Mathematics High School

Find the 86th term of the arithmetic sequence 21, 15, 9, ...21,15,9,...

Answers

Answer 1

The 86th term of the arithmetic sequence is [tex]$-489$.[/tex]

To find the 86th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

[tex]\[ a_n = a_1 + (n - 1) \cdot d \][/tex]

where:

- [tex]$ a_n $[/tex] is the nth term,

- [tex]$ a_1 $[/tex] is the first term,

- ( n ) is the term number,

- ( d ) is the common difference.

In this sequence:

- [tex]$ a_1 = 21 $,[/tex]

- [tex]$ d = 15 - 21 = -6 $.[/tex]

Now, we can plug these values into the formula to find the 86th term:

[tex]\[ a_{86} = 21 + (86 - 1) \cdot (-6) \][/tex]

[tex]\[ a_{86} = 21 + 85 \cdot (-6) \][/tex]

[tex]\[ a_{86} = 21 - 510 \][/tex]

[tex]\[ a_{86} = -489 \][/tex]

So, the 86th term of the arithmetic sequence is [tex]$-489$.[/tex]

Related Questions

What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.

To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.

Answers

we know that
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²

so
the volume of a sphere=(r/3)*surface area of sphere
therefore

if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere

if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere

if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere

example
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area

2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area

3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area

Name three properties that a square and a rhombus share.

Answers

They are quadrilateral.
Their all sides are equal.
Diagonals bisect at 90° ( right angle )

Please someone help Me with this problem. I really need help.

Answers

The distance between (4, 7) and (2, 2) might be A, 10. Hope this helps, sorry if I'm wrong.

A restaurant manager recorded the number of people in different age groups who attended her food festival: Histogram with title Food Festival Participants, horizontal axis labeled Age Group (yr) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50. Which of the following frequency tables represents the data in the histogram accurately? Age Group (year) Number of People 0–19 20 20–39 60 40–59 40 60–79 50 Age Group (year) Number of People 0–19 20 20–39 60 40–59 50 60–79 40 Age Group (year) Number of People 0–19 20 20–39 40 40–59 60 60–79 50 Age Group (year) Number of People 0–19 60 20–39 20 40–59 40 60–79 50

Answers

The third choice is the correct answer because the information provided to you about the histogram shows the height of the first bar going to 20, the second bar going to 40, the third bar going to 60, and the fourth bar going to 50. The third frequency table organized this same information in the same way.

Answer:

There are 3 times as many participants in the 40-59 age group than the 0-19 age group.

Step-by-step explanation:

Because when we take 20 and times it by three we get 60 and the 40-59 age group is 60 so there you go. Hope This Helps:) Brain-list would be greatly appreciated.

Factor completely: 6b - 8ab + 15 - 20a

Answers

For this case we have the following expression:
6b - 8ab + 15 - 20a
We can rewrite the expression factoring.
We have then:
(4a-3) * (- 2b-5)
Checking we have:
-8ab-20a + 6b + 15
The resulting expression is the same.
Answer:
(4a-3) * (- 2b-5)

Can someone help me in this trig question, please? thanks
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12

Answers

[tex]\bf \textit{the position of the rider is clearly }20cos\left( \frac{5\pi }{12} \right)~~,~~20sin\left( \frac{5\pi }{12} \right)\\\\ -------------------------------\\\\ \cfrac{5}{12}\implies \cfrac{2+3}{12}\implies \cfrac{2}{12}+\cfrac{3}{12}\implies \cfrac{1}{6}+\cfrac{1}{4} \\\\\\ \textit{therefore then }\qquad \cfrac{5\pi }{12}\implies \cfrac{1\pi }{6}+\cfrac{1\pi }{4}\implies \cfrac{\pi }{6}+\cfrac{\pi }{4}\\\\ -------------------------------[/tex]

[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ -------------------------------\\\\ cos\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=cos\left( \frac{\pi }{6}\right)cos\left(\frac{\pi }{4} \right)-sin\left( \frac{\pi }{6}\right)sin\left(\frac{\pi }{4} \right)[/tex]

