Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 – n, where a0 = 4.

Answers

Answer 1

The closed formula for an = an-1 – n will be found using the formula for arithmetic sequence given by:
an=a+d(n-1)
where
a=first term
d=common difference
n=number of terms
From the formula given:
a=4
d=n
thus the formula will be:
an=a+n(n-1)
an=4+n(n-1)

Related Questions

A math club took a test. Twelve of the members had an average score of 80. Eighteen of the members had an average score of 86.

what was the class average score?

Answers

2508/30=83.6
hope tis helps

The classes average score is 83%

Marisol and Mimi walked the same distance from their school to a shopping mall. Marisol walked 2 miles per hour, while Mimi left an hour later and walked 3 miles per hour. If they reached the mall at the same time how far is the mall from their school?

Answers

Let the time in hours after Marisol starts walking be t and so the time in hours after Mimi starts walking is (t-1)
The distance walked by Marisol=speed*time=2t
Distance walked by Mimi=3(t-1)

When they've reached school they've all walked the same distance so:
3(t-1)=2t
3t-3=2t
3t-2t=3
t=3
Thus the distance from the mall to their school is 2t=2*3=6 miles

[tex]42 \times 42 \times 29 = [/tex]

Answers

The correct answer is 51156

Hope this helps :)

Use complete sentences to describe the domain of the cosine function.

Answers

The domain of a function is the set of the possible input values of the function. For example: consider the function f(x) = cos x, the domain of the function is the set of possible values of x.

The cosine function takes x values from all real numbers.

Therefore, the domain of the cosine function is a real numbers.

im posting several questions i need help with in an image

Answers

Answers:
(1) n = 4
(2) x = 30
(3) a = -4
(4) n =10
(5) n = -46.2

Explanation:
(1) Given
9n-8 = 28
9n = 28 + 8
9n = 36
n=4

(2) Given
-1-x = -31
-x = -31 + 1
x = +31 - 1
x = 30

(3) Given
9-4a = -5a + 5
-4a + 5a = 5 - 9
a = -4

(4) Given
n/2 = 5
n=5*2
n = 10

(5) Given
29.5 = -16.7 -n
n = -16.7 - 29.5
n = -46.2

1.
9n = 28 + 89n = 36n=4
2.
-x = -31 + 1x = 31 - 1x = 30

3.
9-4a = -5a + 5-4a + 5a = 5 - 9
a = -4

4.
n/2 = 5n=5*2 n =10

5.
29.5 = -16.7 -nn = -16.7 - 29.5n = -46.2

Form a sequence that has two arithmetic means between -1 and 59.
a.
-1, 29, 29, 59
c.
19, -1, 59, 39
b.
-1, 19, 39, 59
d.
-1, 14, 29, 44, 59

Answers

The formula for solving the problem is as follow:
an = a1 + (n - 1)d
Where:
n = number of figure in the sequence = 4
d = difference between successive number =?
a1 = -1
a4 = 59
Insert the given values into the formula,
59 = -1 + (4 - 1)d
59 = -1 + 3d
59 + 1 = 3d
60 = 3d
d = 60/3 = 20
Therefore, d = 20. This implies that, there is a difference of 20 between successive numbers.
The number sequence is as follow:
-1, 19, 39, 59.

two arithmetic means between -1 and 59.
b.-1, 19, 39, 59

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.
The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.

Answers

Answer: 25

Step-by-step explanation:

Pythagorean theorem

c=√a²±b²

So it was 7=A

And it was 24=b

solving that it gives us 25

This isn’t that much of help sorry but this is the basic info on how to solve it you can learn more by searching videos about the Pythagorean thermom.

Hope this helps-A

The maximum width of the slot is 25cm (Option A).

To find the maximum width of the mail slot, we need to calculate the length of the diagonal (the dotted line) in the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem.

Given:

- The length of the rectangle (one side) = 24 cm

- The height of the rectangle (other side) = 7 cm

The formula for the diagonal [tex]$ d $[/tex] is:

[tex]\[ d = \sqrt{(length)^2 + (height)^2} \][/tex]

Substituting the given values:

[tex]\[ d = \sqrt{24^2 + 7^2} \][/tex]

[tex]\[ d = \sqrt{576 + 49} \][/tex]

[tex]\[ d = \sqrt{625} \][/tex]

[tex]\[ d = 25 \, \text{cm} \][/tex]

So, the maximum width of the mail slot is 25cm.

