Mathematics Middle School

NEED HELP!!!!!!


For the following geometric sequence find the recursive formula and the 6th term in the sequence.
{36, 12, 4, ...}

Answers

Answer 1
1st term = 36
2nd term = 12
3rd term = 4

recursive formula
q = 12/36 = 1/3

If you use this formula and continue going down, you'll eventually find that the 6th term will be 4/27.

Hope that helps!
Answer 2

The 6th term is ( 4 / 27 ) and the recursive formula is q = 1/3.

What is geometric progression?

When there is a constant between the two successive numbers in the series then it is called a geometric series.

The 6th term of the series is calculated as:-

1st term = 36

2nd term = 12

3rd term = 4

The recursive formula is,

q = 12/36 = 1/3

The 6th term is,

[tex]a_n = a_1( r )^{n-1}[/tex]

[tex]a_6=36 ( \dfrac{1}{3})^5=\dfrac{4}{27}[/tex]

Therefore, the 6th term is ( 4 / 27 ) and the recursive formula is q = 1/3.

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Related Questions

Evaluate. 6+5|4-3^2| A. -19 C. 31 D. 55

Answers

Answer:

6 + 5|4 - 3²| =

6 + 5|4 - 9| =

6 + 5|-5| =

6 + 5(5) =

6 + 25 = 31

The correct answer is C.

What is the area of the triangle in this coordinate plane? 9.0 units² 14.0 units² 16.5 units² 24.5 units² A graph with a triangle drawn on it

Answers

I took the test, the correct answer is 16.5 units²

Simplify each expression. Select the correct answer from the drop-down menu.

−6(3i)(−2i) =

2(3 − i)(−2 + 4i) =

Answers

-6(3i)(-2i)= -36

2(3-I)(-2+4i)= -4 + 28i



the answer is:

−6(3i)(−2i) = -36

2(3 − i)(−2 + 4i) = -4+28i

2i(4 − 5i) = 10+8i

hope this helps! :o)

In a dog show, there will be a gold, a silver, and a bronze medal awarded. There are
5 finalists. In how many different ways can the 3 medals be awarded?

Answers

Answer
60 ways

Explanation
In permutation the order really matters unlike combination where order does not matter.
The question wants you to find how many time you can choose 3 out of 5 with order.
This means we should find 5 permutation 3.

5P3=5!/3!
=(5×4×3×2×1)/(3×2×1)=5×4 
                                     =60 

Answer:

60 ways

Step-by-step explanation:

There are five finalist and 3 medals.

For getting the first medal, there are 5 choices, any of the finalist can get that.

For getting the second medal, we are left with 4 choices.

For getting the third medal we are left with 3 choices.

Hence, the number of ways 3 medals can be awarded are:

5×4×3=60 ways

If a(x) is a polynomial function and b(x) is a polynomial function, then which of the following could be the sum of a(x) + b(x)?


A. ex + 2
B. x2 + 2x − log(x)
C. x6 − x4 + 9x
D. 5x² − 3x

Answers

The sum of two polynomial functions will also be a polynomial function. The exponents of the variables in the polynomial function are non-negative integers. Option A is an exponential function. Option B is a logarithmic function. 

The formatting is not proper in the options C and D. Only 1 option can be the correct answer.

If the options are:

[tex]C) x^{6} - x^{4} +9x \\ \\ D) 5x^{2} -3^{x} [/tex]

Then option C would be the correct answer as in option D variable is in the exponent which is against the definition of polynomial function.

