two terms of an arithmetic sequence are a10=16 and a35=66 find the sum of the first 75 terms

Answers

Answer 1

The sum of the first 75 terms of the arithmetic sequence that has 10th term as 16 and the 35th term as 66 is 5400.  

How to find the sum of terms using Arithmetic sequence formula

aₙ = a + (n - 1)d

where

a = first termd = common differencen = number of terms

Therefore, let's find a and d

a₁₀ = a + (10 - 1)d

a₃₅ = a + (35 - 1)d

Hence,

16 = a + 9d

66 = a + 34d

25d = 50

d = 50 / 25

d = 2

16 - 9(2) = a

a = 16 - 18

a  = -2

Therefore, let's find the sum of 75 terms of the arithmetic sequence

Sₙ = n / 2 (2a + (n - 1)d)

S₇₅ = 75 / 2 (2(-2) + (75 - 1)2)

S₇₅ = 37.5 (-4 + 148)

S₇₅ = 37.5(144)

S₇₅ = 5400

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Related Questions

help please thank you!!!

Answers

Answer:

3/4 · 1/4 = 3/16

Step-by-step explanation:

We can see from the picture that

yellow is

4 boxes out of the entire group of 16 boxes, hence 4/16

OR simplified

1 horizontal strip out or 4 total same horizontal strips, hence 1/4

blue is

12 boxes out of the entire group of 16 boxes, hence 12/16

OR simplified

3 vertical strips out or 4 total vertical strips, hence 3/4

The multiplication problem is

1/4 · 3/4 = 3/16 or 3/4 · 1/4 = 3/16

The result is 3 green boxes out of all 16 boxes.

(3/16 can not be simplified)

change 1.77 tones to kilograms

Answers

Answer:

1.77 Tones = 1770 Kilograms

Step-by-step explanation:

Multiply the value of the tone by 1000 to get KG

1.77 x 1000 = 1770

1770 kilograms
Multiply the mass value by 1000

Select the correct answer. Sharla wanted to know how many minutes per hour a radio station typically plays music. She collected the following data from seven radio stations. 30 , 31 , 37 , 36 , 31 , 35 , 34 By how many minutes would her median time change if she added another radio station playing 37 minutes? A. the median did not change B. 0.5 C. 0.4 D. 0.45

Answers

Answer:

D. 0.45

Step-by-step explanation:

Median is everything added up, then divide by the amount of numbers you have.

30+31+37+36+31+35+34=234

then divide by 7 and you get 33.42

30+31+37+36+31+35+34+37=271

then divide by 8 and you get 33.87

33.87 and 33.42 have a difference of 0.45

Can sombody solve this please. :)

Answers

144 x m - 309.6 = 50.4

Add 309.6 to both sides:

144 - 309.6 + 309.6 = 50.4 + 309.6

Simplify the arithmetic:

144 x m = 50.4 + 309.6

Simplify the arithmetic:

144 x m =360

m = 5/2

Find the missing value in the table
(Ignore all the writing I did already I think it’s wrong but I’m not sure)

Answers

Answer:

Step-by-step explanation:

#1 is correct

#2 is correct

#3 is correct

#4 is correct

#5  is correct

#6 is 29.6

Select the values that would satisfy the following inequality:
K ≤ 12.75

|12.75|

|-12.75|

13

|-15|

0

Answers

Answer:

If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.

Step-by-step explanation:

In which quadrant is the value of the x-coordinate of a point on the unit circle always greater than the y-coordinate?

Answers

Answer:

IV

In the fourth quadrant (IV).

Step-by-step explanation:

In the IV quadrant the x coordinate is always positive and the y coordinate is always negative. So the x coordinate is always larger than the y coordinate.

Identify the correct explanation for why the triangles are similar. Then find TO and US.