Full Question:

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.

The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.

What is the maximum width of the mail slot?

A) 25

B) 31

C) 22

D) 20

some help help help help help help help help help help help help help help help help help help help help me please please please some

Answers

The answer would be 24. The answer would be 24 because 6+6+6+6 = 24, or a shortcut of 6*4 which would be 24. Hope this helps!

a student has test scores of 92%, 87%, and 78%. what must she need to score on thenlast test to maintain 80% or better?

Answers

We'll solve this equation in order to find the score of the 4th test, which we denote with x. [tex] \frac{92+87+78+x}{4}=80 [/tex]. Solving it we find that x=63. And it is the final answer for this problem.

you have $120 to donate equally to several charities. Does this situaton represent direct or inverse variation? Explain.

Answers

This situation represents inverse variation.

The difference between direct and inverse variation is in direct variation, as one variable goes up the other does too, while in inverse, as one variable goes up the other falls.

In this case, as you donate to more charities, the amount you donate to each charity falls, because you donate an equal amount. This means it's inverse variation.

Hope this helps!

Rex painting the garage in the shed he uses 3 gallons of paint on the garage he uses 3/4 of that amount on the shed enter the amount of paint in gallons Rex uses on the shed

Answers

(3/4) of 3 gallons is ...
0.75×(3 gallons) = 2.25 gallons

Rex uses 2.25 gallons of paint on the shed.

Rex uses 2.25 gallons of paint on the shed, which is [tex]$ \frac{3}{4} $[/tex] of the 3 gallons of paint he uses on the garage.

To find out how much paint Rex uses on the shed, we need to calculate [tex]$ \frac{3}{4} $[/tex] of the amount of paint he uses on the garage.

Rex uses 3 gallons of paint on the garage.

Therefore, the amount of paint he uses on the shed is:

Paint used on the shed = [tex]\frac{3}{4} \times 3[/tex]

Calculating this:

Paint used on the shed = [tex]\frac{3 \times 3}{4}[/tex]

= [tex]\frac{9}{4}[/tex]

= 2.25

So, Rex uses 2.25 gallons of paint on the shed.

What are the dimensions of the image at fraction 1 over 2 times its current size?

Length = 4 inches, width = 5 inches
Length = 6 inches, width = 8 inches
Length = 10 inches, width = 12 inches
Length = 16 inches, width = 20 inches

Answers

length= 4 inches, width= 5 inches

Answer:

Length = 4 inches, width = 5 inches

Step-by-step explanation:

A cylindrical thermos has a radius of2 in. and is 5 in. high. It holds 10 f oz. To the nearest ounce, how many ounces will a similar thermos with a radius of 3 in. hold? Show your work

Answers

let
A--------> larger thermos with radius 3 in
B-------> smaller thermos with radius 2 in

we know that
scale factor=radius larger thermos/radius smaller thermos
scale factor=3/2----> 1.5

volume larger thermos=[scale factor]³*volume smaller thermos
volume larger thermos=[1.5]³*10 f oz-----> 3.375*10-----> 33.75 f oz----> 34 f oz

the answer is
34 f oz

This graph shows the solution to the inequalities y>3/2x-2 and y<3/2x-10. Does the system of inequalities have solutions? If so, which region contains the solution?

A) there is no solution
B) there is a solution, and it’s shown by region A.
C) there is a solution, and it’s shown by region C
D) there is a solution, and it’s shown by region B.

Answers

we know that

the region A satisfies only the inequality-------> y>3/2x-2

the region C satisfies only the inequality-------> y<3/2x-10

the region B
does not satisfy any of the two inequalities

there is no region that satisfies both inequalities

therefore
the answer is the option
A) there is no solution

Answer:

there is no solution

Step-by-step explanation:

the cost of 10 yearbooks $250 what is the cost of one yearbook

Answers

$25 per yearbook

The cost is x and the amount is 10
So the equation is 10x=$250
Divide 250 by 10 and get 25

The per-yearbook cost is
$250/10 = $25

_____
Whether you can actually purchase one yearbook for that price depends on a number of factors.

hey can you please help me posted picture of question

Answers

The correct answer for this completion exercise shown above is the second option (Option B), which is: B. Parent

Therefore, you have:"In each family of function, the parent function is the most basic function in the family"

By definition, the most basic fucntion in each family of functions is called “parent fucntion”. A family of function is a set of function that when you graph them, you can notice that they have common charateristics.

