Mathematics High School

Find an explicit formula for the arithmetic sequence 37, 74, 111, 148

Answers

Answer 1

a₁ = 37
a₂ = 74
d = a₂ - a₁ = 74 - 37 = 37

a(n) = 37 + 37(n-1)

Answer 2

Let us observe the given series 37,74,111,148

Here, the first term (a) = 37

Common difference(d) = 74-37 = 37

Hence, the given series is in Arithmetic progression.

Hence the nth term of the series is given by:

[tex] a_{n}=a+(n-1)d [/tex]

Substituting the values of 'a' and 'd'.

[tex] a_{n}=37+37(n-1) [/tex]

Therefore, it is the required explicit formula.

Related Questions

The sum of three consecutive integers is -96. What is the larger integer

Answers

Let the first integer be x. Since the three integers are consecutive, the next two integers will be x + 1 and x + 2, respectively. Collectively the integers add to equal -96. That means you can set our expressions for the integers to -96, like so:

-96 = x + (x + 1) + (x + 2)

Now we can solve algebraically for x.

-96 = x + (x + 1) + (x + 2)
-96 = x + x + 1 + x + 2
-96 = 3x + 3
-99 = 3x
-33 = x

The first integer is x, so the first integer is -33.
The second integer is x + 1, so the second integer is -32.
The third integer is x + 2, so the third integer is -31.

Let's quickly add these integers to see if their sum is -96.

-33 + (-32) + (-31)
-33 - 32 - 31 = -96

These three consecutive integers add to equal -96. The question asks for the larger integer. Recall that the higher the number in front of a negative sign, the smaller the number. -2 is smaller than -1. That means the order of the integers from largest to smallest is -31, -32, -33.

Answer:
The largest integer is -31.

Which composition of transformations would map LMNO to L''M'N''O''? RM,90° ◦ RN',180° RM,180° ◦ RN',90° rw ◦ RM,180° RM,180° ◦ rw

please help i really need it!
will mark brainliest and if good with geometry please add me and help ! :) Thanks!

Answers

the answer is c since the problem given is not multiple choice - hope this helps

Answer:

The answer is C: rw ◦ RM,180°

Step-by-step explanation:

I had this question on edge

PLEASE HELP ASAP!!
means a lot!!

Answers

The correct answer is:
[tex]B) \: y + 1 = \frac{4}{3} (x - 9)[/tex]

Does the point (3,7) lie on inside or outside the circle

Answers

IM GUESSING OUTSIDE THE CIRCLE

if there was a picture or something it would help a lot but I'm gonna wing it and say inside the circle

can anyone help?....

Answers

The answer two this question is C.

You can get this answer by multiplying the two polynomials and then simplifying. See the steps below:
(4x^2 - 5)(x + 3) ---> Now multiply the two parenthesis.
4x^3 - 5x + 12x^2 - 15 ---> Arrange the numbers by decreasing exponents.
4x^3 + 12x^2 - 5x - 15

No simplifying can be done since there are no like terms.

Answer: [tex] fg(x)=4x^3+12x^2-5x-15[/tex]

Step-by-step explanation:

Given: [tex]f(x)=4x^2-5\text{ and } g(x)=x+3[/tex]

We know that for any function f(x) and g(x), the multiplication function (fg) (x) is given by :-

[tex]fg(x)=f(x)g(x)[/tex]

Now, for the given functions, we have

[tex]fg(x)=(4x^2-5)(x+3)\\\\\Rightarrow\ fg(x)=4x^2(x+3)-5(x+3)\\\\\Rightarrow\ fg(x)=4x^3+12x^2-5x-15[/tex]

helpppppppppppppppppppp

Answers

For this case we evaluate the function when x = 0
We then have to evaluate:
y = 3cosx + 3
y = 3cos0 + 3
y = 3 + 3
y = 6
Then, for x = pi
y = 3cosx + 3
y = 3cospi + 3
y = -3 + 3
y = 0
Answer:
y = 3cosx + 3
option 2

given that cos 42° ~0.743 what is the sine of the complementary angle

Answers

check the picture below, notice that is just an example relating the cosine and sine values in a right-triangle of the complementary angles.

so if the cos(42°) is "whatever", the sin(90° - 42°) is then, well, you know already.

