What are the first three terms of the sequence defined by the recursive function , and ?
Answers
Answer:
The first three terms of the sequence are 6 , 10 , 8 ⇒ 2nd answer
Step-by-step explanation:
* Lets study the rule at first:
- [tex]a_{n}=a_{n-1}-(a_{n-2}-4)[/tex]
∴ [tex]a_{n}=a_{n-1}-a_{n-2}+4[/tex]
* That means to find a term add the difference between
the two consecutive term before it to 4.
* lets start with [tex]a_{6}=a_{5}-a_{4}+4[/tex]
∵ [tex]a_{5}=-2,a_{6}=0[/tex]
∴ [tex]0=-2 -a_{4}+4[/tex]
∴ [tex]0=2-a_{4}[/tex]
∴ [tex]a_{4}=2[/tex]
* Use [tex]a_{5}[/tex] to find [tex]a_{3}[/tex]
∵ [tex]a_{5}=a_{4}-a_{3}+4[/tex]
∴ [tex]-2=2-a_{3}+4[/tex]
∴ [tex]-2=6-a_{3}[/tex]
∴ [tex]a_{3}=6+2=8[/tex]
* Similar use [tex]a_{4}[/tex] to find [tex]a_{2}[/tex]
∵ [tex]a_{4}=a_{3}-a_{2}+4[/tex]
∴ [tex]2=8-a_{2}+4[/tex]
∴ [tex]2=12-a_{2}[/tex]
∴ [tex]a_{2}=10[/tex]
* Finally use [tex]a_{3}[/tex] to find [tex]a_{1}[/tex]
∵ [tex]a_{3}=a_{2}-a_{1}+4[/tex]
∴ [tex]8=10-a_{1} +4[/tex]
∴ [tex]8=14-a_{1}[/tex]
∴ [tex]a_{1}=14-8=6[/tex]
∴ The first three terms of the sequence are 6 , 10 , 8 ⇒ 2nd answer
Related Questions
A rectangular flowerbed is 22 inches long by 8 inches wide. The flowerbed is filled to a depth of 6 inches with dirt. What is the volume, in cubic inches, of the dirt in the flowerbed?
176
180
712
1056
Answers
Answer:
The volume of the dirt in the flowerbed is [tex]1,056\ in^{3}[/tex]
Step-by-step explanation:
we know that
To find the volume of the dirt in the flowerbed, multiply the long by the width by the depth
so
[tex]V=(22)(8)(6)=1,056\ in^{3}[/tex]
Final answer:
To calculate the volume of dirt in a rectangular flowerbed with dimensions of 22 inches by 8 inches by 6 inches, use the formula Volume = length × width × height, resulting in 1056 cubic inches.
Explanation:
The question asks for the volume of dirt a rectangular flowerbed can hold. To find the volume, we use the formula Volume = length × width × height. Given the dimensions are 22 inches (length) by 8 inches (width) by 6 inches (height), we calculate the volume as:
Volume = 22 in. × 8 in. × 6 in. = 1056 cubic inches. Therefore, the volume of the dirt in the flowerbed is 1056 cubic inches.
Why did President Reagan order the CIA to recruit the Contras?
a.) He wanted to use the Contras to help free US hostages being held by terrorists.
b.) He thought they could help the United States sell arms to countries fighting Communism.
c.) He thought they were necessary to oust a Communist-leaning government in Nicaragua.
d.) He felt that it would prompt Congress to change its stand on US involvement in Latin America.
Answers
President Reagan order the CIA to recruit the Contras because of option (c) He thought they were necessary to oust a Communist-leaning government in Nicaragua.
What is meant by Reagan Revolution?Reagan revolution is defined as the era which is basically referring to the changes that happened America during the reign of the president Ronald Reagan.
Reagan, when ruling had many policies that no other ruler before made into the rule.
Some of his policies includes decreasing the income taxes for the people, decreasing the the budget of government, maintenance of low rate of interest, and the other elimination of useless programs.
Along with this, he aims to eliminate the communism globally.
Nicaragua was a region which was highly affected with communism.
The contras' were the one opposing the communism in Nicaragua.
So CIA assisted this contras along with other anti communist causes under the name Reagan Doctrine.
Hence option c is correct.
