Mathematics High School

Find an explicit rule for the nth term of the sequence.

2, -8, 32, -128, ...

Answers

Answer 1
a1=2
a2=-8
a3=32
a4=-128

a2/a1=(-8)/2→a2/a1=-4
a3/a2=32/(-8)→a3/a2=-4
a4/a3=(-128)/32→a4/a3=-4

a2/a1=a3/a2=a4/a3=r=-4

an=a1*r^(n-1)
an=2*(-4)^(n-1)

The explicit rule for the nth term of the given sequence is an=2*(-4)^(n-1) 

Related Questions

L'shanda can choose between 3 sweaters and 4 skirts. if she selects 1 sweater and 1 skirt, how many possible outcomes are in the sample space answer

Answers

Nuber of outcomes = 3 * 4  = 12 Answer

We have been given that L'shanda can choose between 3 sweaters and 4 skirts.

We need to figure out the number of ways in which L'shanda can pick 1 sweater and 1 skirt out of the available items.

We need to use combinations here. First of all, we will figure out the number of ways of choosing 1 sweater out of 3 available sweaters. And then we will determine the number of ways of choosing 1 skirt out of 4 available skirts.

Number of ways of choosing 1 sweater = [tex]_{1}^{3}\textrm{C}=\frac{3!}{2!1!}=\frac{3\cdot 2!}{2!} = 3[/tex]

Number of ways of choosing 1 skirt = [tex]_{1}^{4}\textrm{C}=\frac{4!}{3!1!}=\frac{4\cdot 3!}{3!} = 4[/tex]

Therefore, total number of ways to select 1 sweater and 1 skirt are [tex]3\cdot 4 = 12[/tex]


Can someone help me please!!!!

Answers

Given:
Right triangle DEF right-angled at F.
ED=97 (hypotenuse)
DF=72 (opposite side of angle E)
FE=65 (adjacent side of angle E)

Cosine of angle E
=(adjacent side)/(hypotenuse)
=FE/ED
=65/97
=0.6701   (to four decimal places)

YO! I WILL MAKE YOU LOOK GOOD IF YOU ANSWER MY QUESTION!!!!!!!

Answers

It would be option 2.
Since the turning points are two and the first line came from the negative side and the second is in the positive side, so there for if you will multiple it negative times positive will give you negative.

This is the hint that this is an odd degree. Since if you raise thw power to an odd degree, it wi give you a negative answer. So it will have two different sides, points in the negative and points on the positive side.

If you will consider it an even degree, the graph's shape must be either up, up or down, down. But the graph shows down, up which indicstes its an odd degree. Hope you understand.

Use the Distributive Property to multiply 9 and 37 in your head. What is the answer?

270 + 7 = 277

27 + 63 = 90

30 + 63 = 93

270 + 63 = 333

Answers

270 + 63 = 333
If you did it in your head, it would look like this:
9(30) + 9(7)
270 + 63 = 333

What is the value of ø for the acute angle in a right triangle?

sim (ø)= cos (48 degrees)

Ø=??????

Answers

Sin and cos are related by the following identity:

sin (90 - θ) = cos(θ)

The value of θ in the given case is 48, so the equation becomes:

sin(90 - 48) = cos(48)

sin (42) = cos(48)

Thus, in the given question value of ø will be 42 degrees.


Use the following graph of the function f(x) = 2x3 + x2 − 3x + 1 to answer this question:

(graph of 2x cubed plus x squared minus 3x plus 1)

What is the average rate of change from x = −1 to x = 1?
−1
1
2
4

Answers

the answer to the question is 2


We have been given a polynomial [tex]f(x)=2x^{3} +x^{2}-3x+1[/tex] and we are asked to find average rate of  change from x = −1 to x = 1.

First of all we will find f(-1) and f(1).

[tex]f(-1)=2\cdot (-1)^{3} +(-1)^{2}-3(-1)+1[/tex]

[tex]f(-1)=2\cdot (-1) +1+3+1[/tex]

[tex]f(-1)=-2 +5=3[/tex]

Let us find f(1),

[tex]f(1)=2\cdot (1)^{3} +(1)^{2}-3(1)+1[/tex]

[tex]f(1)=2\cdot 1 +1-3+1[/tex]

[tex]f(1)=2+1-3+1[/tex]

[tex]f(1)=4-3=1[/tex]

Now let us find slope for our values.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{f(1)-f(-1)}{1-(-1)}[/tex]

[tex]m=\frac{1-3}{1--1}[/tex]    

[tex]m=\frac{-2}{1+1}[/tex]

[tex]m=\frac{-2}{2}=-1[/tex]

Therefore, average rate of change from our given x values will be -1.


Write the equation for a parabola that has x− intercepts (−1.6,0) and (−3.2,0) and y−intercept (0,25.6).

