Mathematics Middle School

need an answer as soon as possible.
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Use the sequence: 1, –2, 4, –8, . . .
a. Find the common ratio in the sequence.
b. Write a rule for the sequence.
c. Find the next three terms

Answers

Answer 1
Part A

Answer: The common ratio is -2

-----------------------------------

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2

Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time

Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
The rule for the sequence is 
a(n) = (-2)^(n-1)
where n starts at n = 1

-----------------------------------

Explanation:

Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)

============================================================
Part C

Answer: The next three terms are 16, -32, 64

-----------------------------------

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64

showing that the next three terms are 16, -32, and 64

An alternative is to use the formula found in part B

Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier

Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)

Related Questions

8182÷k=1363.6666667

A- 9
B-2
C-6

Answers

The answer is C, 6.

2 would be around 4000, and 9 would be less than 1000, so C is the only one
The answer is C)6
Hope this helps!
PLEASE MARK BRAINLIEST!

Adam is making a rectangular frame. The frame is 24.2 feet long and 16.25 feet wide.

The formula for the area of a rectangle is A=bh.

What is the area of the frame?

Enter your answer as a decimal in the box.

(__ ft2

Answers

let
b-----> the length of the base of the rectangle
h-----> the length of the width of the rectangle

we know that
Area of the rectangle=b*h
in this problem
b=24.2 ft
h=16.25 ft
so
area=24.2*16.25-----> area=393.25 ft²

the answer is
the area of the frame is
393.25 ft²
393.25 Have a nice day! please tell me if im wrong so i can improve!

What is 98765+009225=

Answers

Hello there, and thank you for posting your question here on brainly.

Short answer: 107990

Why?

One red flag I see here is two zeroes as the first to digits of the second number, so we can take that away. So we can write it as 9225. Set it up into an equation. Add straight down.
  1      1
 98765
+ 9225
**********
107990

Hope this helped you! ♥

What is the smallest 9 digit number ni the form, aaa,aaa,aaa such that is divisible by 9??
Plz help!!

Answers

The smallest 9-digit number in the form aaa,aaa,aaa that is divisible by 9 is 111,111,111 because the sum of its digits is 9, which follows the divisibility rule for 9.

To find the smallest 9-digit number in the form aaa,aaa,aaa that is divisible by 9, we need to use the divisibility rule for 9. A number is divisible by 9 if the sum of its digits is also divisible by 9. Since we are looking for the smallest such number, we start with the smallest non-zero digit, which is 1.

The smallest 9-digit number where all digits are the same would be 111,111,111. Adding all the digits together, 1+1+1+1+1+1+1+1+1 equals 9, which is divisible by 9. Therefore, 111,111,111 is the smallest 9-digit number of the form aaa,aaa,aaa that is divisible by 9.

The price for a parakeet at Lydia's Pet World is $9.99. If you buy a cage and birdseed, the price decreases to $4.25. About what is the percent decrease in price if you buy a cage and birdseed?

Answers

$9.99 represents 100 %
$5.74 represents ? %

9.99-4.25= 5.74 was discaunted

?= (5.74 •100)/9.99
Answer is about 57.46%

Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches. π , √5 ,√8 ,2√5
(a)Without using your calculator, approximate the decimal equivalent of each number to the nearest tenth.
(b)Order the ribbon sizes from least to greatest. Use the original numbers given.

Answers

(a) To approximate [tex] \pi [/tex], we are going to use a compass to draw a cirle of radius 2 and circumference 12.5. Remember that [tex] \pi [/tex] is the ratio between the circumference of a circle and its diameter; since the diameter of a circle is two times its radius, we can find [tex] \pi [/tex] using the equation: [tex] \pi = \frac{cricunference}{2*radius} [/tex]
[tex] \pi = \frac{12.5}{2(2)} [/tex]
[tex] \pi = \frac{12.5}{4} [/tex]
[tex] \pi =3.125[/tex] 
And to the nearest tenth:
[tex] \pi =3.1[/tex]

To approximate [tex] \sqrt{2} [/tex], we are going to use the Babylonian method:
Step 1. We are going to make a guess. Our guess is 2 because [tex] \sqrt{4} =2[/tex], so [tex] \sqrt{5} [/tex] must be close to 2.
Step 2. We are going to divide 5 by 2: 
[tex] \frac{5}{2} =2.5[/tex]
Step 3.  We are going to find the average between our initial guest and the result of our previous calculation:
[tex] \frac{2+2.5}{2} = \frac{4.5}{2} =2.25[/tex]
And to the nearest tenth: [tex] \sqrt{5} =2.2[/tex]