If the options are:

[tex]C) x^{6} - x^{4} +9^{x} \\ \\ D) 5x^{2} -3x[/tex]

Then option D would be the correct answer as in option C variable is in the exponent which is against the definition of polynomial function.
Answer:
Options C and D are correct

Explanation:
We are given that both functions a(x) and b(x) are polynomial.
This means that adding them will also produce a polynomial function
polynomial a(x) + polynomial b(x) = polynomial c(x)

Now, let's check the given options:
Option A:
e² + 2
This is a exponential function. An exponential function is not a polynomial. Therefore, this option is incorrect

Option B:
x² + 2x - log(x)
This is a logarithmic function. A logarithmic function is not a polynomila.
Therefore, this option is incorrect

Option C:
x⁶ - x⁴ + 9x
This is a polynomial of the 6th degree.
Therefore, this option is correct

Option D:
5x² - 3x
This is a polynomial of the second degree.
Therefore, this option is correct

Based on the above, options C and D are both correct options

Hope this helps :)

A function is a relationship that maps__.
A) many inputs to many outputs or one input to one output
B) many inputs to many outputs or many inputs to one output
C) one input to many outputs or one input to one output
D) one input to one output or many inputs to one output

Answers

Solution:

A function is always a relation but a relation is not always a fucntion.

For example

we can make a realtion of student roll number and their marks obtained in mathematics.

So we can have pairs like (a,b), (c,d)..etc.

Its a realtion but it may not be function. Because function follows that for same input there should not be diffrent output, aslo there could be many inputs to one output in the case of constant function . But this doesn't holds a necessary condition in case of relation.

Because two diffrent students with two diffrent Roll number may have same marks.

Hence the foolowing options holds True in case of a function.

A) many inputs to many outputs or one input to one output.

D) one input to one output or many inputs to one output.

Answer:

The correct answer is D. A function is when an input has one output. An input can only have one output but an output can have multiple inputs. Hope this helps!

Two sides of a triangle measure 20 cm and 30cm. What is the third side?

Answers

Hi there!

It depends on what angles there are, and how many degrees are in each angle. In order to figure this problem out, you need to know at least one angle ;)

Hope this helps!
I think the measure of the third side is 11 cm.

Hope this helped☺☺

You and your friend are standing back to back. Your friend runs 20 feet forward and then 15 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball

Answers

I think its 32 because he runs 20 you run 12 you ran right no forward or backward. hope this helps good luck

A cake recipe requires 1 2/3 cups of milk how many cups altogether are necessary to make 4 cakes

Answers

For four cakes you would need to multiply 4 times 1 2/3 which equals 
6 and 2/3
1 2/3*4=

5/3*4=

20/3=

6 2/3.

Hope this helped☺☺

In which quadrant of the coordinate graph does point F lie? Quadrant I Quadrant II Quadrant III Quadrant IV

Answers

Please provide the graph that shows point F.
But, Quadrant 1 is the top right corner, Quadrant 2 is the top left, and it continues like that in a counterclockwise way. 

The quadrant of the coordinate graph does point F lie in quadrant IV.

What is Quadrant in Graph?

The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant.

The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.

The sign notations for four Quadrants is as follows:

Quadrant I :

both x and y positive.

Quadrant II :

x negative and y positive

Quadrant III:

x and y both negative.

Quadrant IV:

x positive and y negative.

As, the point F has coordinates (1,-5) which shows x is positive and y is negative.

So, point F is in quadrant IV.

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A bag of fruit contains 3 apples, 2 oranges, 1 banana and 4 pears. What is the probability that I will pull out a banana first and a pear second?

Answers

1/2 if simplified. If you don't want it's simplified then it's 5/10
The probability of pulling out a banana is 1 out of 10 (which is not high) and of choosing a pear second is 4 out of 10 (which is higher)

round 49,953 to the nearest hundred

Answers

The correct answer is 50,000
49,953 to the nearest hundred would be 50,00. This would be because the 9 would round to 10 and since 10 ins't a one digit number the number becomes 50,000. 

what is the tangent of 33.0?

Answers

Tan(33) = 0.6494
This is just a problem for your calculator. Most put the number in as
Tan(
3
3
=

write the equation of the parabola below

Answers

Answer:
Equation is: y = 0.5x² + 0.5x - 3

Explanation:
general form of the parabola is:
y = ax² + bx + c

Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.