Which of the following are independent pairs of events? Check all that apply.
A.Flipping two coins and having one show a head and the other show a head
B.Being sneezed on and catching a cold
C.When rolling a pair of dice, getting a total of 6 and having one die show a 3
D.Rolling a 4 on one die and rolling a 2 on another die
E.Seeing clouds and winning the lottery,

Answers

The best answer for these question would be:

A. Flipping two coins and having one show a head and the other show a head

D. Rolling a 4 on one die and rolling a 2 on another die

E. Seeing clouds and winning the lottery

Independent events in math means that the first situation does not affect the other variable. It is generally the individual probability that will happen to the solution. Which means that you have to determine whether the first situation will be affected on the second events that will happen. While the dependent events, have the opposite effect.

Name at least one advantage of credit cards

Answers

You can pay back stores later (or the bank)

A drawer contains 4 red socks, 3 white socks, and 3 blue socks. Without looking, you select a sock at random, replace it, and select a second sock at random. What is the probability that the first sock is blue and the second sock is red?

Answers

The probability that the first sock is blue and the second sock is red is:
(3/10) * (4/10)=3/25.

Answer:

[tex]\texttt{Probability}=\frac{3}{25} [/tex]

Step-by-step explanation:

Probability is the ratio of number of favorable outcome to total number of outcomes.

Total number of socks = 4 + 3 + 3 = 10

Number of blue socks = 3

Number of red sock = 4

[tex]\texttt{Probability of selecting blue sock}=\frac{3}{10} \\ [/tex]

[tex]\texttt{Probability of selecting red sock}=\frac{4}{10} \\ [/tex]

For finding the combined probability we need to multiply both the values

[tex]\texttt{Probability that the first sock is blue and the second sock is red}=\frac{3}{10}\times \frac{4}{10}=\frac{12}{100}=\frac{3}{25} \\ [/tex]

[tex]\texttt{Probability}=\frac{3}{25} [/tex]

1. Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?

2. Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?

3. Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?

Answers

1) The opposite angles of a inscribed quadrilateral are supplementary.

3x - 12 + x = 180
4x - 12 = 180
4x = 192
x = 48

Now we know the value of x we can substitute it for x in the expression of angle B.

3(48) - 12 = 132

Angle B is 132°

2) The opposite angle of an inscribed quadrilateral are supplementary. So first we will find the value of x.

28 + x = 180
x = 152

The value of x is 152 so we can substitute this in for x in the expression of angle A.

152 - 36 = 116

So angle A is 116°

3) To find the measure of angle C we will first find the value of x.

3x + 9 + 2x - 4 = 180
5x + 5 = 180
5x = 175
x = 35

Now we can find the value of angle A an then subtract it by 180 for angle C.

2(35) + 3 = 73

180 - 73 = Angle C
107 = Angle C

Which ordered pair could be removed so that the resulting graph represents a function

Answers

The relation is double-valued for x=1. Removing either of those values will make the relation a function.
.. (1, -2)
or
.. (1, 3)

Answer:

One of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed

Step-by-step explanation:

A relation f is said to be a function if for each and every element of it's domain there exists a unique image in it's codomain.

As per the graph, ordered pairs are [tex]\left ( 1,3 \right )\,,\,\left ( 2,1 \right )\,,\,\left ( -2,2 \right )\,,\,\left (1 ,-2 \right )\,,\,\left ( 5,-4 \right )\,,\,\left ( -4,-4 \right )\,,\,\left ( -5,-3 \right )[/tex]

Here, all the ordered pairs have unique image except [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex]

Here , element 1 of domain has two images 3 and - 2 .

We know that as per definition for each and every element of the domain there should be a unique image in the codomain.