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If sinv=-5/13, pi
1. cos(u+v)=
2. sin(u-v)=
Answers
the answer is number 2 sin (u-v)÷
3/5 divided by 3/10 equals what
Answers
Answer:
2
Step-by-step explanation:
[tex] \frac{3}{5} \div \frac{3}{10} = \\ \frac{3}{5} \times \frac{10}{3} = \\ 2 \: is \: the \: answer[/tex]
YOU GET 100 POINTS!
Find X.
answer:_________
answer needed by 5pm. no later.
Answers
Using the intersecting chord theorem:
(6 * 1) = (2*x)
Simplify:
6 = 2x
Divide both sides by 2:
x = 6/2
x = 3
Answer:
x = 3
Step-by-step explanation:
You have to use the Intersecting Cord Theorem
(6 * 1) = 2x
multiply what's in the parenthesis
6 = 2x
divide 2 from both sides
3 = x
(\) QueTooOfficial (/)What capital leffer appears to have parallel lines?
D or L or N or T?
Answers
Answer:
N, the verticle lines are are parallel
Step-by-step explanation:
Answer:
N
Step-by-step explanation:
Note to the wise: It's letter, not leffer.
Only N has 2 parallel lines.
Use the drawing tool(s) to form the correct answer on the provided number line.
An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.
Answers
Answer:
n < 18
Step-by-step explanation:
The condition you are looking for is that
94 + 4.50n < 175
Subtract 94 from each side 4.50n < 81
Divide each side by 4.50 n < 18
The number of devices must be fewer than 18 for the new plan to cost less than the current plan.
The diagram is a graph of the inequality 94 + 4.50n < 175. Any value of n less than 18 (that is, in the pink zone and not on the vertical dashed line) will satisfy the inequality.
Dawn has 1.20 in nickels, dimes and quarters. For each nickel she has one dime and for each dime she has one quarter. How many total coins does she have?
Answers
Answer:
9
Step-by-step explanation:
"For each nickel, she has one dime"
That means she has the same number of nickels and dimes.
"for each dime she has one quarter"
That means she has the same number of quarters and dimes.
She has the same number of each coin.
Let's say she has x coins of each type.
The nickels are worth 0.05x; the dimes are worth 0.10x. The quarters are worth 0.25x. Altogether, the coins are worth
0.05x + 0.10x + 0.25x
We are told her coins are worth $1.20, so we set those two amounts equal and solve for x.
0.05x + 0.10x + 0.25x = 1.20
0.40x = 1.20
x = 1.20/0.40
x = 3
She has 3 coins of each type. Since there are 3 types of coins, she has 9 coins.
Dawn has a total of 9 coins, which include 3 nickels, 3 dimes, and 3 quarters.
Explanation:The subject of this question is a math problem involving counting coins. In this scenario, dawn has a total of $1.20 in nickels, dimes, and quarters. And the number of nickels, dimes and quarters are equal since for every nickel Dawn has, she also has a dime and a quarter.
Now, the value of a nickel is $0.05, a dime is $0.10 and a quarter is $0.25. So, the total value of a nickel, a dime and a quarter is $0.40. Therefore, since the total amount of money she has is $1.20, we divide that amount by the total value of each group of coins: $1.20 / $0.40 gives us 3.
So Dawn has 3 nickels, 3 dimes, and 3 quarters, for a total of 9 coins.
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need help asap!!!plzz
Find the commission on a sale of $600 with a 5% commission rate.
(A)$45 (B)$30 (C)$60 (D)$15
Answers
Answer: Choice B
Step-by-step explanation:
In order to solve for the amount of commission you need to multiply the amount of the sale times the 5% commission rate.
$600 x .05 = $30
What is the length of a rectangle whose perimeter is P, if the width is 6?
Answers
Answer:
(P-12)/2 = L
Step-by-step explanation:
1. Start off with an equation in terms of perimeter
P = (2)(6) + (2)(L)
2. Multiply the two and the six
P = 12+ (2)(L)
3. Move the terms around so only "L" is on one side
(P-12)/2 = L
hope this helped :)
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Step-by-step explanation:
Answer:
And for people struggling with simpler answers, here!
Step-by-step explanation:
P-12
———-
2
or
P-12/2
Find the arc length of the partial circle..