First point that we will use is (0,-3). 
y = y = ax² + bx + c
-3 = a(0)² + b(0) + c
c = -3

The equation now becomes:
y = ax² + bx - 3

The second point that we will use is (2,0):
y = ax² + bx - 3
0 = a(2)² + b(2) - 3
0 = 4a + 2b -3
4a + 2b = 3
This means that:
2b = 3 - 4a
b = 1.5 - 2a ...........> I

The third point that we will use is (-3,0):
y = ax² + bx - 3
0 = a(-3)² + b(-3) - 3
0 = 9a - 3b - 3
9a - 3b = 3 ...........> II

Substitute with I in II and solve for a as follows:
9a - 3b = 3
9a - 3(1.5 - 2a) = 3
9a - 4.5 + 6a = 3
15a = 7.5
a = 7.5 / 15
a = 0.5

Substitute with the value of a in equation I to get b as follows:
b = 1.5 - 2a 
b = 1.5 - 2(0.5)
b = 0.5

Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3

Hope this helps :)

PLZ HELP!
at the apple orchard workers were asked to put 100 apples in barrels. the following five were filled incorrectly. if the supervisor wrote +5 above a barrel, it meant that the barrel was 5 apples over, -5 meant that a barrel was 5 apples less than 100.
How many TOTAL apples are i the five barrels?
a -480 apples
b 498 apples
c 500 apples
d 520 apples

Answers

B.) four hundred ninety-eight, You would add the number of mistakes in the barrels, then subtract that from five hundred.

Solve each equation. Factor and use the zero product property to solve. Show all work algebraically.

Answers

23.

5n^2 = 4n^2 - 4n

n^2 + 4n = 0

n(n + 4) = 0

n = 0   or   n + 4 = 0

n = 0   or   n = -4

24.

d^2 - 4d = 3d

d^2 - 7d = 0

d(d - 7) = 0

d = 0   or   d - 7 = 0

d = 0   or d = 7

25.

3 - 13h = 3 - 8h + h^2

Subtract 3 from both sides.

-13h = -8h + h^2

Add 13h to both sides.

0 = 5h + h^2

0 = h(5 + h)

h = 0   or   5 + h = 0

h = 0   or   h = -5

-(m-6)=3m+14 what is m

Answers

the answer is
[tex] - m + 6 = 3m + 14[/tex]
[tex] - 4m = 8[/tex]
[tex]m = - 2[/tex]

Jeremiah built a box that was 5 inches long by 6 inches wide by 7 inches high .he started filling it up with 1 cube.he realized quickly that he did not have nearly enough cubes to fill the box .can he still figure out how many cubes it will hold?

Answers

To determine the number of cubes he needs to fill the box (this is assuming the cubes are 1 in cubes, he would need to calculate the volume of the box. To find the volume he would multiply the length by the width by the height. This would be 5 in x 6 in x 7 in. The volume is 210 cubic inches, so he could fill it with 210 one inch cubes.

It is given that y varies directly as x. If y = 5 when x = 4 determine the constant of variation.

A) -4/5
B) 4
C) 5
D) 5/4

Answers

D) 5/4, I had this question on a quiz.
When one thing varies to another there is always a constant of variation. direct variation it is; y = kx

use the x,y values to find k
5 = 4k
5/4 = k

answer is D

PLEASE NEED HELP WITH A-D

Answers

a.
4(d+3c)

b.
6(3x+5y)

c.
7(3a+4y)

d.
8(3f + 7g)
Hello there! I can help you! For this question, we write this in distributive property by finding the GCF of both terms. As far as we see for all 4 of them, there are no like variables, and we find the GCF, just like we would for constants. When you find the GCF, be sure to divide each terms by the GCF, and then place the GCF outside the parenthesis. If you solve this correctly, here are your answers:

a. 4(a + 3e)

b. 6(3x + 5y)

c. 7(3a + 4y)

d. 8(3f + 7g)

if a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 ft, what is the volume of the hole? use 22/7 for pi

Answers

To find the volume of the whole, you will use the formula for finding the volume of a cone. V = 1/3 x r^2 x h.

You will first need to find the radius by using the information given about the circumference and the circumference formula.

C = pi x d
44 = 22/7 d
d = 14 feet.