So, one of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed in order to make it a function.

Find the area and thhe circumference of a circle round your anser to the nearest hundredth if the diameter is 6

Answers

----------------------------------------------------------------------------------------------
Find Radius
----------------------------------------------------------------------------------------------
Radius = Diameter ÷ 2
Radius = 6 ÷ 2
Radius = 3 units

----------------------------------------------------------------------------------------------
Find Area
----------------------------------------------------------------------------------------------
Area = πr²
Area = π (3)²
Area = 28.27 units² (Nearest hundredth)

----------------------------------------------------------------------------------------------
Find Circumference
----------------------------------------------------------------------------------------------
Circumference = πD
Circumference = π(6)
Circumference = 18.85 units (Nearest hundredth)

----------------------------------------------------------------------------------------------
Answer: Area = 28.27 units² ; Circumference = 18.85 units
----------------------------------------------------------------------------------------------

What is the length of each edge of a cube if its surface area is 486 square units?

81 units
18 units
9 units
3 units

Answers

Answer:

the correct answer is 18 i hope this helps you

The length of each edge of a cube with a total surface area of 486 square units is 9 units, obtained by dividing the total surface area by 6 to get the area of one face and then taking the square root.

To find the length of each edge of a cube when you have the total surface area, you need to understand that a cube has 6 faces that are all squares of the same size. Since the total surface area of the cube is given as 486 square units, we can find the area of one face by dividing the total surface area by 6. Once we have the area of one face, we can find the length of one edge by taking the square root of that area because the area of a square is equal to the length of one side squared (Area = side x side).

Let's calculate:

Total surface area of the cube = 486 square unitsArea of one face = 486 / 6 = 81 square unitsLength of one edge = [tex]\\(\sqrt{81})[/tex] = 9 units

Therefore, the length of each edge of the cube is 9 units.

A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

Answers

3.14 x 9^2 x 14/3 = 1186.92

4/3 x 3.14 x 9^3 = 1526.04

1186.92 + 1526.04 = 2712.96 = 2713 cubic inches

Answer: V = 2712.94 cubic inches.

Step-by-step explanation: The prop is formed with two objects: cone and half of a sphere. To calculate the volume, find the volume of the cone and the half-sphere and add them together.

Volume of Cone:

V₁ = [tex]\frac{1}{3}.B.h[/tex]

B is area of the base

h is height

Since the cone has its base as a circle, the volume will be:

V₁ = [tex]\frac{1}{3}[/tex].π.[tex]r^{2}[/tex].h

V₁ = [tex]\frac{1}{3}[/tex] . 3.14 . [tex]9^{2}[/tex] . 14

V₁ = 1186.9 cubic inches

Volume of Half-Sphere:

V₂ = [tex]\frac{2}{3}[/tex].π.[tex]r^{3}[/tex]

V₂ = [tex]\frac{2}{3}[/tex] . 3.14 . [tex]9^{3}[/tex]

V₂ = 1526.04 cubic inches

Total Volume:

V = V₁ + V₂

V = 1186.9 + 1526.04

V = 2712.94 cubic inches

The volume of the prop is V = 2712.94 cubic inches

Michelle works at a store that sells clothing accessories. The supply function for baseball caps is P=Q-6, where P is the price and Q is the quantity of baseball caps. If Michelle sells the baseball caps for $19 apiece, how many baseball caps will the store make?
A. 31 baseball caps
B. 6 baseball caps
C. 19 baseball caps
D. 25 baseball caps

Answers

All you have to do is substitute the price with P because P is the price.

19 = Q - 6

You'll add 6 on both sides.

25 = Q

So the answer choice D is the right answer.

Answer:

Step-by-step explanation:

Given : The supply function for baseball caps is P=Q-6, where P is the price and Q is the quantity of baseball caps.

To Find: If Michelle sells the baseball caps for $19 apiece, how many baseball caps will the store make?

