequence is given by:
[tex]a_{n} =a_{n-1}+d[/tex]
We get: d = -3
Substitute the given values:
[tex]a_{n} =4+(n-1)(-3)[/tex]
[tex]a_{n} =4-3n+3[/tex]
=7-3n
The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].
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The explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is known as the common difference of the arithmetic sequence.For example, [tex]2,5,8,11,...[/tex] is an arithmetic sequence with the first term [tex]a=2[/tex] and the common difference [tex]d=3[/tex].The formula for the nth term [tex]a_n[/tex] of an arithmetic sequence whose first term is [tex]a[/tex] and the common difference is [tex]d[/tex] can be given by [tex]a_n=a+(n-1)d[/tex].Given the recursive formula for an arithmetic sequence: [tex]a_1=4, a_n=a_{n-1}-3[/tex].
Thus, the first term of the arithmetic sequence is [tex]a=a_1=4[/tex]. using the recursive formula, we can get the 2nd term by putting [tex]n=2[/tex], [tex]a_2=a_1-3=4-3=1[/tex].
So, the common difference of the given arithmetic sequence is [tex]d=a_2-a_1=1-4=-3[/tex].
Thus, the nth term of the arithmetic sequence is given by [tex]a_n=a+(n-1)d\\\Longrightarrow a_n=4+(n-1)\times(-3)\\\Longrightarrow a_n=7-3n[/tex]
Therefore, the explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].
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The dialogue of a square is X units what is the area of the square in terms of X
The area of the square in terms of x unit is x²/ 2
Diagonal of a square
The expression for the diagonal of a square is written as'
d^2=s^2+s^2
Where
s² is the area of the squared² is the diagonal of the same squareBut from the given question we have that the diagonal of the said square is 'x'
Now, let's substitute the values into the expression of the diagonal given above,
d^2=s^2+s^2
d² = s² + s²
We have,
x² = s² + s²
Collect and add like terms
x² = 2s²
But we know that s² represents the area of the square
So,
x² = 2 × area
Make 'area' subject of formula
Area = x²/ 2
Now, we can say that the area of the square in terms of x units is x²/2
Therefore, the area of the square in terms of x unit is x²/ 2
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NO LINKS!! Please help me with this problem
Answer:
y²/324 -x²/36 = 1
Step-by-step explanation:
Where (0, ±b) are the ends of the transverse axis and y = ±(b/a)x describes the asymptotes, the equation of the hyperbola can be written as ...
y²/b² -x²/a² = 1
ApplicationHere, we have transverse axis endpoints of (0, ±18) and asymptotes of y = ±3x, so we can conclude ...
b = 18
b/a = 3 ⇒ a = 18/3 = 6
The equation of the hyperbola in standard form is ...
y²/324 -x²/36 = 1
A rectangular table is six times as long as it is wide. If the area is 150 ft2, find the length and the width of the table.
The width of the table is
The length of the table is?
Answer:
Length = 30ft, Width = 5ft
Step-by-step explanation:
Let x be the width.
Area of Rectangle = Length * Width
Given from the information in the question,
Length = 6x ft
Width = x ft
Substitute the values into the formula:
6x * x = 150
[tex]6x^{2}[/tex] = 150
[tex]x^{2} =\frac{150}{6}[/tex]
[tex]x^{2} =25[/tex]
[tex]x=\sqrt{25}[/tex]
x = 5 ft.
Therefore,
Length = 6 * 5 = 30ft
Width = 5 ft.
Of the stamps in a book, 5/12 came from Brian's collection and 24 came from Amy's. Of the rest, 15 were Jo's, 3/10 were Carl's and 27 were purchased. How many stamps are there in the book? HELPPP
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Thus the number of stamps in the book is 66[tex]\frac{43}{60}[/tex] (67).
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Majorly, the alphabet in the expression is referred to as the unknown value which has to be determined.
When the power of any of the alphabets contained in an algebraic expression is more than one, then it can be referred to as a polynomial.