[tex]\bf cos\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}-\cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{6}}{4}-\cfrac{\sqrt{2}}{4}\implies \boxed{\cfrac{\sqrt{6}-\sqrt{2}}{4}} \\\\\\ sin\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=sin\left( \frac{\pi }{6}\right)cos\left( \frac{\pi }{4} \right)+cos\left( \frac{\pi }{6}\right)sin\left(\frac{\pi }{4} \right)[/tex]

[tex]\bf sin\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=\cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}+\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}+\cfrac{\sqrt{6}}{4}\implies \boxed{\cfrac{\sqrt{2}+\sqrt{6}}{4}}\\\\ -------------------------------\\\\ 20\left( \cfrac{\sqrt{6}-\sqrt{2}}{4} \right)\implies 5(-\sqrt{2}+\sqrt{6}) \\\\\\ 20\left( \cfrac{\sqrt{2}+\sqrt{6}}{4} \right)\implies 5(\sqrt{2}+\sqrt{6})[/tex]

The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

The position

Since the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°

So, substituting the value of θ into the positions, we have

(20cos75°, 20sin75°)

The value of 20cos75°

20cos75° = 20cos(45 + 30)

Using the compound angle formula

cos(A + B) = cosAcosB - sinAsinB

With A = 45 and B = 30

cos(45 + 30) = cos45cos30 - sin45sin30

= 1/√2 × √3/2 - 1/√2 × 1/2

= 1/2√2(√3 - 1)

= 1/2√2(√3 - 1) × √2/√2

= √2(√3 - 1)/4

= (√6 - √2)/4

= (-√2 + √6)/4

So, 20cos75° = 20 × (-√2 + √6)/4

= 5 (-√2 + √6)

The value of 20sin75°

20sin75° = sin(45 + 30)

Using the compound angle formula

sin(A + B) = sinAcosB + cosAsinB

With A = 45 and B = 30

sin(45 + 30) = sin45cos30 + cos45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= 1/2√2(√3 + 1)

= 1/2√2(√3 + 1) × √2/√2

= √2(√3 + 1)/4

= (√6 + √2)/4

= (√2 + √6)/4

So, 20sin75° = 20 × (√2 + √6)/4

= 5(√2 + √6)

Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).

So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

Learn more about position here:

https://brainly.com/question/11001232

At noon joyce drove to the lake at 30 mph, but she made the long walk back home at 4 mph. how many hours did she walk if she was gone for 17 hours

Answers

By definition we have the following equation:
t = d / v
Where,
t: time
d: distance
v: speed
For this case we have:
d / 30 + d / 4 = 17
Rewriting we have:
2d + 15d = 17 (60)
17d = 17 (60)
d = 60 mi
Then, the walking time is
t = d / v
t = 60/4
t = 15 hours
Answer:
She walked
t = 15 hours

Answer:

i just did this on a quiz the answer was 15 hours

Step-by-step explanation:

NEED HELP ASAP!
Subtract.
(4x^2+8x−2)−(2x^2−4x+3)
Answer in standard form

Answers

[tex](4x^2+8x-2)-(2x^2-4x+3)\\\\=4x^2+8x-2-2x^2+4x-3\\\\=(4x^2-2x^2)+(8x+4x)+(-2-3)\\\\=\boxed{2x^2+12x-5}[/tex]

If a scare as side lengths of 5 inches what is the lengths of the diagonal to the nearest 10th of in inch

Answers

A 5 by 5 square would have a diagonal equal to

square root (25 + 25) =
square root (50) =
7.07106781 =
7.1 (rounded to nearest 10th of an inch.

Which regular polygon would have each of its interior angles measure 120°? hexagon heptagon octagon nonagon?

Answers

Sum of angles of regular polygon = 180*(n-2), n - number of sides, or angles.

120n=180*(n-2)

120n=180n-360
180n-120n=360
60n =360
n=6

It is hexagon.