Answers

Answer:

The correct explanation is option B;

B. ∠L ≅ ∠L  By Reflexive Prop. ≅.

Since  ║ , ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6

Step-by-step explanation:

The given parameters are;

= 5

= 10

=  +  = 15

= x - 3

= x + 1

A two column proof is presented as follows;

Statement          Reason

∠L ≅ ∠L             By Reflexive property of congruency

║           Given

∠LOP ≅ ∠LMN   By the Corresponding angles Postulate

Therefore

ΔLOP ~ ΔLMN   By AA similarity Postulate

Where we have that ΔLOP and ΔLMN, we get;

/  = / = 5/15 = 1/3

∴ (x - 3)/(x + 1) = 1/3

3·(x - 3) = 1·(x + 1)

3·x - 9 = x + 1

3·x - x = 1 + 9 = 10

2·x = 10

x = 10/2 = 5

x = 5

= (x - 3) = 5 - 3 = 2

= 2

= x + 1 = 5 + 1 = 6

=  6

Therefore, the correct option is ∠L ≅ ∠L  By Reflexive Prop. ≅.

Since  ║ , ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6.

/TO/ and /US/ are parallel so the angles at TOS (©)and the external angle at OSU (©) are equal ( Z angles) therefore the internal angle at OSU will be 180 - © similarly the angle at POT is also 180 - ©

Haruto simplified the value below. Cosecant (StartFraction 19 pi Over 4 EndFraction) = StartRoot 2 EndRoot Which statement explains whether Haruto is correct? Haruto is correct because the angle is coterminal with StartFraction 3 pi Over 4 EndFraction and the reference angle is StartFraction pi over 4 EndFraction. Haruto is correct because the angle is coterminal with StartFraction pi Over 4 EndFraction, which is also the reference angle. Haruto is not correct because the angle is coterminal with StartFraction 3 pi Over 4 EndFraction, and Cosecant (StartFraction 3 pi Over 4 EndFraction) = StartFraction negative 1 Over StartRoot 2 EndRoot EndFraction = StartFraction negative StartRoot 2 EndRoot Over 2 EndFraction. Haruto is not correct because the angle is coterminal with StartFraction pi over 4 EndFraction, and Cosecant (StartFraction pi Over 4 EndFraction) = StartFraction 1 Over StartRoot 2 EndRoot EndFraction = StartFraction StartRoot 2 EndRoot Over 2 EndFraction.

Answers

If the value of the cosecant 19π/4 and 3π/4 are the same then they are coterminal angles. Then the correct option is A.

What is an angle?

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

The expression is given below.

[tex]\rm cosec \ \dfrac{19\pi}{4} =\sqrt2[/tex]

The angle is 19π/4.

Coterminal angle - The angles in a standard position that have a common terminal side.

Then we have

[tex]\Rightarrow \dfrac{19\pi}{4} - 2*2\pi\\\\\Rightarrow \dfrac{19\pi - 16\pi}{4} \\\\\Rightarrow \dfrac{3\pi}{4}[/tex]

More about the angled link is given below.

https://brainly.com/question/15767203

Answer:

A

Step-by-step explanation:

Props to the otha guy

Find area of shaded region.

Answers

area of shaded region = 1/4 of the circle area - triangle area

circle area = pi x r² = 3,14 x 2² = 12,56 m²

so 1/4 circle area = 12,56 : 4 = 3,14 cm²

and

triangle area = 1/2 x 2 x 2 = 2 m²

=> area of shaded region = 1,14 cm²

One number is 32 more than another. Their product is −256.

Answers

Answer:

ok so this is a system of equations

x+32=y

x*y=-256

so lets just make y x+32

x^2+32=-256

-32

x^2=-288

find root

this can't be solved since negitive numbers don't have roots

Hope This Helps!!!

Help what do I do do i just write y-3x+5 or solve it ​

Answers

Answer:

y=-3x+5

Step-by-step explanation: Yes you have it correct. The question is asking for you to put it into an equation that fits the slope and y-intercept which is slope-intercept form. Additional note, when you have a problem like this and it doesn't say what type of equation form to put it in, put it in slope-intercept form for simplicity's sake.

Answer:

  y = -3x +5

Step-by-step explanation:

In general, do what the question asks you to do: write the equation of the line.

__

The slope and y-intercept of the line are given, so the easiest, most direct way to write the equation is to use "slope-intercept form." That form looks like ...

  y = mx + b . . . . . . where m is the slope, b is the y-inercept

You are given m = -3 and b = 5, so the equation you are asked to write can be ...

  y = -3x +5 . . . . . . this equation is the answer to the question

__

Additional comment

There are many forms of the equation for a line. Another one in common use for problems like this is the "point-slope form." You would use that one for a simple, direct answer to writing an equation for a line with a given slope through a given point.