Solution:

The supply function for baseball caps is P=Q-6

where P is the price

Q is the quantity of baseball caps.

Now we are given that Michelle sells the baseball caps for $19 a piece.

So, P = 19

Substitute the value in the function:

19=Q-6

19+6=Q

25 =Q

Thus If Michelle sells the baseball caps for $19 apiece, the store make will make 25 baseball caps .

A cookie recipie states for every 3 cups of flour, 1 1/2 teaspoons of vanilla are needed.How many teaspoons are needed for 5 cups of flour?

Answers

[tex]\text {3 cups of flour : } 1\dfrac{1}{2} \text{ teaspoons of vanilla}[/tex]

----------------------------------------------------------
Find 1 cup
----------------------------------------------------------
[tex]\text {1 cups of flour : } 1\dfrac{1}{2} \div 3 \text{ teaspoons of vanilla}[/tex]

[tex]\text {1 cups of flour : } \dfrac{3}{2} \times \dfrac{1}{3} \text{ teaspoons of vanilla}[/tex]

[tex]\text {1 cups of flour : } \dfrac{1}{2} \text{ teaspoons of vanilla}[/tex]

----------------------------------------------------------
Find 5 cups
----------------------------------------------------------
[tex]\text {1 cups of flour : } \dfrac{1}{2} \text{ teaspoons of vanilla}[/tex]

[tex]\text {5 cups of flour : } \dfrac{1}{2} \times 5 \text{ teaspoons of vanilla}[/tex]

[tex]\text {5 cups of flour : } \dfrac{5}{2} \text{ teaspoons of vanilla}[/tex]

[tex]\text {5 cups of flour : } 2\dfrac{1}{2} \text{ teaspoons of vanilla}[/tex]

----------------------------------------------------------
[tex]\bf \text {Answer : } 2\dfrac{1}{2} \text{ teaspoons of vanilla}[/tex]
----------------------------------------------------------

1) What is the solution to x - 5 = 27?

Answers

x - 5 = 27

Isolate the x, add 5 to both sides (because of equal sign)

x - 5 = 27
x - 5 (+5) = 27 (+5)
x = 27 + 5
x = 32

x = 32 is your answer

hope this helps

The dimensions in inches of a shipping box can be expressed as width x, length x+1, and height x-4. The volume is 84ft sq. Find the dimensions of the box in feet.

1,1,4
2,2,21
2,6,7
3,4,7

Answers

The volume of a box is (width)(length)(height).
V = W*L*H
Plug in all the information we have:
84 ft^3 (incorrectly written as ft sq in the question)
84 ft^3 = (x)(x+1)(x-4) = (x)(x^2-3x-4) = x^3 - 3x^2 - 4x.
Next, think of the factors of 84. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
The value is x = 6.
(6)(6+1)(6-4) = (6)(7)(2) = 84

Answer:

(1 pt) ~2,6,7~

Step-by-step explanation:

when using the binomial formula which of the following is the correct step in the expansion of (x+y)^4

Answers

Final answer:

The correct step in the expansion of (x+y)^4 is to determine the coefficients for each term using the binomial formula.

Explanation:

The correct step in the expansion of (x+y)^4 using the binomial formula is to determine the coefficients for each term.

In this case, the coefficients can be found using the formula n choose k, where n is the exponent (4) and k is the power of either x or y in each term.

For example, the term with x^3*y would have a coefficient of 4 choose 3, which is equal to 4.

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The true conditional statement, "If 5x+7=2x-1 then 3x+7=-1," illustrates which property of equality?
A.Addition
B.Subtraction
C.Multiplication
D.Division
Will Give Medal And Be Fan For Answer!,

Answers

The difference between the two inequalities involves subtracting the value of 2x from both sides, so this illustrates the subtraction property of equality.

