Given the arithmetic sequence A1, A2, A3, A4, 58,69,80,91
What is the Value of A21?

*PLEASE HELP****

Answers

Answer 1

an arithmetic sequence, means that there is an equal difference between each number of the sequence.

i.e. a, a+d, a+2d, a+3d...

where a is the first term, and d is the difference

in your case, a (first term) = 58

to find the difference, subtract 58 (a) from 69 (a+d) to get d.

d = 69 - 58 = 11

(you can always check your calculation on another two consecutive terms: 91 - 80 also equals 11)

the general formula for any term in an arithmetic sequence is:

T(n) = a + (n-1)d ...(or A(n))

in your case, n = 21

subbing into the formula:

A21 = a + (21-1)d = 58 + 20(11) = 278

hope that helps :)

Related Questions

what is the proportion for 2/3 and 8/10

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there is no solution I believe since 2/3 and 8/10 cross multiplied are 2 times 10 and 3 times 8 which is 20 = 24 which does not equal and there is no answer

what is the solution to y=x+16 and y=-x+4??

Please show work and explanation in how its done...
so i can understand better cause I'm new to these problems...
so i can get all the help i can get (:

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y=x+16
y=-x+4

All you have to do is substitute.
Put the second equation into the first equation.

-x + 4 = x + 16
4 = 2x + 16
-12 = 2x
-6 = x

Now substitute the x into one of the equations to get y.

y = (-6) + 16
y = 10

The solution to these equations is (-6, 10).

What is the 32nd term of the arithmetic sequence where a1 = −32 and a9 = −120?

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firstly we have to find d:
[tex]d = \frac{a_{n}-a_{m}}{n-m} [/tex] ⇒
[tex]d = \frac{-120-(-32)}{9-1} = \frac{-88}{8} = -11[/tex]
now, when we know d, we can find the 32nd term by using a following formula:
[tex]a_{n}=a_{1}+(n-1)*d[/tex]
[tex]a_{32} =-32+31*(-11) = -32-341 = -373[/tex]
the answer is [tex]a_{32} = -373[/tex]

Answer:

-373

Step-by-step explanation:

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341

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If vertex T' is at (2,-2) what are the coordinates of vertex s

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wheres the grid????????

What's the 6th term in a sequence that starts with -7.5 and has a common ratio of 9?

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[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-7.5\\ r=9\\ n=6 \end{cases}\implies a_6=-7.5\cdot 9^{6-1}[/tex]

Yi's average for her first 3 tests is 88. what musit she score on her last test to bring her average up to 90

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Her average now is 88.
She needs to bring it up to a 90.

Let's start with if she gets a 90.
88 + 90 = 178
178/2 = 89
A 90 would only get her an average of 89, so you need to go higher.

88 + 91 = 179
179/2 = 89.5

88 + 92 = 180
180/2 = 90

She must get at least a 92 to get an average of 90.

Prove or disprove the identity. If you find the identity is true, state the first line of the proof. If you find the identity is false, write the correct equation by replacing the right side.
sin x cos x tan x cot x = 1

A) the identity is true. sin x cos x tan x cot x = cos x
B) the identity is true. sin x cos x tan x cot x = sin x tan x
C) the identity is false. sin x cos x tan x cot x = sin x cos x
D) the identity is false. sin x cos x tan x cot x = sin x

Answers

sin x cos x tan x cot x

Change to sin's cos's:-

= sin x cos x sin x cos x
------- -------
cos x sin x

= sin x cos x

C is correct

Final answer:

The identity sin x cos x tan x cot x = 1 is false. By using the definitions of tan and cot, we can show that sin x cos x tan x cot x simplifies to sin x cos x.

Explanation:

The student has asked to prove or disprove the identity sin x cos x tan x cot x = 1. To verify this identity, we need to remember the definitions of the trigonometric functions. The tangent (tan) of an angle is the ratio of the sine (sin) to the cosine (cos) of that angle, and the cotangent (cot) is the reciprocal of the tangent.

Therefore, tan x = sin x / cos x, and cot x = cos x / sin x. When we multiply tan x by cot x, we get:

tan x × cot x = (sin x / cos x) × (cos x / sin x) = 1

Now, multiplying this result by sin x cos x gives:

sin x cos x tan x cot x = sin x cos x × 1 = sin x cos x

Therefore, the correct equation is sin x cos x tan x cot x = sin x cos x, which means the correct answer is:

Gabby solved x2 - 3x = 4 as shown below:
x2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = -4 and x = 1

Caitlyn says Gabby is wrong and believes this is the solution:
x2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = 4 and x = -1

Is Gabby or Caitlyn correct? What mistake was made by the incorrect girl? Type your response in the box provided.