Simplify the expression. (x1/8 y1/4)2

Answers

Answer:

Step-by-step explanation:

C) x1/4y1/2

hey can you please help me posted picture of question

Answers

The real part of two complex numbers will be added together and the complex parts will be added together. So the sum will be:

( 6 - 2i) + ( 11 + 6i)

= 6 + 11 - 2i + 6i

= 17 + 4i

So the answer to this question is option D

a plumber has a 36in. pipe that he has to cut into two pieces so that one piece is 8 in. longer than the other. find the length of each piece?

Answers

one piece is 14 in the other is 22 in

one is 22
and the other one is 14

A = LW ; for L whats the answer step by step

Answers

divide W on each side ( A/W =L)

The answer is: " W = L / A " .
_________________________________________________
Explanation:
_________________________________________________
Given:
_________________________________________________
" A = LW " ; Solve for "L" ; {step-by step} ;
_________________________________________________
A = L * W ;

↔ L * W = A ;

Divide each side of the equation by "W" ;
to isolate "L" on one side of the equation; & to solve for "L" ;

→ { L * W } / L = A / L ;

to get:

→ W = L / A .
________________________________________________________
The answer is: " W = L / A " .
________________________________________________________

PLEASE ANSWER!!! WILL MARK BRAINLIEST :D

When Alina was hungry she ate c cookies, which was 30% of all the cookies she had. How many cookies did she have in the beginning?

Answers

30/100=x
0.30a=x
x/0.30

What’s 3.192 rounded to the nearest hundredth ?

Answers

3.19 is the answer to your problemo.

Yes, the soulution is 3.19

If Dr. Suzuki rides his bike to his office, he averages 9 miles per hour. If he drives his car, he averages 27 miles per hour. His time driving is one third hour less than his time bicycling. How far is his office?

Answers

Speed
Riding speed = 9 mph
Driving speed = 27 mph

Time
If x hours is the time taken when riding, (x - 1/3) hours is the time taken when driving.

Distance in both instances is the same, D= Speed * time

Therefore,
9*x = 27(x-1/3)
9x = 27x - 27/2
9x = 27x - 9
(9-27)x = -9
-18x = -9
x = 9/18 = 1/2 hours

Distance, D = 1/2 *9 = 4.5 miles

Michelle collects US, Canadian and Mexican stamps. In her collection 80% of the stamps are U.S. and Mexican stamps. there are 3 times as many U.S. stamps as Mexican stamps. WHat percent of Michelle's collections is made up of U.S. stamps?

Answers

We know that 80% of the stamps are US and Mexican.
The US stamps are 3 times the Mexican stamps. That means that of the 80%, Mexicans comprised of the 20% and US comprised of the 60% to satisfy the relationship of their ratios.

Therefore, 60% of Michelle's collection is made up of US stamps.

Final answer:

Michelle's stamp collection consists of 60% U.S. stamps, determined by solving equations based on the given information that U.S. and Mexican stamps make up 80% of her collection and there are three times as many U.S. stamps as Mexican stamps.

Explanation:

The student asked what percent of Michelle's stamp collection is made up of U.S. stamps if 80% are U.S. and Mexican stamps and there are 3 times as many U.S. stamps as Mexican stamps. To solve this, let's call the percentage of U.S. stamps 'U' and the percentage of Mexican stamps 'M'. According to the given information, U + M = 80%, and U = 3M.

We substitute the second expression into the first to get 3M + M = 80%, which simplifies to 4M = 80%. Dividing both sides by 4 gives M = 20%. As the number of U.S. stamps is three times the number of Mexican stamps, we calculate U as 3 × 20% = 60%. So, the percentage of U.S. stamps in Michelle's collection is 60%.

hey can you please help me posted picture of question

Answers

The correct answer is option D.