Answers
Answer:
The arc length of the partial circle is [tex]6\pi\ units[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
In this problem we have a 3/4 of a circle
so
the circumference is equal to
[tex]C=(\frac{3}{4})2\pi r[/tex]
[tex]C=\frac{3}{2}\pi r[/tex]
we have
[tex]r=4\ units[/tex]
substitute
[tex]C=\frac{3}{2}\pi (4)[/tex]
[tex]C=6\pi\ units[/tex]
Which triangle is NOT labeled correctly
WILL MARK BRAINLIEST!!!
Answers
red triangle
hypotenuse is the longest side of the right triangle; the opposite of the right angle
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has no oil and the test predicts it has oil?
Answers
Answer:
Don't take my word for it but I think it would be 55% chance. I'm Probably wrong.
Step-by-step explanation:
Answer:
9% or 0.09
Step-by-step explanation:
Given, chance of land having oil is 45%. Which is 0.45
So, chance of land NOT having oil is percent. Which is 0.55
Given, kit's accuracy rate of finding oil as 80%. Which is 0.80
So, kit's accuracy rate of NOT finding oil is percent. Which is 0.20
These 2 events are INDEPENDENT, which means that the probability of one event occurring does not affect the probability of another event occuring.
The formula, if we let the two evens be A and B, is:
P(A and B)=P(A) * P(B)
Now, "the probability that the land has oil (event A)AND the test predicts that there is no oil (event B)" will be:
P(A and B) = P(A) * P(B)
Hence, the probability is 0.09 or 9%
Chen completed the division problem below.
Answers
Answer:
B. He multiplied the dividend by 100 instead of 10.
Step-by-step explanation:
Chen had to divide [tex]1.926[/tex] by [tex]0.9[/tex]. To make it easier to divide, he thought of multiplying both the dividend and the divisor by 10.
Chen multiplied the divisor by 10 but mistakenly multiplied the dividend by 100 instead of 10.
So his whole division problem was changed.
Therefore, the correct answer option is B. He multiplied the dividend by 100 instead of 10.
Answer:
option B
He multiply the dividend by 100 instead of 10
Step-by-step explanation:
Given that,
divisor = 0.9
dividend = 1.926
Chen decided to multiply each by 10 to get
divisor = 0.9 x 10 = 9
dividend = 1.926 x 10 = 19.26
but unfortunately he multiply the dividend by 100
As,
1.926 x 100 = 192.6
So,
Chen's error was that he multiply the dividend by 100 instead of 10.
URGENT!!! Write the product as a sum or difference.
18cos(29x)cos(17x)
Select the correct answer below:
9sin(46x)+9sin(12x)
9sin(46x)−9sin(12x)
9cos(46x)+9cos(12x)
9cos(46x)−9cos(12x)
9cos(46x)+9sin(12x)
9sin(46x)−9cos(12x)
Answers
Answer:
9cos(46x) + 9cos(12x)
Step-by-step explanation:
18cos(29x)cos(17x)
According to Product-Sum identities
cos(α)cos(β)= (1/2)[cos(α+β)+cos(α-β)]
Putting α=29x and β=17x in Product-Sum identity we get
= 18×(1/2)[cos(29x+17x)+cos(29x-1`7x)]
Dividing 18 by 2 we get 9
= 9[cos(46x)+cos(12x)]
Multiplying 9 with both the terms we get
= 9cos(46x)+9cos(12x)
he front of an A-frame house is in the shape of a triangle.The height of the house is 20 feet.The area of the A-frame is 600 square feet.Write and solve an equation to find the base of the A-frame house.
Answers
Answer:
Equation: [tex]600=\frac{20b)}{2}[/tex]
Base: 60 feet.
Step-by-step explanation:
The formula for calculate the area of a triangle is:
[tex]A=\frac{bh}{2}[/tex]
Where:
A: is the area of the triangle.
b: is the base of the triangle.
h: is the heigth of the triangle.
Knowing the area of the triangle and its height, you can write the equation:
[tex]600=\frac{20b}{2}[/tex]
Where b is the base in feet of the A-frame house.
To solve it:
Multiply both sides of the equation by 2.
Divide both sides of the equation by 20.
