Given an arithmetic sequence -2,-13,-24, . . . , the recursive formula is: a(n) = a(n-1) -11 and the explicit formula is a(n) = 9 - 11n
Suppose we are given an arithmetic sequence:
a(1), a(2), a(3), a(4), ....
Then, in an arithmetic sequence, the next term is obtained by adding a constant to the previous term. This constant is called a common difference.
Let d = common difference, then
a(2) = a(1) + d
a(3) = a(2) + d
and so on, until
a(n) = a(n-1) + d
This is a recursive formula. Here a(n) = nth term, and a(n-1) = (n-1)th term.
The sequence in the problem:
-2,-13,-24, . .
Notice that:
-13 = -2 + (-11)
-24 = -13 + ( -11)
Hence, d = -11, and therefore, the recursive formula for the nth term is:
a(n) = a(n-1) -11
To find the nth term, we can also use the explicit formula:
a(n) = a(1) + (n-1).d
In the given sequence, a(1) = -2, and d = -11. Substitute these parameters:
a(n) = -2 + (n-1) . (-11)
= -2 - 11n + 11
= 9 - 11n
Thus, the explicit formula is a(n) = 9 - 11n.
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1My little sister, Savannah, is three years old and has a piggy bank that she wants to fill. She
started with five pennies and each day when I come home from school, she is excited when I give her three pennies that are left over from my lunch money. How much money will Savannah have after 10 days? How many days will it take for her to have at least $1.50? Justify your answer with a mathematical model of the problem situation.
Answer:
Savannah will have 35 pennies after 10 days.
It will take her 49 days to have at least $1.50
Step-by-step explanation:
Start Value = .05
Linear Increase = .03
.05 + .03x = TV
TV = Total Value
10 days = .05 + .03(10)
10 days = $.35
.05 + .03x = 1.50
1.50 - .05 = 1.45
1.45/.03 = 48.33
48 days is not enough for her to have 1.50 as she is not gaining hourly but rather daily so it would take her 49 days to have at least 49
2, 12, 72, 432, ... match the sequence to its equation
Answer:
This is a geometric sequence since there is a common ratio between each term.
Step-by-step explanation:
2592
read warriors
by eren hunter
Answer: the sequence by 6 gives the next term.
Step-by-step explanation: hope this helps!!!
Find following measure.
m AC
When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two.
The measure of m AC is 48.
What is meant by inscribed arc?
The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.
Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.
According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.
An angle's measure exists equivalent to the intercepted arc's measure divided by two when it is surrounded by a circle.
m AC = 2(m ∠B)
m AC = 2(m ∠B) = 48
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2 < n + 6 </= 10
help she didn't go over this in class and it's due tomorrow
Answer:
- 4 < n ≤ 4
Step-by-step explanation:
2 < n + 6 ≤ 10 ( subtract 6 from each interval )
- 4 < n ≤ 4
Don was thinking about buying a flat screen TV. The store marks it as
55 inches. (TV dimensions are given as diagonals.) If the length of the
TV is 35.51 inches, how tall is the TV?
The height of the television is 13.268 inches.
The television is in the shape of a rectangle and when we draw an imaginary diagonal line it would become a right-angle triangle in which the diagonal line would become the hypotenuse and the length would become base.
We need to find out the tallness of the television which is the perpendicular of our imaginary right-angle triangle
By applying the Pythagoras theorem [tex]H^{2}[/tex]= [tex]P^{2} + B^{2}[/tex]
As we need perpendicular the formula would become P = [tex]\sqrt{H^{2} -B^{2} }[/tex]
After putting the values in the above equation,
we get = [tex]\sqrt{(55) – (35.51)}[/tex]
=[tex]\sqrt{3025-1260.96}[/tex]
=[tex]\sqrt{1764.04}[/tex]
=13.268 inches
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Expand each binomial. (p+q)⁶
The binomial expansion of the given expression is:
p⁶ + q⁶ + 8p⁵q + 17p⁴q² + 20p³q³ + 11p²q⁴ + 4pq⁵
What is a polynomial?A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.
Depending on the number of terms it can be :
monomialbinomialtrinomialWe solve first by perfect square trinomial, then we apply the distributive property.
(p + q)⁶ = (p + q)²(p + q)²(p + q)²
(p + q)²= p² + 2pq + q²
(p² + 2pq + q²)(p² + 2pq + q²)p⁴ + 2p³q + p²q² + 2p³q + 4p²q² + 2pq³ + q²p² + 2pq³ + q⁴
p⁴ + 4p³q + 6p²q² + 2p³q + 2pq³ + q⁴
(p⁴ + 4p³q + 6p²q² + 2p³q + 2pq³ + q⁴)(p² + 2pq + q²)
p⁶ + 4p⁵q + 6p⁴q² + 2p⁵q + 2p³q³ + p²q⁴
+( 2p⁵q + 8p⁴q² + 12p³q³ + 4p⁴q² + 4p²q⁴ + 2q⁵p)
+(p⁴q² + 4p³q³ + 6p²q⁴ + 2p³q³ + 2pq⁵ + q⁶)
p⁶ + q⁶ + 8p⁵q + 17p⁴q² + 20p³q³ + 11p²q⁴ + 4pq⁵
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What is the area of the smaller figure, in square centimeters?