The steps to find the inverse are listed below.

[tex]f(x)= \frac{2x}{7}+4 \\ \\ y= \frac{2x}{7}+4 \\ \\ y-4= \frac{2x}{7} \\ \\ 7(y-4)=2x \\ \\ x= \frac{7(y-4)}{2} \\ \\ f^{-1}(y)= \frac{7(y-4)}{2} \\ \\ f^{-1}(x)= \frac{7(x-4)}{2} \\ \\ [/tex]

y equals x + z + 5 Z equals -3 y - 3 2x minus y equals negative 4 How can i solve using 3 variable systems of equation

Answers

To solve a set of linear equations in 3 variables, you need 3 equations. As far as I can tell, you have 2 equations here, so the best you can do is write expressions for 2 of the variables in terms of the third.

If you have
x +z +5z = -3y -3
3x -y = -4
Then you can rewrite as
x = -1.5 -0.6z
y = -0.5 -1.8z

_____
You can get this by any of the usual methods of solving linear equations. Just treat the system as two equations in x and y with the z terms on the right side of the equal sign:
x +3y = -3 -6z
3x -y = -4

What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12 the width is 4.6 x 10 pw5 pw is the power

Answers

The caret (^) is the symbol conventionally used to indicate an exponent.

You have
area = 2.76·10^12
width = 4.6·10^5

You want to find the perimeter of the rectangle with these dimensions.

The perimeter of a rectangle is twice the sum of length and width.
perimeter = 2*(length + width)
The length can be figured from the area using the formula for area.
area = length*width
area/width = length . . . . . . . . . divide by width
Filling in the numbers, we have
perimeter = 2*((2.76·10^12)/(4.6·10^5) +(4.6·10^5))
perimeter = 2*(6.0·10^6 +0.46·10^6)
perimeter = 2*6.46·10^6 = 1.292·10^7

The perimeter of the rectangle is ...
1.292·10^7

Final answer:

To calculate the perimeter of a rectangle in scientific notation, divide the given area by the width to find the length, then use the perimeter formula (P = 2×length + 2×width), accounting for the power of 10 in your calculations to maintain proper notation.

Explanation:

The perimeter of a rectangle can be found using the formula P = 2×length + 2×width. Given the area of the rectangle (2.76 x 10^12 square units) and the width (4.6 x 10^5 units), we can find the length by dividing the area by the width. The length would therefore be the area divided by the width which is (2.76 x 10^12) / (4.6 x 10^5) = 6 x 10^6 units. Now that we have the length and width, we can calculate the perimeter by substituting into the formula: P = 2×(6 x 10^6) + 2×(4.6 x 10^5) = 1.2 x 10^7 + 9.2 x 10^5. Converting the width to the same power of 10, we get P = 1.2 x 10^7 + 0.092 x 10^7 = 1.292 x 10^7 units. This expresses the perimeter in scientific notation.

Which ordered pair is a solution of y = x - 4?

( -3, -7 )

( 3, -7 )

( -3, 7 )

( 3, 7 )

Answers

(-3, -7) is your answer

an order pair follows the (x, y) pair, in which (in this case), x = -3, and y = -7

plug in to the respective places inside the equation.

y = x - 4

(-7) = (-3) - 4

-7 = -7 (true)

Therefore, (-3, -7) is your answer

hope this helps

The correct answer is (-3,-7). This is because you can plug it in and the two sides are equal to each other. When you plug -3 in for x, you subtract for from it and get -7 since the y term is -7 the answer is -7=-7, thus (-3, -7) is the answer.

hey can you please help me posted picture of question

Answers

The correct answer is: Option (D) 36

Explanation:
Multiply all the items to get all the possible outcomes (in this case sandwiches).
Kinds of breads = 3
Kinds of meat = 4
Kinds of cheese = 3

Hence 4*3*3 = 36 (Option D)

which is the coefficient in the algebraic expression 12x + z^4 ?

Answers

I think the coefficient is the 12, before the variable

Remember a coefficient is any number that comes before a variable as a multiplicative. So, in the equation 12x+z^4 our coefficient would be 12.

Hope this helps!

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