In the given question, let the number of stamps in the book be represented by N.
So that;
N - 5/12 + 24 + 15 + 3/10 + 27 = 0
N - (5/12 + 24 + 15 + 3/10 + 27) = 0
N - [tex]\frac{8006}{120}[/tex] = 0
N - 66[tex]\frac{43}{60}[/tex] = 0
N = 66[tex]\frac{43}{60}[/tex]
= 66.72
N ≅ 67
Therefore the number of stamps in the book is approximately 67.
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What is the equation of a line that goes through the point (0, -5) and
has a slope of -3?
O -5y = - 3x
O y = 3x - 5
O y=-3x - 5
O y = -5x - 3
Answer:
Equation of a line has a form as below:
y=ax+b
Given:
b ( the y intercept)= -5
a ( the slope)= -3
so, y= -3x -5 is the equation of the line.
Please give me Brainliest [:)
PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
Given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
What is the height of the building?
Given the data in the question;
Angle of elevation θ = 35°Distance between the person and the building | Adjacent = 80ftHeight of the person h = 4ft.Height of the building from the eye level | opposite = xSince the scenario depicts a right angle triangle, we use trigonometric ratio.
tanθ = Opposite / Adjacent
We height of the building from the eye level x
Substitute given into the equation,
tan( 35 ) = x / 80ft
x = tan( 35 ) × 80ft
x = 0.7002075 × 80ft
x = 56ft
Now, to get the height of the building, we add the height of the person and the height of the building from the eye level of the person.
Height of building = x + 4ft
Height of building = 56ft + 4ft
Height of building = 60ft
Therefore, given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
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Find the midsegment of the triangle which is parallel to CA.
Answer:
[tex] \pmb{ \pink{QUESTION�}}[/tex]
Find the midsegment of the triangle which is parallel to CA.
[tex] \pmb{ \pink{ANSWER:-}}[/tex]
Tip
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle.This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.If two segments are congruent, then they have the same length or measure.In other words, congruent sides of a triangle have the same length.[tex] \frak{Explanation:-} [/tex]
We have to find the segment which is parallel to CA.
From the given data,
The segment EG is the midsegment of the triangle[tex]\triangle[/tex] ABC.
So we have,
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side.
[tex]\implies\rm{midsegment \: EG \: parallel \: to \: CA}[/tex]
[tex]\frak{RainbowSalt}[/tex]~
Answer:
[tex]\fbox {EG}[/tex]
Step-by-step explanation:
Based on the given diagram, we can clearly see the midsegment (lies in the middle of the figure) that is parallel to AC is EG
I hope it helped you solve the problem.
Good luck on your studies!
Mrs. Oliver drew a box plot to represent her students’ scores on a mid-term test.
Answer:
About 1/4 scored higher and 3/4 scored lower
Step-by-step explanation:
84 is on the right side line
Each line represents 25 % of the score
It is 75 percent ( 3 lines) of the way
She scored higher than 75% of the students and lower than 25% of the students
About 1/4 scored higher and 3/4 scored lower
HELP!!! (05.06 HC) During a laboratory experiment, a 2.36g sample of NaHCO3 was thermally decomposed to generate 1.57g of carbonic acid (H2CO3). Calculate the percent yield of carbonic acid for the reaction. Show all your work (10 points). NaHCO3 → Na2CO3 + H2CO3
The percentage yield of carbonic acid is 66 percent.
How to find percentage yield?The percentage yield of the carbonic acid can be found as follows:
NaHCO₃ → Na₂CO₃ + H₂CO₃
Hence, 2.36g sample of NaHCO₃ was thermally decomposed to generate 1.57g of carbonic acid (H₂CO₃)
Using law on conservation, the mass of the reactant is equals to the product.
Therefore,
percentage yield of carbonic acid = 1.57 / 2.36 × 100
percentage yield of carbonic acid = 157 / 2.36
percentage yield of carbonic acid = 66.2447257384
percentage yield of carbonic acid = 66 %
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Find the area and perimeter
for each polygon.