04
08
O 20
O 40
Answer:
020
Step-by-step explanation:
I hope it will be helpful for u
Kylie swam 6 feet below sea level and Bryan swam 8 feet below sea level. Find the difference between the absolute values for each depth.
The difference between the absolute values of Kylie's and Bryan's depth is 2 feet.
Here, we are given that Kylie swam 6 feet below the sea level and Bryan swam 8 feet below sea level.
This implies,
Kylie's distance from the ground level = -6 feet
and Bryan's distance from the ground level = -8 feet
We need to find the difference between the absolute values of their depth.
Thus, we ignore the minus (-) sign and find the difference as follows-absolute difference = | 6 - 8 |
difference = 2 feet
Thus, the difference between the absolute values of their depth comes out to be 2 feet.
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9,5 centimeters is the same as 9,50 centimeters???? YES NO and why please
Answer:
Yes
Step-by-step explanation:
9.50=9.5+0.00 ==> The only difference between 9.50 and 9.5 is that it has an extra zero in the right hand side of .5. Hence, you add 0.00 to 9.5 to get 9.50. 0.00=0. Whenever you add 0 to a number, that number won't change. Hence, 9.5=9.50.
What is an integer number that is also a rational number 
Answer:
all integers are rational numbers
$1 on the first friday. Each Friday after that, the payment will increase by 20% until the end of the school year or $50 every Friday
Subsets and proper subsets — PLEASE HELP.
Using the concepts of subsets and proper subsets, the statements are classified, respectively, as:
False.True.False.False.What are the subsets and proper subsets of a set?Suppose we have a set given by:
A = {a, b, c}.
The subsets will be all possible combinations involving at least one element of A, or the empty subset, hence:
S(A) = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b,c}, {a,b,c}}
In which S(A) is composed by the subsets of A.
The proper subsets are all the subsets, except the empty set, hence:
PS(A) = {{a}, {b}, {c}, {a, b}, {a, c}, {b,c}, {a,b,c}}
In which PS(A) is composed by the proper subsets of A.
Hence:
The first statement is false, as the proper subsets of {1,3} are: {{1}, {3}, {1,3}}The second statement is true, as 12 and 14 both belong to the second set, hence {12, 14} is a subset.The third statement is false, as every set will be a subset of itself.The fourth statement is false, as the only subset of the empty set is the empty set.More can be learned about subsets and proper subsets at https://brainly.com/question/17514113
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I need help now!!!!
Problem 2 Got It? Reasoning: How can you prove ∠1 ≅ ∠2 ≅ ∠3 ≅ ∠4 without using the Vertical Angles Theorem? Explain in the response field.
Answer:
use the math skills 9+9+9
Step-by-step explanation:
If f(x)=x³- x²- x , what is the value of f(-3)?
A. -39
B. -33
C. -21
D. -15
E. -12
-33 is the value of f(-3) if the equation is If f(x)=x³- x²- x .
Explain what a linear equation is.
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.f(x)=x³- x²- x
f(-3) = ( - 3)³ - ( -3)² - ( -3)
= - 27 - 9 + 3
= - 36 + 3 = -33
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Write a recursive definition and an explicit formula for each sequence. Then find a₁₂. 10,20,40,80,160, . . . .
Geometric Progression is a type of recursive mathematical sequence in which the next term is generated by multiplying the previous term with a fixed number that is called the Common Ratio represented by 'r'.It is calculated by the ratio of two consecutive terms.
The formula to calculate the 12th term of a Geometric Progression is :
=> [tex]a_{12} = a.r^{(12-1)}[/tex]
Here a = first term, r = common ratio calculated by => r=(a2/a1), and n = [tex]n^{th}[/tex] term to find
In the given question, First term a = 10, n = 12, and calculating r,
=> r = (a2/a1) => r = (20/10) = 2
Calculating,
[tex]a_{12\\} = (10).(2^{(12-1)})[/tex] => [tex](10).(2048)[/tex]
[tex]a_{12} = 20480[/tex]
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There are four integers in a set, and each integer must be no less than 1 and no greater than 36. The sum of the four integers in that set must be no less than 118 and no greater than 144. What are ALL of the possible number combinations that fit the criteria?
e.g. [tex]34+28+25+34=121[/tex]
The number combinations that fit the criteria will be 25 + 30 + 32 + 38.
