Find the first term, the common difference, and the sum of the first thirty-three terms of an arithmetic sequence in which t5=8, t10 = 15.5

Answers

Answer 1

The first term, the common difference, and the sum of the first thirty-three terms of the arithmetic sequence is 2, 1.5 and 68.5 respectively.

Arithmetic sequence

t5 = 8t10 = 15.5

First term = aCommon difference = d

a + 4d = 8

a + 9d = 15.5

Subtract to eliminate a

9d - 4d = 15.5 - 8

5d = 7.5

d = 7.5/5

d = 1.5

substitute into

a + 4d = 8

a + 4(1.5) = 8

a + 6 = 8

a = 8 - 6

a = 2

Sum of the first 33 terms

S33 = n/2 + {2a (n - 1)d}

= 33/2 + {2×2 + (33 - 1)1.5}

= 16.5 + {4 + (32)1.5}

= 16.5 + (4 + 48)

= 16.5 + 52

= 68.5

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Related Questions

Which relation is a function?

Can someone help me please?!!!

Answers

Answer:

The second one is a function.

Step-by-step explanation:

The other 3 have one-to-many mappings.

For example the first relation has  1 mapping to 2, 3, 4 and 5.


1. Find the value of two numbers if their sum is 12 and their difference is 4.

Answers

Answer:

8 and 4

Step-by-step explanation:

Answer:

8+4

Step-by-step explanation:

8-4 is equal to 4 and 4+8 is equal to 12

HELP ME PLEASE!!!!
.
.
.
.
.
.
WITH QUESTION A!

Answers

Answer:

Cohesion and Adhesion. The complementary action of these two forces allows water to rise in a narrow capillary tube such as the xylem tissues of plants.

Step-by-step explanation:

Cohesion: the water molecules attract each other and are responsible for the surface tension of water.

Adhesion: the water molecule is also able to attract other non-water molecules. This allows water to be able to ‘cling’ to the sides of a capillary tube.

The complementary action of these two forces allows water to rise in a narrow capillary tube such as the xylem tissues of plants.

please let me know if you need a deeper/ more complex explanation, i am always happy to help :)

Question 38.
Write the first six terms of the arithmetic sequence with the first​ term, a1 = 240, and common difference, d= 24.

The first six terms are a1 = ,a3= , a4= ,a5= , and a6= .

Answers

[tex]a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360[/tex]

9. Royanne determined that it cost her $.75 a day to make her own lunch
for school. If she ate in the cafeteria, lunch would cost $2.25. In five days,
how much money would Royanne save by bringing her own lunch to
school?
O $5.50
O $7.50
$9.50

Answers

She would save $7.50.
If you calculate how much money it would cost her to make her own lunch times the five days which you will get…
0.75 *5= $3.75
And then calculate how much money it would cost her to eat in the cafeteria times the five days..
$2.25*5=11.25
Now you want to subtract the amount she makes her own lunch and the amount that she would eat in the cafeteria so…
11.25 - 3.75 = $7.50

So in the end she would save $7.50 if she was to bring her own lunch to school.

I hope this helps, have a good day! :D

Select the correct answer. What is this expression in simplified form? 2√2-7√18 OA 18√5 OB. 84√2 OC. 84 OD. 14sqrt6​

Answers

The expression in simplified form is -19√2

How to write this expression in simplified form?

The expression is given as:

2√2 - 7√18


Express 18 as 9 * 2

So, we have:

2√2 - 7√18 = 2√2 - 7√(9 * 2)

Take the square root of 9

2√2 - 7√18 = 2√2 - 7 * 3√2

This gives

2√2 - 7√18 = 2√2 - 21√2

Evaluate the difference

2√2 - 7√18 = -19√2

Hence, the expression in simplified form is -19√2

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The inverse of f(x)=9x^2

Answers

Given function:

f(x) = 9x²

Let the inverse is y = f⁻¹(x).

Swap x and y in the given function and solve for y:

x = 9y²y² = x/9y = √(x/9)y = √x / 3

The inverse of the given function is:

f⁻¹(x) = √x / 3

Answer:

f-¹(x) = √(x)/3

Step-by-step explanation:

Now we have to,

→ find the inverse of f(x)=9x²

Then the inverse function will be,

→ f(x) = 9x²

→ y = 9x²

→ 9y² = x

→ y² = x/9

→ y = √(x/9)

→ [ y = √(x)/3 ]

Hence, the inverse is √(x)/3.

I NEED HELP FAST PLEASE‼️‼️

SIMPLIFY TO SIMPLEST FORM‼️

Answers

I think the answer is 9/32

Answer:

1/2

Step-by-step explanation:

-put 3/8 and 3/4 side-by-side.

-keep 3/8

-change the division sign to a multiplucation sign

-flip 3/4 to 4/3

-multiply

What is the value of the expression 3 -4?