Answer:
5. P = 23 m
A = 15 [tex]m^{2}[/tex]
6. P = 24.4 in
A = 15.3 [tex]in^{2}[/tex]
Step-by-step explanation:
Area formula of a triangle is A = 1/2 bh
Area formula of a parallelogram is A = bh
5. The height of a triangle is perpendicular to the base.
A = 1/2 * 10 * 3
A = 15 [tex]m^{2}[/tex]
6. The height of the parallelogram is also perpendicular to the base.
A = 9 * 1.7
A = 15.3 [tex]in^{2}[/tex]
Perimeter means you add all the side lengths.
5. The side lengths are 5m, 8m, and 10m. Adding those together, you get 23m.
6. A parallelogram has congruent opposite sides. That means your side lengths are 9 in, 3.2 in, 9 in and 3.2 in. Adding those together, you get 24.4 in.
A person needs to fill 15 water jugs with a hose. Filling the first 3 jugs has taken 4 minutes. How long to finish filling the remaining jugs?
Answer:
20 minutes
Step-by-step explanation:
Rate x Time = jobs
The rate is 3 jugs/ 4 minutes.
The number of jobs is 15
Use T for time
3/4T = 15 Multiply both sides by 4/3 to get the variable T by itself
(4/3) 3/4 T = 15(4/3)
T = 20 minutes
4. Raquel is presented with two loan options for a $60,000 student loan. Option A is a 10-year fixed rate loan at 4% interest compounded monthly, while Option B is a 20-year fixed-rate loan at 3% interest compounded monthly. What is the monthly payment under each option? What is the total interest for each option? Round your answers to the nearest cent.
5. Write a paragraph discussing what factors might influence Raquel’s decision when choosing between Option A and Option B for her student loan. Please discuss at least two different factors. Your paragraph should be at least 4 sentences.
Step-by-step explanation:
chicken nuggets are so bussing that the answer is c
e) 1 cubic centimetres = 1÷1000000 cubic meter. Rewrite in scientific notation
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{1000000} \: \: m {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{10 {}^{6} } \: \: m {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = {}{10 {}^{ - 6} } \: \: m {}^{3} [/tex]
Merger_Model_Evaluation_-_Question.xlsx 19 The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is: $92,165 $30,498 $92,661
$91,669
The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is $91,669
How to calculate the value?Share Price, P = 44.29
Premium on the acquisition, p = 20%
Therefore, effective share price for acquisition, P* = P x (1 + p) = 44.29 x (1 + 20%) = $ 53.15
Number of shares outstanding, N = 1,734 MM
Equity value, E = P* x N = 53 x 1,734
= $92,158.63 MM
Net Debt, D = - 496
Hence, the implied enterprise value:
= Equity value + net debt
= 92,158.63 + (- 496)
= $$91,669
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Suppose that the base salary of a salesperson is $30,000 per year. The salesperson gets an additional $50 for every sale. Let x represents the number of sales. How can we model the scenario with a linear function? How many items does the salesperson need to sell to earn $50,000
Answer:
See below
Step-by-step explanation:
Salary (y) = 30 000 + 50 x
y = 30 000 + 50x where x is the number of sales
How many sales for 50 000 ?
50 000 = 30 000 + 50 x
20 000 = 50 x
x = 400 sales
I. Model Problems
A linear model is a linear equation that represents a real-world
scenario. You can write the equation for a linear model in the same way
you would write the slope-intercept equation of a line. The y-intercept
of a linear model is the quantity that does not depend on x. The slope is
the quantity that changes at a constant rate as x changes. The change
must be at a constant rate in order for the equation to be a linear model.
Example 1 A machine salesperson earns a base salary of $40,000 plus
a commission of $300 for every machine he sells. Write an equation
that shows the total amount of income the salesperson earns, if he sells
x machines in a year.
The y-intercept is $40,000; the salesperson earns a $40,000 salary in a
year and that amount does not depend on x.