Answers

Caitlyn is correct.
Both factored correctly but the reason Gabby is wrong is because of the Zero Product Property, which says if (x-4)(x+1)=0, then (x-4)=0 or (x+1)=0.

If (x-4)=0, then the value of x must be 4.
If (x+1)=0, then the value of x must be -1.

Samantha loves to download new music. She originally had 52 songs but plans to purchase 2 new songs each week. She wants to know how many songs she will have after 93 weeks. Which equation should she use?

a93 = 93 + 2(52 − 1)
a93 = 93 + 2(52 + 1)
a93 = 52 + 2(93 + 1)
a93 = 52 + 2(93 − 1)

Hint: It's either A, B, C, or D

Answers

[tex]a_1=52\\ d=2\\ n=93\\\\ a_n=a_1+(n-1)\cdot d\\\\ a_{93}=52+(93-1)\cdot2=52+2(93-1) [/tex]

They want to construct this in the form of an arithmetic sequence which as the form:

a(n)=a+d(n-1), where a=initial value, d=common difference.

In this case a=52 and d=2, so our formula is:

a(n)=52+2(n-1) and if we are looking for the 93 term we have

a(93)=52+2(93-1)

(02.07)Solve for L: A = L ⋅ W ⋅ H

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A = LWH
/WH = L

Therefore L = A / WH

A = L ⋅ W ⋅ H
Let's solve for l.a=lwhStep 1: Flip the equation.hlw=aStep 2: Divide both sides by hw.hlw/hw=a/hwl=ah/w

The mass of mercury is 330,200,000,000,000,000,000,000 kilograms. how can this number be written in scientific notation?

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Final answer:

The mass of mercury, 330,200,000,000,000,000,000,000 kg, can be written in scientific notation as 3.302 × 10²⁰ kg. Scientific notation helps to express very large numbers in a more manageable form, using a coefficient between 1 and 10 multiplied by a power of ten.

Explanation:

To write the mass of mercury in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of ten. The mass given is 330,200,000,000,000,000,000,000 kilograms, which can be written as 3.302 × 10²⁰. Since there are 20 digits to the right of the first digit (3), the exponent in the scientific notation will be 20.

In scientific notation, the mass of mercury is thus written as 3.302 × 10²⁰ kg.

When converting to scientific notation, we use multiplication and division techniques to adjust the original number, so the resulting coefficient is a value from 1 up to, but not including, 10. This method is commonly used by scientists and astronomers when dealing with astronomical numbers, as in this case with the mass of a planet or in chemistry with the mass of an atom.

One way to recognize a line of symmetry is to look for a line that divides the original image into

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yes that is correct
like a square if you half it both sides equal each other but if you half a elephant then it is not equal

2 equal halves

for example a line of symmetry fro an isosceles triangle is a line from vertex to midpoint of the opposite side.

What is the square root of 75 in simplified form?

Answers

√75 = 5√3

so yeah this is filler text

Answer:The answer is

5 3

Step-by-step explanation:

which of the following is an example of conditional probability.
A: probability of hitting a home run
B: Probability of getting an A on a test, given that you didn't fail the test
C: probability of drawing a club from a deck of 52 cards
D: probability of getting an A on a test

Answers

it would be b because first off it is different from all the others and it has probability of a given b

The example of conditional probability is Probability of getting an A on a test, given that you didn't fail the test.

What is conditional probability?

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

For Conditional probability, the event should be dependent events.

Also, the probability of an event and the condition is that the other event has already been occurred.

Here, in Probability of getting an A on a test, given that you didn't fail the test is example of conditional probability because " you didn't fail the test " already occurred and now find the probability of getting A.

Learn more about conditional probability here:

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How to factor x^2+27

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Hello,

If you know complex, than:

x²+27=x²-i²*3*9=(x-i*3√3)(x+i*3√3)

A golfer would like to test the hypothesis that the variance of his golf score equals 10.0. a random sample of 28 rounds of golf had a sample standard deviation of 3.5. what is the number of degrees of freedom for this hypothesisâ test?