Answers

Answer:

-1

Step-by-step explanation:

3 - 4 = -1

When dealing with subtraction, you must be very careful with the order you place your numbers in. Let alone, subtraction is important in real-world situations, so just something to help. :)

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Wrapping up:

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A regular hexagon is divided into 6 congruent triangles. If the perimeter of the hexagon. is 48 centimeters, what is the height of each triangle?
A 4 \mathrm{~cm}
B 4 \sqrt{3} \mathrm{~cm}
C 6 \sqrt{3} \mathrm{~cm}
D 8 \mathrm{~cm}
E 8 \sqrt{3} \mathrm{~cm}

Answers

Answer:Your answer would be E

Step-by-step explanation:8 times 6 would be 48

The measure of height of each triangle will be 4√3 cm. Then the correct option is B.

What is the perimeter of the regular polygon?

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

A regular hexagon is divided into 6 congruent triangles. If the perimeter of the hexagon is 48 centimeters.

Then the Side length of each triangle will be given as,

48 = (Side length) x 6

Side length = 8 cm

Then the measure of the height of each triangle will be calculated as,

tan 60° = h / (8 / 2)

√3 = h / 4

h = 4√3 cm

The measure of height of each triangle will be 4√3 cm. Then the correct option is B.

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How many lines appear in a square

Answers

Answer: 4?

Step-by-step explanation:

Rewrite: [tex]15\frac{1}{6}[/tex]% as a decimal. Round to the nearest thousandths.

Answers

Answer:

15.17

Step-by-step explanation:

Multiply whole number by denominatorAdd product to the numeratorDivide the sum by the denominatorRound your number to the neaests thousandth

Write an
inequality that represents the
temperatures (in degrees Fahrenheit)
of the interior of the iceberg.
-20°C to
-15°C

Answers

The inequality representation can be expressed as: -4 < x < 5

Representation of real number into inequality.

An inequality is a mathematical connection that exists between two expressions and may be expressed by one of the following:

"greater than >" "less than < ""less than or not equal to ≤: "greater than or equal to" ≥:

From the given expression, the conversion of °C to F is estimated by using the formula:

(°C × 9/5) + 32

For  -20°C , we have:

= (-20°C × 9/5) + 32

= -4 F

For -15°C, we have:

= (-15°C × 9/5) + 32

= 5 F

Therefore, this can be represented in inequality form as: -4 < x < 5.

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What is the slope of the line that passes through the points (1,-6) and (-2,-8) ?

Answers

We can conclude that the slope of the line is (-2, -3).

What do we mean by the slope?The slope of a line indicates its steepness. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The formula of slope: y₂ - y/x₂ - x₁

Put the values in the formula as follows:

y₂ - y/x₂ - x₁-8 - (-6)/-2 -1-2/-3

Therefore, the slope of the line is (-2, -3).

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3+9(5)
8
2 is equal to

Answers

Answer:768

Step-by-step explanation:

I don't get this, I would be happy if someone helped me.

Answers

Answer:

Step-by-step explanation:

(5/8 + 6/8)/(-4/6 - 5/6)

(11/8)/(-9/6)

(11/8)*(-6/9)

= -66/72 = -11/12

Answer:

11/12

Step-by-step explanation:

5/8 + 3/4 = 1 3/8

-2/3 - 5/6 = 1 1/2

1 3/8 divided by 1 1/2 = 11/12

What is 943,158,670.3491 rounded to the 100 millions? PLEASE ANSWER ASAP!

Answers

Answer:

I believe the answer is 943,158,670.349

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

7. The top of a tree is 35 feet above ground level. The roots reach down 22 feet below ground
level. What is the difference between the top of the tree and the bottom of the roots?

Answers

Answer:

57?

Step-by-step explanation:

35-(-22)

Pls help I dont get this

Answers

Answer:

Step-by-step explanation:

Pls show steps on how u got the answer and thank u

Answers

Answer:

A=3

Step-by-step explanation:

-7a+28=7

subtract 28 from both sides to eliminate it from the first side

-7a=-21

Two negatives equals a positive

7a=21

divide both sides by 7

a=3

What is the distance between -6 2/3 and 4 1/3 on a number line, in units?

Select ALL that apply.

Answers

The distance between the points = |-6 2/3 - 4 1/3| = |-20/3 - 13/3| = |-33/3| = |-11| = 11 units.

How to Find the Distance between Two Points on a Number Line?

The distance between two points on a number line is the absolute difference between their coordinates.

Given the following points are on a number line:

-6 2/3 and 4 1/3

The distance between the points = |-6 2/3 - 4 1/3|

The distance between the points = |-20/3 - 13/3|

The distance between the points = |(-20 - 13)/3|

The distance between the points = |-33/3| = |-11|

The distance between the points = 11 units.