How to calculate the numbers?It should be noted that the information illustrated that the sum of the four integers in that set must be no less than 118 and no greater than 144.
Therefore, the numbers that fit this will be:
= 25 + 30 + 32 + 38
= 125
Therefore, the number combinations that fit the criteria will be 25 + 30 + 32 + 38.
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3r^5 - 7r name each polynomial by degree and number of terms. if the polynomial is not win standard form rewrite it in standard form
The polynomial is quintic binomial.
The given polynomial is [tex]3r^5-7r[/tex]. The polynomial is given in standard form. i.e., terms are arranged in the decreasing order of its powers.
The degree of the polynomial is the highest power of 'r' in the polynomial.
So degree of the polynomial [tex]3r^5-7r[/tex] is 5.
Polynomials of degree 5 are called quintic.
The polynomial has 2 terms: [tex]3r^5, 7r[/tex]
Since the number of terms are two, we can call it binomial.
So the polynomial [tex]3r^5-7r[/tex] is quintic binomial.
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The length and width of a rectangle are consecutive odd integers the perimeter of the rectangle is 96 cm find the length and the width of the rectangle
The lengthof the rectangle is 23 cm and width of the rectangle is 25cm.
Consecutive odd integers are odd integers that follow each other and they differ by 2.
Given that Length and width are consecutive odd integers then
Let length be x so width will be x+2.
The [tex]Perimeter \ of \ Rectangle = 2 (Length \ + \ Width)[/tex]
Perimeter of Rectangle= 96cm
[tex]96 = 2 (Length \ + \ Width)\\(Length \ + \ Width) = 48\\x + x + 2 = 48\\2x = 46\\x = 23[/tex]
So, length = x = 23cm
therefore, width = x+2 = 25cm
Therefore, Length of the rectangle is 23 cm and the Width of the rectangle is 25 cm.
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Simplify by combining like terms. 2(h+2 g)-(g-h)
The simplification by combining like terms of 2(h + 2g) - (g - h) is 3(h + g).
According to the given question.
We have an expression 2(h + 2g) - (g - h).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression
2(h + 2g) - (g - h).
Here 2h, and h and 2g and -g are the like terms.
So, we add and subtract coeffcients of h and g to simplify the given expression.
Therefore, the simplification of 2(h + 2g) - (g - h) is given by
= 2(h + 2g) - (g - h)
= 2h + 4g - g + h
= 3h + 3g
= 3(h + g)
Hence, the simplification by combining like terms of 2(h + 2g) - (g - h) is
3( h + g).
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Please help with #13
Using the formula for the distance between two points, the relationship between RA and R'A is given by:
RA = R'A.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
The coordinates of the points of interest to find the segments' lenghts are given as follows:
R(-5,-5).A(1.5, 1.5).R'(8,8).Applying the formula, the length of RA is given by:
[tex]RA = \sqrt{(1.5 - (-5))^2+(1.5 - (-5))^2} = 9.19[/tex]
Applying the formula, the length of R'A is given by:
[tex]R^{\prime}A = \sqrt{(1.5 - 8)^2+(1.5 - 8)^2} = 9.19[/tex]
Hence the relationship for the length of the segments is:
RA = R'A.
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A store manager decides to clear out atlases to make room for new inventory. Now a $50 atlas will be on sale for only $21. What percentage is the discount? Write your answer using a percent sign (%).
The percentage discount is 58%
How to calculate the percentage discount ?The old price is $50
The new price is $21
The percentage discount can be calculated as follows
old price-new price/old price × 100
= 50-21/50 × 100
= 29/50 × 100
= 0.58 × 100
= 58
Hence the percentage discount is 58%
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Plot the point and label it with its name.
1. A(0,0)
2. B (2,3)
3. C(-2,-3)
4. D(-5,0)
5. E(4,-4)
6. G(3,2)
7. H(-1,0)
8. /(-1,-5)
9. K(0,-4)
10. J(-4.5, 2.5)
Find x, y, z. EXPONENTS!! please hurry.
[tex]3^{9} . 2^{12} .5^{11}[/tex]
Power :
An expression that represents repeated multiplication of the same factor is called a power.
Factor: The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.
the expression 5 x 5. This expression can be written in a shorter way using something called exponents.
5⋅5=5^2
An expression that represents repeated multiplication of the same factor is called a power.
The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.