To approximate [tex] \sqrt{8} [/tex], we are going to use the Babylonian method one more time:
Step 1. Our guess is 3 because [tex] \sqrt{9} =3[/tex], so [tex] \sqrt{8} [/tex] must be close to 3.
Step 2. We are going to divide 8 by 3:
[tex] \frac{8}{3} =2.6[/tex]
Step 3.  We are going to find the average between our initial guest and the result of our previous calculation:
[tex] \frac{3+2.6}{2} = \frac{5.6}{2} =2.8[/tex]
[tex] \sqrt{8} =2.8[/tex]

To approximate [tex]2 \sqrt{5} [/tex] we are going to multiply our approximation of [tex] \sqrt{5} [/tex] and multiply it by 2:
[tex]2 \sqrt{5} =2*2.2[/tex]
[tex]2 \sqrt{5}=4.4[/tex]

(b) Since we have our irrational numbers expressed as decimal approximations, we can compare them to arrange them form least to greatest:
2.2,2.8,3.1,4.4
Now, we just need to replace the decimal approximations with the original numbers:
[tex] \sqrt{5} [/tex],[tex] \sqrt{8} [/tex],[tex] \pi [/tex],[tex]2 \sqrt{5} [/tex]

We can conclude that ordering the ribbon sizes from least to greatest we get:
[tex] \sqrt{5} [/tex],[tex] \sqrt{8} [/tex],[tex] \pi [/tex],[tex]2 \sqrt{5} [/tex]

The function rule for the following graph is y = 2x + 2. What is the value of y in the ordered pair (2, y)? 24 4 10 6

Answers

i think the answer is 6

Answer:

The correct answer is 6.

Step-by-step explanation:

I just did this question as well and 6 was the correct answer. Hope this helped :)

John's dog weighted 7 pounds when we got him. The dog's weight tripled each year for two years. How many ounces does John's dog now weigh?

Answers

21 pounds

7 pounds x 3(tripled) = 21 pounds
If the dog weighed 7 pounds at first then its times 3 for each year for 2 years.
7*3*3=63 pounds and converting pounds to ounces, 63 pounds is 1,008 ounces.

If the height of your he sailboat is 3 centimeters, what is the height in meters, of the actual boat

Answers

Is there a ratio? bc that doesnt look like the full question
if there is no proportion, then 4,5 meters.4,5:3=1,5(coefficient)

I NEED HELP I WILL GIVE BRAINLEST!!!!!!!!!!!

Answers

The answer is 81 because if we plug in 9:

9^2  * 9^0

We know that anything to the zero power is one, so we are left with

9^2 which equals 81

A small submarine starts at –1,260 feet in relation to sea level. Then it descends 5 feet per minute for 12 minutes. What is the new position of the submarine in relation to sea level? –1,260 + (–5)(12) = –1,260 + 60 = –1,200

Answers

The submarine is at -1260 ft.
It descends 5 ft/min for 12 min.
12 min * 5 ft/min = 60 ft.
It descended 60 ft, so you must subtract 60 ft from -1260 ft.
-1260 ft + (-5)(12) ft = -1260 ft - 60 ft = -1320 ft

The error in the last line in the problem is that (-5)(12) = -60, not 60.
The correct line is:
-1260 + (-5)(12) = -1260 - 60 = -1320

The new position of the submarine in relation to sea level is -1,200 feet.

Your calculation is correct. To find the new position of the submarine in relation to sea level after descending at a rate of 5 feet per minute for 12 minutes, you can use the formula:

New position = Initial position - (Rate of descent * Time)

In this case:

New position = -1,260 feet - (5 feet/minute * 12 minutes)

= -1,260 feet - 60 feet

= -1,200 feet

So, the new position of the submarine in relation to sea level is -1,200 feet.

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I don’t know I need help fast

Answers

the answer is 3 kilometers

You have two exponential functions. One function has the formula g(x) = 5 x . The other function has the formula h(x) = 5-x . Which option below gives formula for k(x) = (g - h)(x)?

k(x) = 10x
k(x) = 5x + 5-x
k(x) = 5x - 5-x
k(x) = 2(5x)

Answers

Hmm it would be k(x)=2(5x) or it could be k(x)=10x

Hope this helps!

g(x) = 5x

h(x) = 5 - x

k(x) = (g - h)(x)

k(x) = g(x) - h(x)

k(x) = 5x - (5 - x)

Hence, the correct option is k(x) = 5x - 5-x


Part a) What do you know that will help you set up the equation to solve this problem?