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two vertices of an obtuse triangle are $(6,4)$ and $(0,0)$. the third vertex is located on the negative branch of the $x$-axis. what are the coordinates of the third vertex if the area of the triangle is 30 square units?

Answers

Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).

The types of triangle.

In Geometry, there are different types of triangle based on the length of their sides and angles, and these are;

Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangle

How to calculate the area of a triangle?

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

b is the base area.h is the height.

Note: The height of this triangle is the y-axis of (6, 4).

Substituting the given parameters into the formula, we have;

Area = 1/2 × b × h

30 = 1/2 × b × 4

2b = 30

b = 30/2

b = 15 units.

Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).

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Complete Question:

Two vertices of an obtuse triangle are (6,4) and (0,0). The third vertex is located on the negative branch of the x-axis. What are the coordinates of the third vertex if the area of the triangle is 80 square units?

try these using the above pattern, find the value of the following. (i) 73 – 63 (ii) 123 – 113 (iii) 203 – 193 (iv) 513 – 503

Answers

The value of the given question by using the above pattern is (i)127, (ii)397, (iii)1141, (iv)7651.

What do you mean by pattern?

In the real world, in artificial design, or in abstract concepts, a pattern is a regularity. As a result, a pattern's components repeat in a predictable way. Any of the senses can directly witness patterns, which are types of patterns made of geometric shapes and frequently repeated like wallpaper designs. On the other hand, abstract patterns in science, math, or language might only be visible through analysis. In actuality, direct observation entails recognizing visual patterns, which are common in both nature and art. Natural visual patterns are frequently chaotic, hardly ever precisely repeat, and frequently contain fractals. Spirals, meanders, waves, foams, tilings, fissures, and patterns produced by rotational and reflective symmetries are examples of natural patterns.

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A cell phone company charges an initial price of $500 for a new phone and then $60 each month after the purchase. if c (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function? (2 points) r: (0, 500) r: (60, 560) r: ℠r: (−[infinity], [infinity])

Answers

The range of the given function is: (500, ∞).

What is the range of a function?

The collection of potential output values for a function is known as its range.

Now,

Given:

Initial price of the cell phone = $500Monthly charge = $60

Let 't' be the number of months. Then, the function C(t) can be calculated as:

C(t) = 500 + 60t

For range:

The minimum value will be when t = 0, i.e., when no charge has been charged by for each month.

Thus, C(0) = 500 + 60(0)

=> C(0) = 500

The maximum value will be when t = ∞, i.e., for infinite number of months.

=> C(∞) = 500 + 60(∞)

=> C(∞) = 500 + ∞

=> C(∞) = ∞

Thus, the range of the function will be: (500, ∞).

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The image of the point (2, -3)under a translation is (1, -6)Find the coordinates of the image of the point (9, -5)under the same translation.

Answers

The image of the point (2, -3)under a translation is (1, -6).  the coordinates of the image of the point (9, -5)under the same translation is (9,-8).

With the aid of mirror-related concepts, we will first build a diagram of the image position in order to determine the coordinates of the image location. We will use trigonometry to determine the necessary coordinates after sketching the diagram.

Without needing to change its orientation, a translation relocates an item from its original location on the coordinate grid.

An illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape.

Image of the point (2,-3)

under the translation (2,-6)

2+a=2

a=2-2

a=0

-3+b=-6

b=-6+3

b=-3

By applying the translation (x+0,y-3) to (9,-5)

(9+0,-5-3)

(9,-8)

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from the top of a 160-ft lighthouse, the angle of depression to a ship in the ocean is 26°. how far is the ship from the base of the lighthouse? (round your answer to the nearest foot.)

Answers

The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.

What is Angle Of Depression?The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item. When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.

Given:

Height of lighthouse = 160 feetAngle of depression = 26°

To find: Distance of ship from the base of the lighthouse.

Finding:

Let 'x' be the distance of the ship from the base of the lighthouse and θ be the angle of depression.

Then, tanθ = [tex]\frac{160}{x}[/tex]

=> x = [tex]\frac{160}{tan26}[/tex]

=> x = [tex]\frac{160}{0.487}[/tex]

=> x = 328.54m

Hence, The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.

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a train is travelling at a speed of 90 miles per hour. the driver of the train plans on maintaining this speed for the next 120 miles, plus or minutes 15 miles. find the minimum and maximum numbers of hours the train will travel at that speed.

Answers

The minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5

How to find the minimum and maximum numbers of hours the train will travel at that speed?

The given parameters are

Speed = 90 miles per hour

Current speed = next 120 miles, plus or minutes 15 miles.