The length of a rectangle is increasing at a rate of 6 cm/s and the width is increasing at a rate of 4 cm/s. when the length is 16 cm and the width is 12 cm, how fast is the area of the rectangle increasing?

Answers

The area is 192 and the speed it’s increasing at is 24 cm^2/s

sketch one cycle of the cosine function y=-cos 3 theta

Answers

The graph of the equation given by y=-cos³θ will be as follows:

Answer with explanation:

The given cosine function is

y= - cos 3 (theta)= -3 cos A, where , theta =A.

→→Domain of Cos A

= All Real number

= Period is from (-π , π)

Range of Cos A=[-1, 1]

→Domain of Cos 3 A,will be also, all real number.

Period is from,

[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]

But range of Cos 3A,will be same as ,Cos A which is equal to ,[-1,1].

→Plotted the graph of ,y=-cos 3 A, having cycle ,

[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]

Determine whether quantities vary directly or inversely and find the constant of variation. If 5 bushels of wheat weigh 136 kg, how much do 3.5 bushels of wheat weigh?

Answers

Well if 5 bushels = 136kg then 1 = 27.2 then 3.5 = 95.2 so it is directly and th vriation is 27.2

Let the bushels of wheat is b and weight of the wheat is w.

We can say that more the bushels of wheat more will be the weight of the wheat.

Hence, the quantities vary directly.

Therefore, we have

[tex]b=kw[/tex], where k is the constant of variation.

Now, we have been given that 5 bushels of wheat weigh 136 kg. Thus, we have

[tex]5=136k\\ \\ k=\frac{5}{136}[/tex]

Thus, the constant of variation is [tex]\frac{5}{136}[/tex]

Now, we have been given 3.5 bushels of wheat. Hence, we have

[tex]3.5=\frac{5}{136} w\\ \\ w=\frac{136\times 3.5}{5} \\ \\ w=95.2[/tex]

Therefore, 3.5 bushels of wheat weigh 95.2 kg

If p(x) = 2x^3 - 3x + 5, what is the remainder of p(x) divided by (x - 5)

Answers

Dividing the function given, P(x) by (x-5) will give us the following
P(x)/(x-5)
=(2x^3-3x+5)/(x-5)
=(2x^2+10x+47)+240/(x-5)
thus the remainder is:
240

Final answer:

Using the Remainder Theorem, after substituting 5 into the polynomial p(x), we find that the remainder when p(x) is divided by (x - 5) is 240.

Explanation:

To find the remainder of p(x) divided by (x - 5), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial p(x) divided by (x - a) is p(a). Thus, we need to evaluate p(5).

Let's substitute x with 5 in the polynomial p(x):

p(5) = 2(5)^3 - 3(5) + 5
= 2(125) - 15 + 5
= 250 - 15 + 5
= 240.

Therefore, the remainder when p(x) is divided by (x - 5) is 240.

HELP!! Drag values to complete each equation.

Answers

(12²)³ x 12^-4 = 144 which means it is 12² = 144.

12^7 x 12^-5 / 12² which equals 1.

Hope this Helps!!

Answer:

a.[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

Step-by-step explanation:

We have to complete each equation

We are given that

[tex]((12)^2)^3\cdot (12)^{-4}[/tex]

[tex](12)^6\cdot (12)^{-4}[/tex]

Using identity

[tex](a^x)^y=a^{xy}[/tex]

[tex](12)^{6-4}=(12)^2[/tex]

Using identity: [tex]a^x\cdot a^y=a^{x+y}[/tex]

[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}[/tex]

[tex]\frac{(12)^2}{(12)^2}[/tex]

[tex](12)^{2-2}=(12)^0=1[/tex]

Using identity: [tex]\frac{a^x}{a^y}=a^{x-y},a^0=1[/tex]

[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

un joyero vende 13 anillos de oro y 18 de plata por 9405 euros. sabiendo que el anillo de oro cuesta el triple que el de plata ¿cual es el precio de cada anillo?