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

If you are given the x- and y-intercepts, you can use "intercept form" to write the equation:

  x/a +y/b = 1 . . . . . for x-intercept 'a' and y-intercept 'b'

Another useful form is "standard form", which has ...

  ax +by = c . . . . where a > 0, and a, b, c are mutually prime

For example, the equation for your line could be written in standard form as ...

  3x +y = 5

A‌ ‌drink‌ ‌recipe‌ ‌calls‌ ‌for‌ ‌papaya‌ ‌juice‌ ‌and‌ ‌water.‌ ‌This‌ ‌equation‌ ‌represents‌ ‌the‌ ‌proportional‌ ‌relationship‌ ‌between‌ ‌the‌ ‌number‌ ‌of‌ ‌milliliters‌ ‌of‌ ‌papaya‌ ‌juice‌ ‌(‌p‌)‌ ‌and‌ ‌water‌ ‌(‌w‌)‌ ‌in‌ ‌the‌ ‌recipe.‌ ‌
‌5‌p‌‌ ‌=‌ ‌85‌w‌ ‌
‌Enter‌ ‌the‌ ‌number‌ ‌of‌ ‌milliliters‌ ‌of‌ ‌water‌ ‌used‌ ‌for‌ ‌1‌ ‌milliliter‌ ‌of‌ ‌papaya‌ ‌juice.‌ ‌

Answers

Answer:

1/17 mL of water

Step-by-step explanation:

5p = 85w

Divide both sides by 85.

5p/85 = 85w/85

p/17 = w

w = p/17

For 1 mL of papaya juice, p = 1.

w = 1/17

1/17 mL of water is used for 1 mL of papaya juice.

(w+9)+3 write an expression equivalent

Answers

Answer:

[tex]\displaystyle 12 + w[/tex]

Explanation:

Just combine like-terms to arrive at your answer:

[tex]\displaystyle \boxed{12 + w} \Rightarrow [w + 9] + 3[/tex]

I am joyous to assist you at any time.

Use the standard normal distribution to find P(-1.23 Sz<2.12).

Answers

Answer:

  (d)  0.8736

Step-by-step explanation:

Unless you have a table of the normal distribution available, this is a calculator problem. Your calculator, or any spreadsheet, can tell you the probability is ...

  P(-1.23 ≤ z ≤ 2.12) ≈ 0.8736

Draw and label a triangle with a base that is 3 times its height and has an area that is less than 50 square inches.

Answers

Answer: i dont knpw how to do tht can u tell me where to draw im just getting points

Step-by-step explanation:

(03.01 MC)
Which equation justifies why 103 = 3/10
1
-1046-10
O
= 10
= 10
dho
°
(103)
(103)-1olia)
0(101) 105)=0
(103)*=106-)-10
=
= 10
=
Previous Question

Answers

Answer:

The choice B

Step-by-step explanation:

[tex]( {10}^{ \frac{1}{3} } )^{3} = {10}^{ \frac{1}{3} \times 3} = {10}^{ \frac{3}{3} } = {10}^{1} = 10[/tex]

What is the measure of angle w°? Show all work.

Answers

It is 100 degrees because angles z and w need to equal 180 and a triangles angles always answer 180 degrees with angle y being 20 and an 80 degree angle making angle z 80 degrees making angle w 100 degrees.

A triangle has two sides of length 4 and 2. What is the smallest possible whole-number length for the third side?

Answers

Answer:

19

Step-by-step explanation:

PLSSS HELP IF YOU TURLY KNOW THISS

Answers

Answer: A

Step-by-step explanation:

2 2/5 is a larger number than 1 4/5.

The easiest way to know this is to look at the first number. 2 is larger than 1.

Hope this helps!

Answer:

A.

Step-by-step explanation:

2 2/5 is a bigger number than 1 4/5, so  you would us greater than sign

Struggling on this one

Answers

Answer:

x=98

Step-by-step explanation:

Alright, so..