Let the time travelled be x

So, we have the following equation

Speed * Time = Distance

This gives

|90x - 120| =15

Remove absolute bracket

90x - 120 = ±15

Add 120 to both sides

90x = 120 ±15

This gives

90x = (120 - 15, 120 + 15)

Evaluate

90x = (105, 135)

Divide by 90

x = (1.17, 1.5)

Hence, the minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5

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Ethan works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 25% of his total sales for the week. How much would Ethan make in a week in which he made $1250 in sales? How much would Ethan make in a week if he made xx dollars in sales?

Answers

Ethan makes in a week = $812.5

Given :

Total sales for the week = $1250

a guaranteed salary = $500

paid a commission on top of his base salary (Percentage commission) = 25%

Time and work problem:

Work Done = Time Taken × Rate of Work

Rate of Work = 1 / Time Taken

Time Taken = 1 / Rate of Work

If a piece of work is done in x number of days, then the work done in one day = 1/x

Total Wok Done = Number of Days × Efficiency

Efficiency and Time are inversely proportional to each other

X:y is the ratio of the number of men who are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be y:x

Solution :

Amount of commission earned = 25% of $1250

= 25/100 × $1,250

= 0.25 × 1250

= $312.5

Total earnings = Base salary + Amount of commission earned

= $500 + $312.5

= $812.5

Ethan makes in a week = $812.5

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Grace has read 2 chapters in each of her 9 books. How many chapters has read in all

Answers

Answer:18

Step-by-step explanation:2*9=18 hope this helps

Answer:

18 chapters have been read in total.

Step-by-step explanation:

(PLEASE HELP) -5 - (-5/3)

Answers

Answer:

steps

-5-5(-5/3)

=-5-(-25)

=10/3

=3 1/3

Step-by-step explanation:

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Please help at least 2 paragraphs why do we bound to certain places? in a recent study investigating a link between walking and improved health, researchers reported that adults walked an average of 6.4 days in the past month for the purpose of health or recreation. specify the null and alternative hypotheses for testing whether the true average number of days in the past month that adults walked for the purpose of health or recreation is higher than 6.4 days. operations and sales are the two functional areas that exist to support activities in other functions such as accounting, finance, it, and human resources. PLEASE HELP!!!!!!!!!! how might mike huckabee respond to brutus's statements on natural rights? answer in a minimum of three complete sentences, using supporting evidence from the lesson. how might congressman steve king respond to brutus's statements on natural rights? answer in a minimum of three complete sentences, using supporting evidence from the lesson. how might congressman tim huelskamp respond to brutus's statement on natural rights? answer in a minimum of three complete sentences, using supporting evidence from the lesson. Find the volume (in units3) generated when the region between the curves is rotated around the given axis. y = x3, y = 0, and y = 27 rotated around the y-axis The deeds of some people are extraordinary, but not so extraordinary that other employees cannot perform the same deeds. these people are referred to as? Well-established scientific ideas may be abandoned for new explanations due to new technologies and data. these paradigm shifts often ______. The amount of a chemical that is administered at one time is always the threshold dose. true/ false 2. the olmec also invented a calendar, and they carved hieroglyphic writing into stone. which group of people shared the characteristics described in this text? What does the underlined sentence on page two suggest about the urban garden site?A. It teaches the community residents valuable skillsB. It helps to support the communityC. It encourages people to participate in volunteer workD. It brings people of all ages and backgrounds together 3. Consider the technology behind each type of microscope. Why can light microscopes produce images in their natural color, while scanning electron and transmission electron microscopes only produce grayscale images?first one to answer i will give a brainiest too Historians argue that wwii was a significant factor in the establishment of our current employer-sponsored health insurance system. explain how and why this possible. What role does complementary base pairing play in the functions of nucleic acids? Find the value of x.15X36 15.91 kilometers to meters The length of a rectangle is four less than twice its width. If the perimeter of the rectangle is 76 units, what is its width? a13 b14 c20 d26 e28 cynthia besch wants to buy a rug for a room that is 19 ft wide and 29 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 299 square feet of carpeting. what dimensions should the rug have? there is no prior information about the proportion of americans who support gun control in 2019. if we want to estimate 97% confidence interval for the true proportion of americans who support gun control in 2019 with a 0.27 margin of error, how many randomly selected americans must be surveyed? Analyze the map below and answer the question that follows.A topographic map of Southern Africa with labels A, B, C, and D. River A is near the Democratic Republic of the Congo. River B is near Zambia and Zimbabwe. Lake C is near Malawi. Lake D is near Uganda and Kenya.Image by Tom Patterson and Eric GabaWhich of the waterforms on the map above is not identified correctly?A. Letter A -- Congo RiverB. Letter B -- Zambezi RiverC. Letter C -- Lake MalawiD. Letter D -- Lake TanganyikaPlease select the best answer from the choices provided A B C D