Answers

To solve this problem you must apply the proccedure shown below:

1. You have that:

- He sales 13 gold rings and 18 silver rings in 9405 euros.
- The cost of the silver ring is three times the cost of the gold ring.

2. Keeping the information above on mind, you have the following system of equations:

x: the gold ring.
y: the silver ring.

x+y=9405
x=3y

3. Then, you have:

(3y)+y=9405
y=9405/4
y=2351.23 euros

x=3y
x=3(2351.23)
x=7053.75 euros

The answer is:
- Gold ring=7053.75 euros
- Silver ring=2351.23 euros

An equiangular triangle can be scalene. A. True B. False

Answers

False is correct answer.

Because equiangular triangle is not to be scalene.

Hope it helped you.

-Charlie

:)

False, Scalene triangles have three unequal sides and equilateral have three equal sides

Ms. Acosta received a job as a teacher with a starting salary of $34,000. According to her contact, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in 7 years

Answers

The total amount that Ms. Acosta will earn in 7 years will be given by:
A=P(1+r/100)^n
where:
P=principles
r=rate
n=time
From the information given:
P=$34000, r=1.5%, n=7
thus
A=34000(1+1.5/100)67
A=$37,734.73

what expression is equivalent to the division expression 3/4 divided by 4/5

Answers

3/4 ÷ 4/5 =

3/4 times 5/4 =

15/16 = .9375

Answer:

3/4 ÷ 4/5 = .75 ÷ .80

Step-by-step explanation:

3/4 ÷ 4/5

= .75 ÷ .80

= 0.9375

Help Asap! 30 Points!
What is the volume of this sphere? r = 2.5 m

Answers

The volume would be,

65.45 m^3

Good Luck ^-^

The equation:
V = 4/3πr^3
input r:
V = 4/3π(2.5^3)
Multiply:
V = 4/3π(15.625)
V = 4/3(3.14)(15.625)
Multiply:
V = 4/3(49.0625)
Multiply by 4:
V = 196.25/3
V = 65.4166
Round up:
V = 65.42 m^3

On the first test, the mean is 70, the standard deviation is 5, and your score is 80. on the second test, the mean is 70, the standard deviation is 15, and your score is 85. compared to other students, how well did you do on the two tests?

Answers

85+88+87+80+x all divided by 5= 82

340+x=410

410-340=70

Ethan correctly answers 80% of the total questions on his history test. He correctly answers 32 questions. What is the number of questions on Ethan's history test?

Answers

32 is 80% of x
x=40
Did most of the math in my head, I think 40 is the answer tho. xD gl!

hope this helps........

Eight pounds of ground beef are divided into quarter-pound hamburger patties. How many hamburger patties are there in total?

Answers

8 times 4 equals 32, the total number of patties would be 32

The measure of an angle is 8 times the measure of its complement. tina writes an equation and finds the correct measure of each angle. which shows the equation tina could have written and the angle measures she could have found?

Answers

One of the unknown angles (let's called it n) has a complement (meaning their sum adds up to 90 degrees) and the other angle is 8 times the unknown angle (8n)

With all this information, you should have the equation:

n + 8n = 90

To solve, combine like terms to get:

9n = 90

Divide by 9 on both sides to isolate the variable n.

n = 10

Now we plug back in to find our angle measurements. The first angle, n, is 10 degrees. The second angle, 8n, is 8 * 10 which is 80; the second angle is 80 degrees.

The measure of angles are 10 and 80 degree.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

We have,

let the complementary angle = x

and, the another angle is = 8x

We know the complementary angle sum to 90 degree.

