Answer:
Explicit rule [tex]a_n=5n-100[/tex]Recursive rule [tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms [tex]-675[/tex]
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Let the first term be a and common difference be d.
Use equations for nth term and sum of the first n terms[tex]a_n=a+(n-1)d\\[/tex][tex]S_n=n(a+a_n)/2[/tex]Use the first equation to find the values of a and d[tex]a_{18}=a+17d=-10[/tex][tex]a_{40}=a+39d=100[/tex]Substract the first equation from the second and solve for d39d - 17d = 100 + 1022d = 110d = 110/22d = 5Find aa + 17*5= - 10a + 85 = - 10a = - 95Explicit rule[tex]a_n=-95+5(n-1)=-95+5n-5=5n-100[/tex]Recursive rule[tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms[tex]S_{30}=(-95-95+29*5)*30/2=(-45)*15=-675[/tex]The explicit rule is a(n) = - 95 + 5 · (n - 1), whose recursive rule is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5. The 30th element of the arithmetic sequence is 50.
How to derive an arithmetic sequence
Arithmetic sequences are sets of elements generated by a formula of the form:
a(n) = a + r · (n - 1), for n ≥ 1
Where:
a - First element of the sequence.r - Common raten - Index of the n-th element of the sequence.Please notice that the common rate is the difference between any two consecutive elements of the sequence. The recursive form is described by the following form:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + r
Now we should determine the elements of the explicit rule by solving the following system of linear equations:
n = 18
- 10 = a + r · (18 - 1)
a + 17 · r = - 10
n = 40
100 = a + r · (40 - 1)
a + 39 · r = 100
Then, we solve the system of linear equations by numerical methods:
(a, r) = (- 95, 5)
And the 30th element of the arithmetic series:
a(n) = - 95 + 5 · (n - 1)
a(30) = - 95 + 5 · (30 - 1)
a(30) = 50
And the recursive form is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5.
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match the following each letter may be used more than once.a. 12/15b. 15/12c. 9/15d. 9/12e. 12/9f. 15/9
We have a right triangle and we have to write some of the trigonometric ratios.
A trigonometric ratio relates a trigonometric function of an angle of the tiangle with a quotient of two of the sides of the triangle.
The basic trigonometric ratios are:
[tex]\begin{gathered} \sin (\alpha)=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \cos (\alpha)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \end{gathered}[/tex]We can also write the trigonometric ratio for the tangent:
[tex]\tan (\alpha)=\frac{\sin (\alpha)}{\cos (\alpha)}=\frac{\text{Opposite}}{\text{Adyacent}}[/tex]Now, we can write sin(x):
[tex]\sin (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XZ}=\frac{12}{15}[/tex]The opposite side to X is YZ and the hypotenuse is XZ, so sin(X) = YZ/XZ = 12/15.
In the same way, we can calculate cos(x):
[tex]\cos (X)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{XY}{XZ}=\frac{9}{15}[/tex]The tan(x) can be calculated as:
[tex]\tan (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XY}=\frac{12}{9}[/tex]For Z, the opposite and adyacent angles are different than for X, so we can write:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{YZ}=\frac{9}{12}[/tex]Answer:
sin(X) = 12/15
cos(X) = 9/15
tan(X) = 12/9
tan(Z) = 9/12
It costs mrs. barazal $245 for her and 6 people to take a day-long guided tour of the Everglades how much does the guided tour cost per person?
For Barazal and 6 persons the cost is $245
So, the number of persons = 7
so, the cost per person = 245/7 = $35
So
the guided tour cost per person = $35
5m+3m+ 3 n- m + 6n +8
The given expression is
5m+3m + 3n - m + 6n + 8
We would simplify the expression by collecting like terms.
The terms containing m are like terms
The terms containing n are like terms
8 is a constant
Thus, we have
5m + 3m - m + 3n + 6n + 8
7m + 9n + 8
The final expression is
7m + 9n + 8
Quinn needs to collect at least 90 toys for a toy drive to earn community service credit. He has already collected 16 toys.
Let's define the next variable:
t: number of toys that Quinn still needs to collect
The number of toys that he already collected plus the number of toys that Quinn still needs to collect is: 16 + t
Quinn needs to collect at least 90 toys, then 16 + t must be greater than or equal to 90, that is,
16 + t ≥ 90
or
90 ≤ 16 + t
Subtracting 16 at both sides, we get:
90 - 16 ≤ 16 + t - 16
74 ≤ t
Number 9 please on this packet, I need it for a class presentation
9)
Let x represent the amount that she gets for 1/7 of a working day.