Then:
[tex](2)(600)=(\frac{20b}{2})(2)\\\\1200=20b\\\\\frac{1200}{20}=\frac{20b}{20}\\\\60=b[/tex]
The base of the A-frame house is 60 feet.
Simplify the expression. 3(2y - 8) - 2y(5 - y)
options-
2y 2 + 16y - 24
-5y - 8
2y 2 - 4y - 24
2y 2 + 16y - 24
some of the 2's in the answer options are exponents.
Answers
Answer:
[tex]\boxed{\bold{2y^2-4y-24}}[/tex]
Step By Step Explanation:
Expand [tex]\bold{3\left(2y-8\right): \ 6y-24}[/tex]
[tex]\bold{6y-24-2y\left(5-y\right)}[/tex]
Expand [tex]\bold{-2y\left(5-y\right): \ -10y+2y^2}[/tex]
[tex]\bold{6y-24-10y+2y^2}[/tex]
Simplify [tex]\bold{6y-24-10y+2y^2}[/tex]
[tex]\bold{2y^2-4y-24}[/tex]
What is the slope of the line through the points (–2, –1) and (8, –3)?
Answers
-3 + 1 = -2
8 + 2 = 10
-2/10 = -1/5
Answer = -1/5
The slope of the line through the points (2, 1) and (8, 3) is calculated using the slope formula and is -1/5.
To find the slope of a line passing through two points, you will need to use the slope formula, which is:
(change in y) / (change in x)or (y2 - y1) / (x2 - x1).
For the points given (–2, –1) and (8, –3), you would calculate the slope as follows:
Slope (m) = (-3 - (-1)) / (8 - (-2)) = (-3 + 1) / (8 + 2) = (-2) / (10) = -1/5.
So, the slope of the line through the points (–2, –1) and (8, –3) is -1/5.
Please answer ASAP
Answers
Answer:
m = -3/4
Step-by-step explanation:
We can see two points : (0,1) and (4,-2).
Then we find the change of Y/change of X.
This comes out to -3/4, which is the second answer choice.
I was supposed to determine the length of the winding path through the circle.
my answer is
[tex]12.56 \: in {}^{2} [/tex]
Is this correct?
Answers
Check the picture below.
the idea being, the winding path is made out of semi-circles, each semi-circle has a diameter of 3, as you see there in the picture.
now, if we could just take two semi-circles, we'd have a full circle, with a diameter of 3, so from all 4 semi-circles we can actually get two full circles, as you see there, and the circumference of those two full circles, is the length of the winding path.
[tex]\bf \textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=3 \end{cases}\implies C=3\pi \qquad \stackrel{\textit{two circles added together}}{3\pi +3\pi \implies 6\pi ~~\approx~~18.85}[/tex]
A flag measures 110 feet by 55 feet. Find it’s area
Answers
Answer:
6050
Step-by-step explanation:
Area = length * width
Area = 110 * 55
Area = 6050
Answer:
6050 sq ft (or you could write 6050ft and a little two at the top right next to it at the end)
Step-by-step explanation:
To find the area of something, you must multiply length x width, so in this situation, you would multiply
110 x 55
that would equal 6,050
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answers
Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x------> the length of rectangle
y----> the width of rectangle
we know that
The area of the constructed figure is equal to
[tex]A=xy+2x^{2} +2y^{2}\\A=120\ cm^{2}[/tex]
so
[tex]120=xy+2x^{2} +2y^{2}[/tex] -----> equation A
[tex]x=y+5[/tex] -----> equation B
substitute equation B in equation A
[tex]120=y(y+5)+2(y+5)^{2} +2y^{2}\\120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\5y^{2}+25y+50-120=0\\5y^{2}+25y-70=0[/tex]
using a graphing calculator to resolve the quadratic equation
the solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
The perimeter of rectangle is equal to
[tex]P=2(x+y)\\P=2(7+2)=18\ cm[/tex]
Which number is 4 units from-1
Answers
Or -1 - 4 = -5
I would put 3.
caitlin had some money. after her shopping spree at redmond town center she had $5 left. she bought a new pair of shoes for $48, 2 pais of jeans at $19 each, and 2 t-shirts at $13 each. how much money did she have at the beginning
Answers
Answer:
$117
Step-by-step explanation:
Add 48 + 19 + 19 + 13 + 13 + 5 = 117
Please, can someone graph this for me and include a file?
g(x) = x3 − x2 − 4x + 4
Answers
See attachment
EXPLANATION
The given function is
[tex]g(x) = {x}^{3} - {x}^{2} - 4x + 4[/tex]
The y-intercept is
[tex]g(0) = 4[/tex]
To find the x-intercepts, we equate the function to zero.