The slope is $300 because the salesperson’s income increases by $300
for each machine he sells.
Answer: The linear model representing the salesperson’s total income
is y = $300x + $40,000.
Linear models can be used to solve problems.
Example 2 The linear model that shows the total income for the
salesperson in example 1 is y = 300x + 40,000. (a) What would be the
salesperson’s income if he sold 150 machines? (b) How many
machines would the salesperson need to sell to earn a $100,000
income?
(a) If the salesperson were to sell 150 machines, let x = 150 in the linear
model; 300(150) + 40,000 = 85,000.
Answer: His income would be $85,000.
(b) To find the number of machines he needs to sell to earn a $100,000
income, let y = 100,000 and solve for x:
Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 20 more adult tickets han student tickets to the fall play. to If the
class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution
Answer:
80
Step-by-step explanation:
Let the number of adult tickets sold be a and the number of student tickets sold be s.
"The drama class sold 20 more adult tickets han student tickets to the fall play." means that a-20=s."the class collected $880 from ticket sales" means that 8a+4s=880, which is the same as 2a+s=220.Substituting the first equation into the second,
[tex]2a+a-20=220 \\ \\ 3a-20=220 \\ \\ 3a=240 \\ \\ a=80[/tex]
A ship left a port and sailed east at the rate of 30 miles per hour. One hour later, a second ship left the same port at the rate of 40 miles per hour, also traveling east. In how many hours did the second ship overtake the first ship?
Answer:
3 hours
Step-by-step explanation:
When the ships meet each other, that means the the distance travelled for both ships are the same, that is where the 2nd ship will overtake the ship.
Distance = Speed * Time
So, given information from the question, and letting x be the time in hours (from when the 1st ship departs), we can deduce:
Distance travelled of 1st ship = Distance travelled of 2nd ship
30x = 40(x-1)
30x = 40x - 40
-10x = - 40
x = [tex]\frac{-40}{-10}[/tex]
= 4
Since we are calculating based on the 2nd ship,
Time taken for 2nd ship to overtake first ship = x - 1 = 4 - 1 = 3 hours.
PLEASE HELPPPPP PLEASE so confused
Answer:
105°
Step-by-step explanation:
EFGH is an isosceles trapezoid (a trapezoid with congruent legs is an isosceles trapezoid)
∠G=75° (base angles of an isosceles trapezoid are congruent)
∠F=105° (same-side interior angles theorem)
Please select the best answer from the choices provided:
A. Unbounded
B. Infeasible
C. One optimal solution.
D. Alternate optimal solutions
The system of inequalities has Infeasible solutions option (B) Infeasible is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The inequality:
2x + y ≤ 5
3x + y ≤ 12
First plot the above two inequality on a coordinate plane.
As we can see the intersection region on a coordinate plane for both the inequality:
f(x, y) = 2x + 2y
As we can see there is so many points in the intersection region for the above function so there will no single solution.
Thus, the system of inequalities has Infeasible solutions option (B) Infeasible is correct.
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Coach Kirby is forming dodgeball teams from students in her physical education class.
She wants teams that each have 6 students. There are fewer than 48 students in the class,
so Coach Kirby can't form as many full teams as she wants.
1)) Let x represent how many full teams Coach Kirby can form. Which inequality describes
the problem?
6x < 48
6x > 48
Solve the inequality. Then, complete the sentence to describe the solution.
1) Coach Kirby can form fewer than 8|
full teams.
Please hurry
Answer:
6x<48
Step-by-step explanation:
ik its this one because theres 48 players and 6 teams both are even numbers so if you did 48÷6x you would get 8 but theres fewer than 48 kids
1.
Find a polynomial f(x) of degree 3 that has the following zeros.
4, 0, -7
Leave your answer in factored form.