3 to the first power 3
4^2 4 to the second power or 4 squared 4 ∙ 4
5^3 5 to the third power or 5 cubed 5 ∙ 5 ∙ 5
2^6 2 to the power of six
= [tex](3.5)^{4} (2.3)^{5} (2.5)^{7}[/tex]
= [tex]3^{4+5} .2^{5+7} .5^{4+7}[/tex]
=[tex]3^{9} . 2^{12} .5^{11}[/tex]
Ans : [tex]3^{9} . 2^{12} .5^{11}[/tex]
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In the figure below, R is between Q and s, and s is between R and T. If RT=9, RS=7,
and QS=13, find QT.
Answer: QT = 15
Step-by-step explanation:
RT=9, RS=7, and QS=13
Find QT=QR+RT
find QR=QS-RS
QR=13-7=6
therefore QT=QR+RT=6+9=15
what value of x makes this equation true 1/5(2x-10)+4x=-3(1/5x+4)
For the equation 1 / 5 (2 x - 10) + 4 x = - 3 (1 / 5 x + 4), we get the value of x as - 2.
We are given the equation that:
1 / 5 (2 x - 10) + 4 x = - 3 (1 / 5 x + 4)
We need to solve the equation to find the value of x.
First, we will open the brackets in the equation:
2 / 5 x - 2 + 4 x = - 3 / 5 x - 12
Combining the like terms, we get that:
22 / 5 x - 2 = - 3 / 5 x - 12
Add 2 and 3 / 5 x to both the sides, we get that:
22 / 5 x - 2 + 2 + 3 / 5 x = - 3 / 5 x - 12 + 2 + 3 / 5 x
5 x = - 10
Divide both the sides by 5, we get that:
5 x / 5 = - 10 / 5
x = - 2
Therefore, for the equation 1 / 5 (2 x - 10) + 4 x = - 3 (1 / 5 x + 4), we get the value of x as - 2.
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What word makes the statement "The domain and range of a(n) ___________ function is the set of all real numbers" sometimes true?
(F) polynomial
(G) logarithmic
(H) exponential
(I) quadratic
The word that makes given statement sometime true is: quadratic.
The correct answer is an option (I)
We know that, the domain of a function is the set of all possible values for which function is well defined.
And the range of a function is the set of all output values for given input.
We know that the domain of polynomial function is the set of all real numbers but the range of a polynomial function depends on the polynomial.
In case of a logarithmic function, the domain is the set of all non-negative numbers and the range is the set of all real numbers.
For exponential function, the domain of a function is the set of all real numbers and the range is all positive real numbers.
The domain as well as the range of a quadratic function is the set of all real numbers.
So the given statement would be, "The domain and range of a(n) quadratic function is the set of all real numbers."
Therefore, the word that makes given statement sometime true is: quadratic.
The correct answer is an option (I)
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Why is a normal distribution "normal"?
Step-by-step explanation:
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
What is the slope of the line that passes through the points (–9, 2) and (0, 4)?
The slope of the line is
.
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
Use slope formula.
y2-y1/x2-x1
Plug in the given info.
4-2/0+9
2/9
Hope this helps!
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Angela wants to practice her sign language for the talent show next month. she decides that she will practice 1.4 hours on a monday, 212 hours on a tuesday, and 5 hours on a saturday. if angela uses this schedule for 4 weeks, how many hours will she have practiced in total?
If angela uses this schedule for 4 weeks, the total number of hours she will many have practiced in total is 35.6 hours
Total time for practicalWeek 1:
Monday = 1.4 hoursTuesday = 2 1/2 hoursSaturday = 5 hoursTotal = Monday + Tuesday + Saturday
= 1.4 + 2 1/2 + 5
= 1.4 + 2.5 + 5
= 8.9 hours
if angela uses this schedule for 4 weeksTotal number of hours she practice for weeks = 8.9 hours × 4
= 35.6 hours
Therefore, if angela uses this schedule for 4 weeks, the total number of hours she will many have practiced in total is 35.6 hours.
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Can someone please help me out? I don’t really understand the problem.
Answer: x=-8 y=7
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{-2x-5y=-19\ \ \ \ (1)} \atop {3x+2y=-10\ \ \ \ \ (2)}} \right.[/tex]
Multiply both parts of the equation (1) by 3 and multiply both parts of the equation (2) by 2:
[tex]\displaystyle\\\left \{ {(-2x)(3)-(5y)(3)=(-19)(3)} \atop {(3x)(2)+(2y)(2)=(-10)(2)}} \right. \\\\\left \{ {{-6x-15y=-57\ \ \ \ (3)} \atop {6x+4y=-20\ \ \ \ (4)}} \right. \\[/tex]
Summarize equations(3) and (4):
[tex]-11y=-77[/tex]
Divide both parts of the equation by -11:
y=7
Hence,
[tex]3x+2*7=-10\\3x+14=-10\\3x+14-14=-10-14\\3x=-24[/tex]
Divide both parts of the equation by 3:
[tex]x=-8[/tex]