From the information given, she gets $35 for 1 working day. Thus, we can set up the equations as follows
35 = 1
x = 1/7
By crossmultiplying, we have
x = 35 x 1/7
x = 5
Ariel will earn $5 for working 1/7 of a day
the rest of the question say what is the length of the tangent line labeled X
To solve this problem, consider the following picture
By the tangent secant segment theorem we have the following equation
[tex]a^2=b\cdot(b+c)[/tex]Note that in our case, we have a=x, b=3 and c=9. So if we replace this values in the equation, we have
[tex]x^2=3\cdot(3+9)=3\cdot12=36[/tex]so, applying the square root on both sides, we get
[tex]x=\sqrt[]{36}=\pm6[/tex]Since x is a distance, it should be strictly positive, so we have that
[tex]x=6[/tex]Hello, I need some assistance with this homework question, please? This is for my precalculus homework. I submitted the answer x<-14 or x>-14 but it was incorrect Q4
To find the domain of the rational function we need to equate the denominator to zero and solve the equation, as follows:
[tex]\begin{gathered} x+14=0 \\ x+14-14=-14 \\ x=-14 \end{gathered}[/tex]Then, all the x-values are valid except x = -14, which makes the denominator equal to zero. Therefore, the domain of R(x) is:
[tex]\lbrace x|x\ne-14\rbrace[/tex]1. The graph shown represents the altitude of a hikerduring a period of time. Write a possible situationrepresented by the graph.Altitude (feet)Time (hours)2. Use the vertical line test to determine if the relation represented on the graph
The vertical line test consists in tracing various vertical lines throughout the function and checking wheter this lines will touch the function more than once.
As we can see none of the lines touch the graph more than once, therefore this graph is a function.
∠ACB is a circumscribed angle. Solve for x.Question options:1) 482) 463) 444) 42
x = 44
Explanations:Note that:
Opposite angles of a cyclic quadrilateral are supplementary
m
mm
(3x + 10) + 38 = 180
3x + 10 + 38 = 180
3x + 48 = 180
3x = 180 - 48
3x = 132
x = 132/3
x = 44
simplify 3y -(2y - 3)/4
The expression is given
[tex]\frac{3y-(2y-3)}{4}[/tex]Simplify the expression
[tex]\frac{3y-2y+3}{4}=\frac{y+3}{4}[/tex]Hence the answer is
[tex]\frac{y+3}{4}[/tex]If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour, how long will it take them to be 3180 miles apart?
SOLUTION:
Step 1:
In this question, we are given the following:
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour,
how long will it take them to be 3180 miles apart?
Step 2:
Let the distance of one of the planes flying west at 520 miles per hour be:
[tex]520\text{ x}[/tex]And let the distance of the other plane flying east at 540 miles per hour be:
[tex]540\text{ x}[/tex]where x , represents the time of flight in hours, such that:
[tex]\begin{gathered} 520\text{ x + 540 x = 3180} \\ 1060\text{ x = 3180} \\ \text{Divide both sides by 1060, we have that:} \\ x\text{ = }\frac{3180}{1060} \\ x\text{ = 3} \end{gathered}[/tex]CONCLUSION:
The time it will take them to be 3180 miles apart will be in 3 hours' time.
James invests 20k in an account that offers a compound interest rate of 8.3% per year for 6 years. I need to know which one is the correct answer 1. a(6)=20,000×(1+0.83)⁶‐¹2. a(6)=20,000×(1+0.083)⁶+¹3. a(6)=20,000×(1+0.083)⁶‐¹4. a(6)=20,000×(1+0.083)⁶
Given,
The principal amount is 20k.
The rate of interest is 8.3%.
The time period is 6 Years.
Required
The amount of investment after 6 years.
The amount is calculated as,
[tex]\begin{gathered} Amount=principal\times(1+\frac{rate}{100})^{time} \\ =20000\times(1+\frac{8.3}{1000})^6 \\ =20000\times(1+0.083)^6 \\ =20000\times(1+0.083)^6 \end{gathered}[/tex]Hence, the amount after 6 years is 2000 x (1 + 0.083)^6.
what should be the value of k so that the trinomial is a perfect square trinomial ?
ANSWER:
5
STEP-BY-STEP EXPLANATION:
The perfect square trinomial is given as follows:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Therefore, in this case would be:
[tex]\begin{gathered} x^2+2kx+25 \\ a=x \\ b=5 \\ (x+5)^2=x^2+2\cdot5x+25 \\ k=5 \end{gathered}[/tex]Therefore the value of k is 5
I need help with number 28 I could be wrong but I think you need to use the rook to match the bishop number 25
Answer:
2 translation vectors.
[tex](A,3)\text{ }+\text{ u(4,0) }=\text{ (E,3)}[/tex][tex](E,3)\text{ + u(0,4) = (E, 7)}[/tex]Step by step explanation:
You have to move a rook from the green circle to the blue one.
Then you have to represent series of the translation vector
You should know that the tower only moves horizontally or vertically.