Your first step is to isolate (or make the x be alone), so you will have to get rid of the "8". We do this by doing the opposite thing to it. So since it is subtracting, we will add 8:

-8+8=0
Now what you do to one side of the "=" has to be done to the other:
6+8=14

now, we have the equation:
14=x/7

Simply repeat the step of isolating the x:
This time, we will multiply since it was originally dividing..

x/7(7)=1x/1

1x/1 is the same thing as 1x, which is the same thing as just "x"

Now, do it to the other side:
14(7)=98

Thus we have:
98=x or x=98

this can be checked by substituting the "x" for 98:

6=98/7-8
98/7=14

14-8=6

6=6

which is correct.

Thus, the answer is: x=98

Hope this helps! Brainliest is always appreciated! :)
Have a great day! cx

~Mitsuna

Use the law of sines to find the value of y. round to the nearest tenth. law of sines: startfraction sine (uppercase a) over a endfraction = startfraction sine (uppercase b) over b endfraction = startfraction sine (uppercase c) over c endfraction 1.4 units 1.6 units 2.5 units 2.6 units

Answers

Using the law of sine on the given triangle, we get the measure of y as given by: Option C: 2.5 units

What is law of sines?

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

For this case, the missing image is attached below.

Applying the sine law, as we have:

The side opposite to angle Y is XZ of length y units,The side opposite to the angle Z is XY of length 2 units,The side opposite to the angle X is YZ

The first two angles Y and Z are enough. (we use angle Z as the length of the side opposite to Z is known).

Using sine law, we get:

[tex]\dfrac{\sin(m\angle Y)}{y} = \dfrac{\sin(m\angle Z)}{2}\\\\y = \dfrac{\sin(75^\circ) \times 2}{\sin(50^\circ)} \approx 2.522 \approx 2.5 \: \rm units[/tex]

Thus, using the law of sine on the given triangle, we get the measure of y as given by: Option C: 2.5 units

Learn more about law of sines here:

https://brainly.com/question/17289163

How to find the area?

Answers

Answer:

63

Step-by-step explanation:

The perimeter of a quarter circle is 10. 71 yards. What is the quarter circle's radius?

Use 3. 14 for ​

Answers

Answer:

r = 3 yds

Step-by-step explanation:

The perimeter of a quarter circle is 1/4 of a circumference of the circle AND two straight edges that are the length of the radius. see image.

The circumference is given and using 3.14 for pi, we'll then solve for r. see image.

The number 175 is 25% of what number?

Answers

Answer: 700

Step-by-step explanation:

175 * 4 = 700

Answer:

700

Step-by-step explanation:

To solve this problem you multiply 175 by 100 and then divide the total by 25 as follows: (175 x 100) / 25

When we put that into our calculator, we get the following answer:

700

Using the tree diagram below, what is the probability of getting tails and an even number?

Answers

Answer:

Can’t really help since there is no tree diagram presented.

But if you want to know the probability just in this context lets put

Tails / total

even / total

Multiply the two

(Tails / total) * (even / total)

A perpendicular bisector is _____ to a line segment and intersects the line segment at its _____.
A. perpendicular; endpoint
B. adjacent; midpoint
C. supplementary; angle
D. perpendicular; midpoint
E. exterior; linear pair

Answers

Answer:

  D. perpendicular; midpoint

Step-by-step explanation:

A perpendicular bisector is perpendicular to a line segment and intersects the line segment at its midpoint .

__

This is a vocabulary question. It is always a good idea to learn the vocabulary, so you can understand statements that make use of these words. In the attached image, the line segment containing C is the perpendicular bisector of segment AB.

What is the value of the expression below?

-(-4)(-6)-3/5(10+15)
______________
1/3

A) -117
B) -13
C) 3
D) 27

Answers

Answer:

Answer is A

- 117

_______________________________________

Answer:

ay wee tologo bo sharmaine?

Please help I will give brainliest.

Answers

Answer:

3 Rd one

Step-by-step explanation:

donee....!!✓give me the branliest

Find the greatest common factor of 27,45and9

Answers

Answer:

9

Step-by-step explanation:

GCF of 27 and 45 is 9.

Look at the image... I hope this image helps you.

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