Answer:
x³+3x²-28x
Step-by-step explanation:
(x-4)(x-0)(x+7)
(x-4)(x)(x+7)
(x-4)(x+7)=(x²+3x-28)
(x²+3x-28)(x)=x³+3x²-28x
7/3 4/2 as improper fraction
Answer:
If the question asked mixed fraction:
7/3 = 2 1/3
4/2 = 2
Step-by-step explanation:
I converted it to mixed fraction because it is already improper fraction.
SOMEBODY PLEASE HELP ASAP
Answer:
40
Step-by-step explanation:
[tex]\frac{RW}{24}=\frac{30}{18} \\ \\ RW=40[/tex]
17 + x =31
i need help
Answer:
x= 14
Step-by-step explanation:
First (and only) we subtract 17 from both sides :
17 + x - 17 = 31 - 17
x = 31 - 17
x = 14
Hope this helped and have a good day
The answer is 14.
To solve this, only one step is required, which is : Subtract 17 from each side.
17 + x - 17 = 31 - 17x = 14Find the equation of the line that passes through point (6, 1) with the x-intercept of 2.
[tex]y = \frac{ - 1}{4} x + \frac{1}{2} [/tex]
given the quadriatic equation
x² + 6x + 9 = 4kx
find the set values for which k has real roots
Answer:
⇒ The given quadratic equation is x2−kx+9=0, comparing it with ax2+bx+c=0
∴ We get, a=1b=−k,c=9
⇒ It is given that roots are real and distinct.
∴ b2−4ac>0
⇒ (−k)2−4(1)(9)>0
⇒ k2−36>0
⇒ k2>36
⇒ k>6 or k<−6
∴ We can see values of k given in question are correct.
HELP PLS
Name the intersection of plane K and plane L.
Answer:
line MN
Step-by-step explanation:
If two planes intersect, then the intersection is a line.
Answer: line MN
Deion misses 4% of the free throws he attempts in a seaon. How many total free throws did he attempt if he missed 17
Answer: 425
Step-by-step explanation:
Think of this problem as 4% of a number equals 17
since in math, the word 'of' usually means multiplication, we can think of it that way.
Also, 4% = 0.04
[tex]x*0.04=17[/tex]
[tex]0.04x=17[/tex]
[tex]\frac{0.04x}{0.04} =\frac{17}{0.04}[/tex]
[tex]x=425[/tex]
Ian is playing video games. For every 11 enemies he defeats, he gets 6 points. If he has 24 points at the end of the game, how many enemies has Ian defeated?
Hi
if he has 24 point he scored 24/ 6 = 4 times
As he score points every 11 ennemies,
He had : 4*11= 44 ennemies.
You decide that you want to purchase a Tesla SUV. You borrow $95,000 for the purchase. You
agree to repay the loan by paying equal monthly payments of $1,200 until the balance is paid off. If
you're being charged 6% per year, compounded monthly, how long will it take you to pay off the
loan?
Answer:
8.5 years
Step-by-step explanation:
It will take 102 more payments
8.5 years
Interest will be $26,239
It would take approximately 15 years to pay back the loan of 95000 which is compounding monthly and the rate of interest is 6%.
What is compound interest?Compound interest is basically the interest which is calculated on the primcipal with addition to aggregate interest. The formula of sum after compounding is as under:
S=P[tex](1+r/n)^{nt}[/tex] in which P is principal amount, r is rate per annum, n is number of times of compounding and t is time period.
How to calculate time?We have been given that the amount of loan is $95000, installment is $1200 , rate of interest is 6% and it is compounded monthly.
First of all we have to find the effective rate=6%/12=0.005.
The future value of 95000 at a rate of 6% compunded monthly should be equal to the amount of all installments. So,
95000[tex](1+0.005)^{12n}[/tex]=12*1200*n
95000[tex]1.005^{12n}[/tex]=14400n
[tex]1.005^{12n}[/tex]=14400n/95000
[tex]1.005^{12n}[/tex]=0.1515n
We have to make graph of this to find the value of n which after graphing will come approx 15.
Hence it would take 15 years to pay back loan amount.
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