The solution to 5 times 1 will be what kind of number

Answers

That would be a prime number

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers

It would be a Prime number

You invest 1000 in an account at 2.5% per year simple interest how much will you hav in your account at the beginning of the 4th year round your answer to the nearest whole dollar

Answers

notice, that, at the beginning of the 4th year, you're only getting interest for the previous 3 years, since the fourth year is just starting and hasn't accumulated any interest yet,

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$1000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\to &0.025\\ t=years\to &3 \end{cases} \\\\\\ A=1000(1+0.025\cdot 3)\implies A=1000(1.075)[/tex]

The sum of 555 consecutive integers is 505505505.
What is the third number in this sequence?

Answers

the correct question is
The sum of 5 consecutive integers is 505. What is the third number in this sequence?
Let
x-----------> first integer
x+1-----------> second integer
x+2-----------> third integer
x+3-----------> fourth integer
x+4-----------> fifth integer
we know that
x+(x+1)+(x+2)+(x+3)+(x+4)=505
then
5x+10=505----------> x=(505-10)/5---------> x=99
therefore
the third integer is (x+2)------> 99+2=101

the answer is 101

please anyone help me

A show is on friday,saturday and sunday
2/5 of the total ticlets are for the saturday show.
240 tickets are sold for the saturday show.
three times as many tickets are sold for the sunday show as for the friday show
How many tickets are sold for the sunday show?

Answers

Hey There!!!!

The Answer Is > 240 x 3 = 720 so 720 is your answer!!

Please Mark Me Brainliest :) :) Annierosehodge (: (:

720 tickets would be you’re answer

a company invest 15000 in an account that compounds interest annually after 2 years the account is worth 160099.44. use the function which R is the annual interest rate p is the principal and A is the amount of money after T years ...what is the interest rate of the account

Answers

Hey there :)

We all know the formula of simple interest
I = prt { You can take a look at the picture attached to see what each stands for }

Given are initial amount invested → $15000
period of time → 2 years
Amount after 2 years → $16099.44

I = Amount as final - Initial
= $1099.44

We need to find the interest
1099.44 = 15000( 2 ) r
1099.44 = 30000r
[tex] \frac{1099.44}{30000}= \frac{30000r}{30000} [/tex]
r = 0.036648

Rate as percentage = 0.036648 x 100 = 3.6648%

The interest rate of the account is 3.6648%

The square of nine less than a number is three less than the number. What is the number ?

Answers

Let n represent the number.
.. (n -9)^2 = n -3 . . . . . the square of 9 less than the number is 3 less than the number
.. n^2 -18n +81 = n -3
.. n^2 -19n +84 = 0
.. (n -7)(n -12) = 0
.. n = 7 or 12

The number could be 7 or 12.

_____
Check:
.. (7 -9)^2 = (-2)^2 = 4 = 7 -3 . . . . answer checks OK
.. (12 -9)^2 = 3^2 = 9 = 12 -3 . . . . answer checks OK

Final answer:

The original problem is translated into a quadratic equation. By following the process of expanding, moving all terms to one side and solving the resulting equation yield the overall possible solutions x = 4 or x = 1.

Explanation:

The question is asking to solve for a number based on a given condition. In this case, let's symbolize this unknown number with x. The problem can be written as an algebraic equation which is (x-9)^2 = x-3. You solve it first by expanding the equation, then move all terms to one side of the equation, to get a quadratic equation. Then, solve the quadratic equation to get the possible values of x. If you follow these steps, you will find that the possible solutions for this equation are x = 4 or x = 1.

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Suppose you and your friends order lunch at a mall restaurant, and the bill for your food is $28.50. If you want to leave a 12% tip, what is the total cost of the food plus the tip?