Answers

It depends on which statistic test we wish to perform, the formula to find a degree of freedom could be different.

for Normal Distribution test, we do not need to find a degree of freedom

for T-test and Chi-Square test, we do n - 1 to find the degree of freedom, where 'n' is the sample size.

if we have two different sample size, then the degree of freedom is given by (n₁ + n₂) - 2

We are given only one sample size, n = 28, hence the degree of freedom is 28 - 1 = 27

Twice a certain number is tripled. The resulting number is _____.

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[tex]2x\cdot3=6x[/tex]

x represents the certain number, now make an equation:
(2x)*3 = 6x

What is h(x) = –3x2 – 6x + 5 written in vertex form?
h(x) = –3(x + 1)2 + 2
h(x) = –3(x + 1)2 + 8
h(x) = –3(x – 3)2 – 4
h(x) = –3(x – 3)2 + 32

Answers

h=-3x^2-6x+5 subtract 5 from both sides

h-5=-3x^2-6x divide both sides by -3

(5-h)/3=x^2+2x halve the linear coefficient, square it, add it to both sides....

(2/2)^2=1 add 1 to both sides...

(5-h+3)/3=x^2+2x+1, now the right side is a perfect square...

(8-h)/3=(x+1)^2 multiply both sides by 3

8-h=3(x+1)^2 divide both sides by -1

h-8=-3(x+1)^2 add 8 to both sides

h=-3(x+1)^2+8

h(x)= -3(x+1)^2+8

Second answer down from the top :)

Answer:

its b

Step-by-step explanation:

I just did the assignment

Determine whether the expression is a polynomial. If it is a polynomial, state the degree of the polynomial.
x^3-9
a. yes, 3
b. yes, 1
c. yes, 2
d. no, it is not a polynomial

Answers

A. the degree of a polynomial is the value of the greatest exponent which in this case is 3

Final answer:

The expression x^3 - 9 is indeed a polynomial because it consists of a variable raised to a non-negative integer exponent and a constant. The highest power of the variable is 3, which makes the degree of the polynomial also 3.

Explanation:

To determine whether the expression x^3 - 9 is a polynomial and to state its degree, we need to look at the characteristics of polynomials. A polynomial is an expression that consists of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

The expression in question, x^3 - 9, fits this definition because it involves a single variable x raised to a non-negative integer exponent (3), and a constant term (-9).

Next, to identify the degree of the polynomial, we look for the highest power of the variable in the expression. The highest power of x in x^3 - 9 is 3. Therefore, this expression is indeed a polynomial, and its degree is 3.

The correct answer to the question is: a. yes, 3.

PLZ HELP I NEED THIS TODAY!!!!Write an expression for the perimeter of the triangle shown below: A triangle is shown with side lengths labeled 2.3x plus 14, 2x, and negative 0.2x plus 15.

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The perimeter of the triangle:
P = a + b + c, where a, b, and c are sides of the triangle.
Here is:
a = 2.3 x + 14, b = 3 x and c = - 0.2 x + 15
P = ( 2.3 x + 14 ) + 2 x + ( - 0.2 x + 15 ) =
= 2.3 x + 14 + 2 x - 0.2 x + 15 = 4.1 x + 29
Answer: The perimeter of the triangle is 4.1 x + 29

A line with a slope of 0 passes through the point (0, -5) . what is its equation i n slope -intercept form?

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It should be y=x-5 because the slope is 0 and the y-intercept is -5.

Lana Powell has cumulative earnings of $110,000 at the end of September. In the first week in October she earns $2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on $110,100 and Medicare of 1.45%):

Answers

Answer:

Step-by-step explanation:

In the first week of October on the $ 2,000, we must deduct the two expenses, that of 6.2% and 1.45%, and then add them between them and subtract them from the $ 2000.

It would be the following: 2000 x 6.2% = $ 124; 2000 x 1.45% = 29; 124 + 29 = $ 153 is the amount to be deducted from the $ 2,000; $ 2000 - $ 153 = $ 1847.

Final answer:

Lana Powell's paycheck for the first week in October would have $124 deducted for Social Security and $29 for Medicare, resulting in a total deduction of $153. Her cumulative earnings are not considered here as she has exceeded the earnings threshold of $110,100 for Social Security tax.