Part b) Write the equation that allows you to solve for the height.

Part c) What is the height of the trapezoid (including units)

Answers

A) You know the formula for the area of a trapezoid is ...
  A = (1/2)(b₁ +b₂)×h


B) You are given the area and the lengths of the two bases. Substituting the given numbers into the formula will give you an equation for h.
  280 cm² = (1/2)(8 cm +20 cm)×h


C) Solving the equation of part B, we have
  280 cm² = (14 cm)×h
  280 cm²/(14 cm) = h . . . . . . . . divide by the coefficient of h
  20 cm = h . . . . . . . . . . . . . . . .. evaluate

The height of the trapezoid is 20 cm.

Can someone help with this please??

Answers

4, 5 & 6 were answered on another question plus the circle isn't shown on this one.

7. semi circle is half a circle, there re 4 arcs smaller then half
 they are DB, DC, AC and AB

last choice is correct

(2-9i)+(-2+7i) complex numbers simplify

Answers

it would be -2i if you simplified it

[tex] (2-9i)+(-2+7i)=-2i [/tex]

can anyone help me please

Answers

i would say "B" but im not always Right

what is the square root of 50 to the nearest tenth

Answers

7.07 so I think you'd leave it at 7 for your answer
The answer is 7.07. You can use your calculator!

Factor completely; 100-9x^2

Answers

Answer:
(10 - 3x)(10 + 3x)

Explanation:

This type of question yields what is called a difference of squares, which is recognizable because of the subtraction (-) operation between the two terms of the binomial. When questions like this are seen, the formula for difference of squares can be implemented. This formula is:

(a² - b²) = (a - b)(a + b)

With this, we can square root both terms of the original binomial and plug our variables for a and b into the formula.

Let 100 = a², let 9x² = b²

√(100) = 10
√(9x²) = 3x

Those values are now a and b, respectively, so when we place them in their spots in the formula, the completed factoring is: (10 - 3x)(10 + 3x)

To check this answer for accuracy, we can use the FOIL method and combine like terms to see if it gives us the original equation. FOIL stands for Firsts, Outsides, Insides, and Lasts, instructing us which terms should be multiplied together so:

Firsts: 10(10) = 100
Outsides: 10(3x) = 30x
Insides: -3x(10) = -30x
Lasts: -3x(3x) = -9x²

We place them in the same equation and combine like terms:
100 + 30x - 30x - 9x²
100 + 0 - 9x²
100 - 9x²

We are back to our original equation so the answer of (10 - 3x)(10 + 3x) is accurate.

At a local used car lot, one out of every three cars is red. If the car lot had 54 cars on it, how many cars are red SHOW WORK PLZ

Answers

Number of cars = 54

Number of red cars = 1/3 x 54 = 18

Answer: There are 18 red cars
Final answer:

To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3. The calculation is: Number of red cars = 54 * (1/3) = 18 cars.

Explanation:

To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3.

To calculate how many cars out of 54 are red, we can multiply the total number of cars by the probability of a car being red:

Number of red cars = 54 * (1/3) = 18 cars

Therefore, there are 18 cars that are red in the lot.

What is the product of the two solutions from the quadratic formula?

Answers

c/a

This is a standard formula you need to know in order to solve. 
The answer is the third option.

[tex] \dfrac{c}{a} [/tex]

You need to know this standard formula to solve the equation.

Hope this helps. - M

Find the coordinate that divides the directed line segment from A(-2,-4) to B(8,1) in the ratio of 2 to 3

Answers

we have that
A(-2,-4)  B(8,1) 

let
M-------> the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3

we know that

A--------------M----------------------B
        2                     3
distance AM is equal to (2/5) AB
distance MB is equal to (3/5) AB
so

step 1
find the x coordinate of point M
Mx=Ax+(2/5)*dABx
where
Mx is the x coordinate of point M
Ax is the x coordinate of point A
dABx is the distance AB in the x coordinate
Ax=-2
dABx=(8+2)=10
Mx=-2+(2/5)*10-----> Mx=2

step 2
find the y coordinate of point M
My=Ay+(2/5)*dABy
where
My is the y coordinate of point M
Ay is the y coordinate of point A
dABy is the distance AB in the y coordinate
Ay=-4
dABy=(1+4)=5
Mx=-4+(2/5)*5-----> My=-2

the coordinates of point M is (2,-2)

see the attached figure

Data Set 1 has a mean of 84 and a MAD of 6. Data Set 2 has a mean of 78 and a MAD of 8. What can be concluded about the two distributions?