You first move it 4 blocks to the right
[tex](A,3)\text{ }+\text{ u(4,0) }=\text{ (E,3)}[/tex]Then you move 4 blocks up.
[tex](E,3)\text{ + u(0,4) = (E, 7)}[/tex]What percent of Kenyans are between the ages of 10 and 20 years old?
In the picture we see that between 10 and 20 years old there are two rectangles . One goes to the 11% aproximately
the other rectangle reach 10% in the Y axis .
So then finally we have to add both percentages to obtain
10% + 11%= 21 %
21 percent are between ages 10 and 20 years old
Given the points (-3,0), (2, 0), (6,0), (0, 12), write the polynomial in factored form.
(1.26 x 10^3) + (1.12 x 10^4)
Work needs to be shown!!!
Answer:
Step-by-step explanation:
1260+11200=12460
so its, 1.246 x 10^4
A plane flew 1225 mi in 5 hr with the wind. It would take 7 hr to travel the same distance against the wind. What is the speed of the plane in still air and the speed of the wind?
Answer:
wind speed 35 miles per hour
plane speed 210 miles per hour
Explanation:
Let us call p the place speed and w the wind speed.
We know that
p + w = 1225/5 = 245
p - w = 1225/7 = 175
adding the two equations above gives
2p = 245 + 175
2p = 420
dividing both sides by 2 gives
p = 210 miles per hour.
putting in the value of p in p + w = 245 gives
210 + w = 245
w = 245 - 210
w = 35 miles per hour
enter the value of y for which LMNO must be a parallelogram
In a parallelogram, opposite sides are equal.
ON = LM
OL = NM
OL = y-6
NM= 1/3 x
ON= 5x-8
LM= 9x-26
First, solve for x
ON = LM
5x - 8 = 9x - 26
-8 + 26 = 9x - 5x
18 = 4x
18/4 = x
x = 4.5
Replace x=4.5 on NM, and solve for y:
OL = NM
y-6= 1/3x
y-6 = 1/3 (4.5)
y-6= 1.5
y= 1.5 + 6
y= 7.5 = 15/2
One number is 9 more than another number. The sum of the numbers is 25. What is one of the numbers?A) 9B) 8C) 16D) 17
Answer
B) 8 or D) 17
Step-by-step explanation
Let's call x to one unknown number and y to the other number.
If one number is 9 more than another number, then:
[tex]y=x+9\text{ \lparen eq. 1\rparen}[/tex]Given that the sum of the numbers is 25, then:
[tex]x+y=25\text{ \lparen eq. 2\rparen}[/tex]Substituting equation 1 into equation 2 and solving for x:
[tex]\begin{gathered} x+x+9=25 \\ 2x+9=25 \\ 2x+9-9=25-9 \\ 2x=16 \\ \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Substituting x = 8 into the first equation:
[tex]\begin{gathered} y=8+9 \\ y=17 \end{gathered}[/tex]Then, one of the numbers is 8 and the other one is 17
Construct a system of equations for the word problem. Do not solve. In the space provided, type the answer without any space between the letters, numbers, or symbols.
Given:
The sum of two numbers is 21, and their difference is 9.
Let x and y be the two numbers.
Equation 1: The sum of two numbers is 21.
[tex]\text{ x + y = 21}[/tex]
Equation 2: Their difference is 9.
[tex]\text{ x - y = 9}[/tex]The following data points represent the number of flying saucers that are owned by each alien on planet nowhere. (a)Arrange the data from the least to greatest 1,4,2,21,8,27(b)Find the median number of flying saucers
The data that represent the number of flying saucers that are owned by each alien on planet nowhere is given below:
[tex]1,4,2,21,8,27[/tex](a)We sort the data from the least to greatest below.
[tex]1,2,4,8,21,27[/tex](b)The median is the middle number.
In this case, we have two numbers in the middle: 4 and 8
Therefore we find their average:
[tex]\begin{gathered} \text{Median}=\frac{4+8}{2} \\ =\frac{12}{2} \\ =6 \end{gathered}[/tex]Answer:
6 is the correct answer.
Step-by-step explanation:
you have a job wich pays double time when working more than 40 hours a week. last week you worked 55 hours and earned $840. what is your regular pay rate?
Explanation
The salary with regular pay rate is calculated as:
[tex]S_{\text{regular}}=R\times h[/tex]S is the salary, R is the regular pay rate and h is the number of hours worked.
The salary with over time is:
[tex]S_{\text{overtime}}=2\text{Rxh}_{\text{overtime}}[/tex]Because it pays double after 40 hours.