A. $3.42
B. $25.08
C. $28.50
D. $31.92

Answers

D because all of the other answers are less than or equal to the bill so $31.92 is the only logical one.

the total cost of food plus the tip is 31.92

Find the average value gave of the function g on the given interval. g(x) = 6 3 x , [1, 8]

Answers

g(×)=63×,[1,8]

9×9=81×63×5,103×[1,8]=9,[18]54

The average rate of change of the function over the interval is 3

Finding the average rate of change

From the question, we have the following parameters that can be used in our computation:

f(x) = 6 + 3x

The interval is given as

From x = 1 to x = 8

The function is a linear function

This means that it has a constant average rate of change

So, we have

f(1) = 6 + 3(1) = 9

f(8) = 6 + 3(8) = 30

Next, we have

Rate = (30 - 9)/(8 - 1)

Evaluate

Rate = 3

Hence, the rate is 3

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Question

Find the average value gave of the function g on the given interval. g(x) = 6 + 3x , [1, 8]

The students spent $15.20 altogether. Each student spent $1.90. How many students were in this group?

Answers

Final answer:

To find the number of students in a group who spent a total of $15.20, with each student spending $1.90, divide the total amount by the amount each student spent, resulting in 8 students.

Explanation:

The question asks how many students were in a group if they spent $15.20 altogether, with each student spending $1.90. To find the number of students, divide the total amount spent by the amount each student spent. This calculation is performed by dividing $15.20 by $1.90.

Calculation: $15.20 ÷ $1.90 = 8 students

Therefore, there were 8 students in the group.

Other Questions

Factor the polynomial. 6x2 - 7x - 3 A)(6x - 1)(x + 3) B)(6x + 3)(x - 1) C)(2x - 3)(3x + 1) D)(3x - 3)(2x + 1) Mr. Macady has an old cylindrical grain silo on his farm that stands 25 feet high with a diameter of 10 feet. Mr. Macady is planning to tear down the old silo and replace it with a new and bigger one. The new cylindrical silo will stand 30 feet high and have a diameter of 15 feet.A. What is the volume of the old silo B. What is the volume of the new siloC. How much greater is the volume of the new silo than the old silo Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens. Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable. How many x intercepts appear on the graph of this polynomial function? F(x)=x^4-5^2. 1 x intercept 2 x intercepts 3 x intercepts 4 x intercepts What is the measure of angle x? Enter your answer in the box. x = Three intersecting lines. Three of the six angles formed by the intersecting lines are labeled. Every other angle is labeled. Going clockwise, they are labeled 56 degrees, x, and 41 degrees. Pleasee hurryyyyAsapCorrect as will get brainliest Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept. The Choices are F(x)=2x^2-4x-3G(x)= -x^2+x+1H(x)= -2x^2+3x-1M(x)=x^2-9N(x)= -3x^2+7 Which of the following are monomials? Check all that apply. A.x - y B.9x C.24 + 2x2 D.2x + 12 E.x20 F.13 20x+13=53solve for x, right?? Help?? Complete the rectangle above. What are the coordinates of the missing vertex?Select one:A. (7, 3) B. (7, 4) C. (6, 3) D. (3, 7) A group of art students are painting a mural on a wall. The rectangular dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted? What is true about oscar casares? a. he was a policeman before he became a writer. b. he is an accomplished bowler. c. he grew up on the mexican border. d. he won a pulitzer prize.? According to Aristotle, a polity is _____. government by privileged citizens unjust governmental authority a good government run by the people _____ identified the challenge of leadership: "the leader must have an ability to inspire by force of personality while making others feel capable to increase and use their own abilities." if a swimmer pushes off a pool wall with a force of 250n, what is her acceleration. Using the periodic table and your knowledge of atomic structure. Compare the number of electrons in a Carbon-12 and Carbon-14 isotope. Who amongst the following had initially hostile and then friendly relations with the Shawnee tribe?A. Davy CrockettB. Daniel BooneC. Jedadiah SmithD. Zebulon Pike Suppose you were asked to demonstrate electromagnetic induction. Which of the following situations will result in an electric current? A magnet is moving toward a wire loop. A wire loop is moving away from a magnet. A wire loop is rotated near a magnet. All of the above What is the value of x? In to Kill a Mockingbird for chapter 5, what does Maudie's comparison between Jem and Jack reveal to us about what Jem might really be thinking about Boo and the items left in the tree?