Select each correct answer.

A. The distributions are somewhat similar.

B. The means-to-MAD ratio is 1.

C. The means-to-MAD ratio is 0.75.

D. The distributions are similar.

Answers

Answer: The actual answers are: "The distributions are similar." & "The Means-to-MAD ratio is 0.75." I took the same test and got it right. I hope this helps anyone reading this. :D Thanks!

~H*****

Answers are C. The means-to-MAD ratio is 0.75. and D. The distributions are similar. hope it helps

please help the temperature in degrees fahrenheit can be estimated by counting the number of times a cricket chirps in one minute write an algebraic expression for the following written expression
the number of chirps divided by 4 added to 37

Answers

you will need to multiply then round to the nearest hundred

you are about take an 8 question multiple choice test .each of these questions has 4 answers (A,B,C,D). how many ways can you answer the test if you leave an answer for each question

Answers

[tex] 4^8=65536 [/tex]

4^8 = 65536 answer is correct

A recent poll taken by the movie theatre industry shows that 28% of the population attends a movie in a theater at least once a month. A sample of 300 people shows that only 12% of people attends a movie in a theater at least once a month. To determine whether this sample supports the population proportion of 0.28, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.12. The minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28. What is the margin of error of the population proportion using half the range?

Answers

Answer:

The margin of error for this population proportion using half the range = ±0.09

Step-by-step explanation:

Confidence Interval is basically an interval of range of values where the true proportion can be found with a certain level of confidence.

Margin of Error is the width of the confidence interval about the central proportion.

For this question, the minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28, hence, the confidence interval for the question is (0.10, 0.28).

The width of this confidence interval = (Upper limit of the interval) - (Lower limit of the interval) = 0.28 - 0.10 = 0.18.

Hence, the margin of error for this population proportion using half the range, is 0.18/2 = 0.09.

Written appropriately as ±0.09.

Hope this Helps!!!

Describe the effect on the SURFACE AREA of multiplying the dimensions by 1/5.

Answers

Surface area changes by the square of the linear dimension scale factor. Multiplying the dimensions by 1/5 will multiply the surface area by (1/5)² = 1/25.

Which word is an antonym for the word thrive?

Jasper knew we was going to thrive in his new school
A) fail
B) learn
C) worry
D) be busy

Answers

The antonym for the word thrive would be A. Fail Hope this helps :)


The required antonym for the word thrive is fall. Option A is correct.

The word "thrive" means to prosper, succeed, or flourish. Therefore, the antonym for "thrive" would be a word that represents the opposite, such as "fail." When someone fails, they do not achieve success or prosper in their endeavors. In the given sentence, Jasper is confident that he will thrive in his new school, indicating that he expects to do well and succeed. Choosing the word "fail" as the antonym creates a clear contrast, as it represents the opposite outcome of not being able to thrive or achieve success.

Thus, the requried antonym for the word thrive is fall. Option A is correct.

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The equation y – 9 + 9 = –17 + 9 is an example of which property of equality?

A.Substitution Property of Equality
B.Addition Property of Equality
C.Reflexive Property of Equality
D. Symmetric Property of Equality

Answers

you add 9 to both sides to get:
y – 9 + 9 = –17 + 9

so it's Addition Property of Equality

answer

B.Addition Property of Equality

Answer:

addition property of equality

Step-by-step explanation:

The equation y – 9 + 9 = –17 + 9 is an example of which property

A.Substitution Property of Equality:

In this property we substitute some particular value for the variable.

B.Addition Property of Equality

This property states that when we add any number to one sides of the equation we do the same on the other side

y – 9 + 9 = –17 + 9

In the equation , 9 is added on both sides of the equation. So it is an example of addition property of equality

C.Reflexive Property of Equality

Reflexive property states that the number is equal to itself

D. Symmetric Property of Equality

It states that if a=b then b=a

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x)=x^2 to the number of x-intercepts in the graph of g(x)=-x^2. Be sure to include the transformations that occurred between tye parent function f(x) and its image g(x)

Answers

The graph of g(x) = -x^2 is a reflection in the x-axis of the graph of f(x) = x^2. Both graphs have one x-intercept as both graphs have their vertices at the origin, (0,0).
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