So, x + 8x = 90

9x = 90

x =10

Thus, the measure of angles are 10 and 80 degree.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ2

CAN SOMEONE HELP ME ON THIS

Answers

We apply the formula of distance between points:
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
We have then:
For WX:
WX = root ((- 3 - (- 10)) ^ 2 + (- 1-4) ^ 2)
WX = 8.602325267
For XY:
XY = root ((- 5 - (- 3)) ^ 2+ (11 - (- 1)) ^ 2)
XY = 12.16552506
For WY:
WY = root ((- 5 - (- 10)) ^ 2+ (11-4) ^ 2)
WY = 8.602325267
The triangle is isosceles because it has two equal sides.
Answer:
WX = 8.60
XY = 12.17
WY = 8.60
Isosceles

A math book sells for $106.50. (a) find the amount of sales tax, to the nearest cent, if the sales tax rate is 8.5%. (b) find the total purchase price

Answers

Answers:
________________________________________________________
a)  " $ 9.05 " .
________________________________________________________
b)  " $ 115 .55 " .
________________________________________________________
Explanation:
________________________________________________________

a)   "FInd the amount of sales tax, to the nearest cent,
if the sales tax rate is 8.5% ."

  → 8.5% of 106.50 = (8.5/100) * 106.50 = 0.085 * 106.50 ;

= 9.0525 ;

→ round to the nearest cent: $ 9.05 .
________________________________________________________
b)  Find the purchase price:

→ $ 106.50
+ 9.05
________________________________________________________
$ 1 1 5.55
________________________________________________________

can someone help me on trigonometry ?

Answers

Using the image I gave you, you don't need to solve for x.
So tan is opposite/adjacent
sin: opposite/hypotenuse
cos: adjacent/hypotenuse
Take theta and do: adjacent/hypotenuse which is cosine
cos theta = adjacent/hypotenuse
cos theta = 1.5/9
inverse cos = 1.5/9 and the answer is: 80.4 degrees

what are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? the figures are not drawn to scale. a. 13/3 and 169/9 b. 13/3 and 16/9 c. 16/3 and 169/9 d. 16/3 and 16/9

Answers

we know that

a) find the ratio of the perimeters

the ratio of the perimeters is equal to the scale factor
scale factor=26/6-----> 13/3
the answer Part a) is
the ratio of the perimeters is 13/3

b) find the ratio of the areas of the larger figure to the smaller figure
we know that
area larger figure=[scale factor]²*area smaller figure
scale factor²=area larger figure/area smaller figure

the ratio of the areas of the larger figure to the smaller figure is equal to scale factor squared
scale factor²=(13/3)²----> 169/9

the answer Part b) is
169/9

the complete answer is
13/3 and 169/9

Subtract.

(x + 1) − (−2x − 5)

Answers

3x+6, you have to distribute the negative to get the parentheses away and simplify

Answer:

3x+6

Step-by-step explanation:

you have to distribute the negative to get the parentheses away and simplify

A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)

Answers

the speed of the car in centimeters per second based on the information given would be 2,145.8

A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)

Solution:

We have 48 [tex] \frac{miles}{hour} [/tex]

To convert, miles to centimeters.

Let us convert miles to feet and then inches and then centimeters.

1miles=5280feet

And, 1 foot=12inches

So, 5280 feet or 1 miles =12*5280inches

So, 1miles=63360inches

Now, Let us convert inches to centimeters

1centimeter=0.39inches

Or, 1 inch= [tex] \frac{1}{0.39} [/tex] centimeter

So, 63360inches (or 1 mile)= [tex] \frac{63360}{0.39} [/tex] centimeter

1mile or 63360inches=162461.54centimeter

1mile=162461.54 centimeter

We have, 48 [tex] \frac{miles}{hour} [/tex]

We have, 48 *[tex] \frac{162461.54 centimeter}{60minutes} [/tex]

We have, 48* [tex] \frac{162461.54 centimeter}{60*60seconds} [/tex]

So, We have, 48* [tex] \frac{162461.54 centimeter}{3600seconds} [/tex]

=48*[tex] \frac{162461.54}{3600} [/tex][tex] \frac{centimeters}{second} [/tex]

=48*45.13[tex] \frac{centimeters}{second} [/tex]

=2166.15[tex] \frac{centimeters}{second} [/tex]

Answer:= Speed of the car in centimeters per second is 2166.15 centimeters/second

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