Explanation:

Lana Powell's earnings for the first week in October are subject to deductions for Social Security at a rate of 6.2% and Medicare at a rate of 1.45%. To calculate these deductions, you multiply her weekly earnings by the respective rates:

Social Security deduction = $[tex]2000*6.2/100 = $124[/tex]Medicare deduction = $[tex]2000*1.45/100 = $29[/tex]

Therefore, the total amount deducted from Lana Powell's paycheck for Social Security and Medicare is $124 + $29 = $153.

Note that you do not consider her cumulative earnings in this case. The Social Security tax is applicable only up to a wage base limit of $110,100 and since her cumulative earnings have already exceeded this limit, she would not be paying any additional Social Security tax beyond this earnings threshold.

Learn more about Payroll tax calculations here:

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is this correct? if not please let me know how to solve it

Answers

It's correct.

All you had to do was distribute and you did that perfectly.

it is correct. you had to use the distributive property and you did that correctly.

Which statement is true about the polynomial after it has been fully simplified? (See picture)

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I think it would be "It has 2 terms and a degree of 2", because the 3x^2y^2 and the -3x^2y^2 cancel out. Then, you're left with -5xy^2+2x^2.
In what remains, there are 2 terms, each with the highest degree of 2, so I would be led to believe A is your answer.

select all tht apply
If n-^2 = 1/16, then n could be which of the following?

-8
-4
-1/4
1/4
4

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[tex] n^{-2}= \cfrac{1}{16} \\ \\ \cfrac{1}{n^2} = \cfrac{1}{16}; \ \ \ n \neq 0 \\ \\ n^2=16 \\ \\ n=б \sqrt{16} \\ \\n=б4[/tex]

Geometry Help Please

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To determine if ABC is a right angle triangle, we need to check whether two lines are perpendicular, in other words, an intersection of 90°.

When two lines are perpendicular to each other, then their slope multiplied to give -1

Formula to find steepness slope is vertical distance ÷ horizontal distance

Slope AB = [tex] -\frac{3}{2} [/tex]
Slope BC = [tex] \frac{2}{3} [/tex]

Slope AB is a negative slope while BC is a positive slope

Slope AB × Slope BC = [tex]- \frac{3}{2} [/tex]×[tex] \frac{2}{3} [/tex] = -1

Angle ABC is right angle, hence triangle ABC is a right-angled triangle

ABCDEFGHIJ is a regular decagon. Find the length of the apothem. Round the answer to the nearest tenth.

A.

8.0

B.
20.5

C.

24.7

D.

26.0

Answers

you find apothem with the formula [tex] \left[a = fn*S] [/tex]

fn is the fixed number (1,539) and S the side of the polygon.

a = 16*1,539 = 24,624 = 24,7

Answer C

Solution:(α=∫nₓS)Use this formula to find apothem

∫n is the fixed number (1,539) and S the side of the polygon.

a = 16 × 1,539 = 24,624 = 247

Answer: C 24.7

Salvage system algebraically. Show all your work in circle your answers

Answers

Use substitution for x
2(y+2)+4y=-2
2y+4+4y=-2
6y+4=-2
6y=-6
y=-1

Plug the y value in to find x
x= (-1)+2
x=1

Final answer: (1,-1)

HELP PLEASE..answer fast please and show all work and explain how to solve

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[tex] \cfrac{a}{sinA}= \cfrac{b}{sinB} \ \ \to \\ sinB= \cfrac{b*sinA}{a} = \cfrac{10*sin15^o}{9}= 0.2875 \ \ \to \ m \angle B=16.7^o \\ \\ \\ m \angle C=180- m \angle A- m \angle B=180-15-16.7=148.3^o \\ \\ \\ \cfrac{a}{sinA}= \cfrac{c}{sinC} \ \ \to \ c= \cfrac{a*sinC}{sinA}= \cfrac{9*sin148.3^o}{sin15^o} \approx 18.3[/tex]

What is the answer to solve negative eight positive negative 2 for integers?

Answers

We will transform the wordings into an equation as follows:
(-8) + (-2)
A positive sigh followed by a negative sign usually yields a negative value.

Therefore, the above equation becomes:
- 8 - 2 which can be easily calculated:
-8 -2 = -10

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Given the arithmetic sequence A1, A2, A3, A4, 58,69,80,91 What is the Value of A21? ***PLEASE HELP******

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Given the arithmetic sequence A1, A2, A3, A4, 58,69,80,91
What is the Value of A21?

*PLEASE HELP****