Then use the diameter to find the radius of 7 feet.

V = 1/3 x r^2 x h
1/3 x 7^2 x 3
V = 49 cubic feet

Final answer:

To find the volume of a cone-shaped hole with a depth of 3 feet and a base circumference of 44 ft, calculate the radius using the circumference formula, then plug the radius and height into the volume formula to get 154 cubic feet.

Explanation:

The volume of a cone-shaped hole can be calculated using the formula V = (1/3) × π × r² × h, where r is the radius of the base and h is the height of the cone. In this case, the circumference of the base, 44 ft, can be used to find the radius. Given that the radius is 14 ft, and the height is 3 ft, you can substitute these values into the formula to find the volume of the hole.

Calculate the radius: Circumference = 2πr, so r = Circumference / 2π = 44 / 2π = 7 ft.

Calculate the volume: V = (1/3) × 22/7 × 7² × 3 = 154 ft³.

What is the value of G in the center and how do you solve it?

Answers

first solve:
7 + 3c = -11 --> c = -6
-9 - a/4 = 5 --> a = -56
b/5 +9 = 6 --> b = 75

second, solve:
a/f = -7 --> substitute -56 in for a --> -56/f = -7 --> f = 8
b/e = 3 --> substitute 75 in for b --> 75/e = 3 --> e = 25
3 = c/d --> substitutie -6 in for c --> 3 = -6/d --> d = -2

third solve:
g = d+e+f --> substitute -2 in for d, 25 in for e, and 8 in for f.
g = -2 + 25+8 
g = 31
Lets find out d first:

3 = c/d => d = c/3

7+3c = -11 => 3c = -11 - 7 => 3c = -18 => c = -18/3 => c = -6.

Now d = c/3 => d = -6/3 => d = -2.

Lets now find out e:

b/e = 3 => e = b/3

b/5 + 9 = 6 => b = (6-9)*5 => b = -15

Now e = b/3 => e = -15/3 = -5

Now we need to find f:

a/f = -7 => f = a/-7

-9 - a/4 =5 => a= (-9-5)*4 = -56

Now f = a/-7 => f = -56 / -7 = 8

So g = d + e + f
= (-2) + (-5) + 8
= 1
Therefore g = 1

What is the volume of this right triangular prism?


A.)144.2 cm3
B.)164.8 cm3
C.) 288.4 cm3
D.) 1153.6 cm3

Answers

You’re answer is B, you just have to multiply all of the sides together and then add your sums.

Hope this helps:)
The volume =0.5* Length * width * height
                     = 0.5* 7 *4* 10.3 =144.2 cm3

Last year, there were 80 students in the orchestra. This year there are 100 students in the orchestra. Determine the percent of increase in the number of students taking orchestra from last year to this year.
A 25%, because 100-80/80= 25%
B 20%, because 100-80/100= 20%
C 80%, because 80/100= 80%
D 125%, because 100/80= 125%

Answers

Hi there!

The answer is A. 

To find the percent increase, you need to 1. Find the difference between the two numbers, and 2. Divide it by the original number. 

100-80/80 = 25%

Hope this helps!

What situation could this diagram represent?

Answers

Answer: B- Flipping two coins once


Step-by-step explanation:


B. Tossing Two Coins Once

I Got it Right i Promise

Write an equition that expresses y in terms of x

Answers

y = 5x + 2

y on the left side is expressed in terms of x on the right side.

Bill says that he can add 23 and 40 without regrouping. Is bill correct? How do you know?

Answers

He can because you can add it mentally. You can just have 23 in your head and count by adding 10 "4" times. 

Hope this helped☺☺
Yes because 23+40 equals to 63 without any twist or turns, it is a simple answer

PLEASE HELP!!!! SOLVE: |2x+1|+|3x−4|=5

Answers

i have no idea what the lines mean :(
2x+1+3x-4=5
5x-3=5 Group like terms
5x=8 Add 3 to the end to isolate x
x=1.6 Divide 8 by 5
Hope this helped 

if a line is tangent to a circle at how many points does it interest the circle?