So the first 40 hours worked you'll get
[tex]S_{\text{regular}}=40R[/tex]The amount of overtime hours is 15 (55-40 = 15), so the overtime salary is:
[tex]S_{\text{overtime}}=2R\times15=30R[/tex]The total Salary is the sum of the regular and the overtime salaries:
[tex]S=S_{\text{overtime}}+S_{\text{regular}}[/tex]If the total salary was $840, then the regular pay rate R is:
[tex]\begin{gathered} 840=30R+40R \\ 840=70R \\ R=\frac{840}{70}=12 \end{gathered}[/tex]Answer
Your regular pay rate is $12 / hour
Rebecca had $100 in her savings accountin the first week. She adds $45 each weekfor 5 weeks. The savings account balancecan be shown by a sequence.
Rebecca had $100
and each week, she add $45
Let the number of weeks is x
So, after x weeks, she will have y
y = 100 + 45x
See the following figure:
After 5 weeks, y = 100 + 45 * 5 = 325
============================================
After 1 week , y = 145
after 2 weeks , y = 190
after 3 weeks , y = 235
and so on
So, The savings account balance can be shown by a sequence.
The sequence will be: 145 , 190 , 235 , 280 , .......
The kind of this sequence will be arthimatic sequence , because there is a common defference between the terms of the sequence which = 45
Pattern A follows the rule "add 2" and Pattern B follows the rule "subtract 2." Pattern A: 1, 3, 5, 7, 9 Pattern B: 10, 8, 6, 4, 2 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers. A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4) I Need Help Please
To get the required combining pairs : B, C , D, E , F
B (1, 10) = Pattern A - 1 and pattern B = 10
C (3, 6) = pattern a = 3 and pattern b = 6
D (5, 4)= pattern A = 5 and pattern B = 4
E (5, 6) = Pattern A = 5 and pattern B = 6
F (7, 4) = Pattern A = 7 and pattern B = 4
Given ; Pattern A : 1, 3, 5, 7, 9
Pattern B: 10, 8, 6, 4, 2
To get ; A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4)
Thus to get the required pair we have to match it the following way
A ( 1, 3 ) = Pattern A - 1 and pattern B - ? thus not correct
B (1, 10) = Pattern A - 1 and pattern B = 10
C (3, 6) = pattern a = 3 and pattern b = 6
D (5, 4)= pattern A = 5 and pattern B = 4
E (5, 6) = Pattern A = 5 and pattern B = 6
F (7, 4) = Pattern A = 7 and pattern B = 4
To know more about matching the combinations you may visit the link which is mentioned below:
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Volunteer drivers are needed to bring a students to the championship baseball game. Drivers either have cars, which can eat 4 students, or vans which can seat 6 students. The equation 4c +60 80 describes the relationship between the number of carse and number of vans v that can transport exactly so students 3 Explain how you know that this graph represents this equation number of vans 2 4 6 8 10 12 14 16 18 20 22 24 number of cars
One featue of the equation is that when c = 0
[tex]\begin{gathered} 4(0)+6v=80 \\ \therefore v=13.33 \end{gathered}[/tex]The other feature is that when v = 0
[tex]\begin{gathered} 4c+6(0)=80 \\ \therefore c=20 \end{gathered}[/tex]Therefore, our graph must contain the points (0, 13.33) and (20, 0), and looking at the graph given we see that it has exactly those points; hence, the graph represents the equation given
a recipe requires 7/8 sticks of butter for each 1 1/4 cups of flour. how many cups of flour to sticks of butter
In order to calculate the rate of cups of flour to stick of butter, just calculate the following quotient:
(1 1/4)/(7/8) = (5/4)/(7/8) = 5·8/7·4 = 40/28 = 20/14 = 10/7
Hence, the required rate is 10/7 or 10:7
that is, 10 cups of flour for 7 sticks of buttter
There are 25 popular trees currently in the park. Park workers will plant morepopular trees today. When the workers are finished there will be 80popular trees in the park. How many popular trees did the workers plant today?
Current trees = 25
trees when workers are finished = 80
Subtract the number of current trees (25) to the number of trees that are when the workers are finished:
80-25 = 55
The workers planted 55 trees today
Hi, I'm having a really hard time doing Multi Step Equations in Math, please help me.
You have the following equation:
4x - 3 = 2x + 5
In order to solve the previous equation, proceed as follow:
4x - 3 = 2x + 5 subtract 2x both sides
4x - 2x - 3 = 5 add 3 both sides
4x - 2x = 5 + 3 simplify like terms
2x = 8 divide by 2 both sides
x = 8/2
x = 4
Hence, the solution to the given equation is x = 4
PLEASE HELP MEEEEMatch the properties with the steps to solving the following equation(Sz - 6) =2+9Distributive Property4x - 3 = x + 9Subtraction Property ofEquality3x - 3=93x = 12Addition Property ofEqualityDivision Property ofEqualityx = 4Previouse
apply the distributive property
[tex]4x-3=x+9[/tex]apply the substraction property