[tex] {x}^{3} - {x}^{2} - 4x + 4 = 0[/tex]
Factor by grouping;
[tex] {x}^{2}(x - 1) - 4(x - 1)= 0[/tex]
[tex]( {x}^{2} - 4)(x - 1)= 0[/tex]
[tex]{x}^{2} - 4 = 0 \: or \: x - 1 = 0[/tex]
[tex]x = \pm \: \sqrt{4} \: or \: x = 1[/tex]
[tex]x = \pm \: 2\: or \: x = 1[/tex]
[tex]x = - 2\: or \: x = 1 \: or \: x = 2[/tex]
The x-intercepts are;
(-2,0),(1,0) and (2,0)
Since the polynomial has an odd degree and a positive leading coefficient, the graph will rise on the left side and also rise on the right side.
Using the intercepts and the end behavior, we obtain the graph as shown in the attachment.
Find the missing side
Answers
[tex]12 \div 3 = 4[/tex]
so
[tex]x = 20 \div 4[/tex]
x = 5
Answer:
x = 5
Step-by-step explanation:
Since the figures are similar then the ratio of corresponding sides are equal, that is
[tex]\frac{3}{12}[/tex] = [tex]\frac{x}{20}[/tex] ( cross- multiply )
12x = 60 ( divide both sides by 12 )
x = 5
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what is the 15th term in the sequence:
3, 12, 48, 192, 768, . . . . ?
please explain how you got your answer :) thanks!
Answers
Answer:
r = 3072. A 4 is multiplied times each term to arrive at the next term. OR ... divide a2 by a1 to find the common ratio of 3072. :)
Step-by-step explanation:
in a game the player wins if he rolls a 6 on a number cube .if the number cube is rolled 18 times then what is the reasonable
prediction for the number of unsuccessful rolls
Answers
Prediction for the number of unsuccessful rolls is 15.
Step-by-step explanation:There is [tex]\frac{1}{6}[/tex] chance of rolling number 6 on the cube. If we want to find out what is the prediction for rolling number 6 in 18 rolls, we need to multiply [tex]6*\frac{1}{6}[/tex] which is 3. So if we roll a cube 18 times, we will probably got number 6 three times. When we subtract 3 from 18 (18-3), we get 15. That is the answer to your question.
I hope I helped you. I will be really happy, If you mark my answer as the brainliest.Your David
(x^4 – x^2 – 6) ÷ (x^2 + 8)
Answers
Answer:
x² - 9 Remainder 66
Step-by-step explanation:
Find the attachment below for a step by step explanation.
Answer:
[tex]x^2-9[/tex]
Step-by-step explanation:
We are given the following expression and we are to divide it:
[tex] \frac { x ^ 4 - x ^ 2 - 6 } { x ^ { 2 } + 8 } [/tex]
We divide the first term [tex]x^4[/tex] by [tex]x^{2}+8[/tex] and get [tex]x^{2}[/tex] in the quotient so then we are left with [tex]-9x^{2} -6[/tex].
Further [tex]-9x^{2} -6[/tex] is divided by [tex]x^{2}+8[/tex] to get [tex]-9[/tex] in the quotient and we are left with 66 as the remainder.
So we get the quotient [tex]x^2-9[/tex] and remainder [tex]66[/tex].
Is √1/√49 rational ???
Answers
The number √1/√49 is a rational number.
Given a number √1/√49.
Here the numerator and the denominator includes the square root.
We can see that both the numbers inside the square root is a perfect square.
So the number can actually be written in the integer form.
So,
√1/√49 = 1/7, since 7² = 49
Now rational numbers are numbers which can be written in the form of p/q where p and q are integers with q not equal to 0.
Here the number can be written as 1/7, where 1 and 7 are integers.
Hence it is rational.
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