Answers

The intersection of a tangent to a circle and the circle is at exactly one point. Don't let a drawing fool you. In a drawing, it looks like there are several points of intersection, but keep in mind that a point has no dimensions, no length, width, or height, and a line has only length but no width. A drawing is just a representation of a point and a line, so we can see them.
If a line is tangent with a circle, it has one point in common with it.

Going against the current, a boat takes 7 hours to make a 120 mile trip. When the boat travels with the current on the return trip, it takes 4.5 hours. If x is the speed of the boat is still water and y is the speed of the current, which of the following system of equations could be used to solve the problem?

Answers

The system of equations that could be used to solve the problem is 7(x - y) = 120; 4.5(x + y) = 120. option A

which of the following system of equations could be used to solve the problem?

If

x is the speed of the boat is still water

y is the speed of the current

7(x - y) = 120

4.5(x + y) = 120

Therefore, the system of equation can be rewritten as;

7x - 7y = 120

4.5x + 4.5y = 120

Complete question:

Going against the current, a boat takes 7 hours to make a 120 mile trip. When the boat travels with the current on the return trip, it takes 4.5 hours. If x is the speed of the boat is still water and y is the speed of the current, which of the following system of equations could be used to solve the problem?

A. 7(x - y) = 120; 4.5(x + y) = 120

B. 7(x + y) = 120; 4.5(x + y) = 120

C. 7(x - y) = 120; 4.5(x - y) = 120

D. 7(x + y) = 120; 4.5(x + y) = 120

Other Questions
solve this problem for N N - (2 x 7) = 7 A.20 B.21 C.22 Valerie drives to and from work 5 days a week. The distance from her home to work is 6 miles. Over the course of 5 days, her car uses 14 of a tank of gas. Complete each sentence. This 1925 book by Adolf Hitler was written while he was in prison, outlining his racial and political beliefs. if you reflect fgh across the y-axis, what will be the coordinates of the vertices of the image f'g'h' Price changes are useful for matching the level of demand to the capacity of a facility. a. True b. False In "how to eat an ice cream cone" what does the author compare a melting ice cream cone to?A runaway trainA machine gunAn atomic bombA hand grenade I need help Fill in the blanks with the correct conjugation of one of the following verbs.almorzarpoderencontrarrecordardormirvolvercostar1. Ella_____en la cafetera.2. La camisa____diez dlares.3. El estudiante no____la respuesta de la pregunta.4. Charlie no____nadar hoy porque no tiene su traje de bao.5. Sophie______muchos peces bonitos cuando va a bucear.6. La mujer____de su viaje en dos das.7. El nio____muchas horas cada noche., HELP WILL MARK BRAINLIEST!!!Write a Poem about a Mountain and a Hill. What was Edmund Burkes view on the violence that was used in the French Revolution? At which of the following angles will the sunlight received at a location on Earth fall over the smallest area? 80 65 40 10 Which of these focused attention on the nuclear arms race between the United States and the Soviet Union? the Vietnam Warthe Berlin Airliftthe moon landingthe Cuban Missile Crisis And explain why please? "many states have adopted the _____ to give statutory protection to trade secrets" What are the roots of the equation?x^2+24=11xEnter your answers in the boxes. the map shows the southeastern United States in 1814. the shaded area on this map shows What allied power pulled out the war in 1917 and why? Which term refers to the hypothetical brain changes associated with the formation of a long-term memory? According to the text, which of the following were precursors to the novel (Mark all that apply.)?epic poetryItalian romancesshort storiesSpanish romancessonnetsFrench Romances Jack is sharing 3 bananas with 3 Friends. Which expression represents the amount each one will get if they share them equally? Which of the following would benefit most from an informational graphic? A comparison of fishing season catch rates over ten years A catalog of the types of fishes caught during a season A count of the number of fish caught at one location A list of the peak fishing season totals for the last year, If a girl were going up a escalator how many steps would she have to take if it was not moving/10929120/99020363?utm_source=registration