Answers

x-intercepts are zeroes of the parabola.
(x-x1)(x-x2)=(x+1.6)(x+3.2)=x² +1.6x+3.2x+5.12=x²+4.8x+5.12
 
y=x²+4.8x+5.12, but the y-int. is (0, 25.6),

So, our parabola should look like
y=5(x²+4.8x+5.12)
y=5x²+24x+25.6
 Answer: y = 5(x + 1.6)(x + 3.2)

∞∞∞∞∞∞∞∞
Explanation:
∞∞∞∞∞∞∞∞

x-intercept = (-1.6, 0) and (-3.2, 0)

=====>   y = a(x + 1.6)(x + 3.2)

Given y-intercept = (0, 25.6)

=====>  25.6 = a( 0 + 1.6)(0 + 3.2) 
=====>  25.6 = 5.12a
=====>  a = 5

Plug in a = 5 into the equation

=====>  y = 5(x + 1.6)(x + 3.2)

THE FIRST ANSWER GETS BRAINIEST The total height of the Statue of Liberty and its pedestal is 153 feet more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.

WRITE THE EQUATION !!

Answers

The complete question is :

The total height of the Statue of Liberty and its pedestal is 305 feet. This is 153 more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.

Question says 153, so we add 153 with the height of the statue

The total height of the Statue of Liberty = Height of the statue + 153

305 = h + 153

To find out h we subtract 153 on both sides

305 - 153 = h + 153 - 153

h = 152

The height of the statue = 152 ft


The height of the statue is 152 feet.

Let's call the height of the statue "h" in feet. According to the problem, the total height of the Statue of Liberty and its pedestal is 305 feet, and this is 153 more than the height of the statue. So, you can write the equation as:

Total Height = Statue Height + Pedestal Height

305 feet = h + 153 feet

Now, to find the height "h" of the statue, you can isolate it on one side of the equation. To do that, subtract 153 feet from both sides of the equation:

305 feet - 153 feet = h

152 feet = h

So, the height of the statue is 152 feet.

To know more about equation:

https://brainly.com/question/10354322


#SPJ3

The complete question is:

The total height of the Statue of Liberty and its pedestal is 305 feet. This is 153 more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.

Emily sold 147 candles for a fundraiser. If she sold 70% of the total number of candles sold for the fundraiser, what is the total number of candles sold for the fundraiser?

Answers

147 candies -----70%
x candies     -----100%

x=(147*100)/70= 210
Total were sold 210 candies.

Emily sold 147 candles for a fundraiser. If she sold 70% of the total number of candles sold for the fundraiser, what is the total number of candles sold for the fundraiser?

Solution:

Candles Emily sold=70% of Total Number of Candles

Emily sold 147 candles.

So, We have,

147=70% of Total Number Of Candles

Let, Total Number Of Candles=x

147=70% of x

147=[tex] \frac{70}{100} [/tex] *x

147=[tex] \frac{70x}{100} [/tex]

Let us multiply by 100 on both sides

147*100=[tex] \frac{70x*100}{100} [/tex]

14700=[tex] \frac{70x*1}{1} [/tex]

14700=70x

To solve for x, Let us divide by 70 on both sides

[tex] \frac{70x}{70}=\frac{14700}{70} [/tex]

x=14700/70

x=210

Total Number of Candles=210

A large pizza has a diameter of 18 inches. How many square inches of pizza does the large pizza have?

Answers

we, know that
the area of a pizza is equal to the area of a circle
so
area of a circle=pi*r²
diameter=18 in
radius=diameter/2-----> r=18/2------> r=9 in
area of a circle=pi*9²------> 254.34 in²

the answer is
254.34 in²

In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 3x – 1, and HE = 5y + 4. Find the values of x and y.

Answers

The diagonals of a parallelogram bisect each other.

DH = HF and GH = HE

x + 5 = 2y
3x - 1 = 5y + 4

Solve the first equation for x.
x = 2y - 5

Now substitute 2y - 5 for x in the second equation.

3(2y - 5) - 1 = 5y + 4

6y - 15 - 1 = 5y + 4

6y - 16 = 5y + 4

y = 20

Now substitute 20 for y in the first original equation.

x + 5 = 2y

x + 5 = 2(20)

x + 5 = 40

x = 35

Answer: x = 35 and y = 20

The values of x and y in parallelogram DEFG are:

x = 35y = 20

Given:

DH = HF and GH = HE

We have the following equations according to the given condition.

x + 5 = 2y ...(1)

3x - 1 = 5y + 4 ...(2)

From equation (1), we can express x in terms of y:

x = 2y - 5 ...(3)

Substitute this value of x in equation (2):

3(2y - 5) - 1 = 5y + 4

Simplify and solve for y:

6y - 15 - 1 = 5y + 4

6y - 16 = 5y + 4

y = 20

Now substitute y = 20 in equation (3) to find x:

x = 2(20) - 5

x = 40 - 5

x = 35

Therefore, the values of x and y in parallelogram DEFG are:

x = 35

y = 20

Learn more about parallelograms here:

https://brainly.com/question/10717345

#SPJ2

Two ships leave a harbor at the same time. one ship travels on a bearing upper s 12 degrees upper w at 18 miles per hour. the other ship travels on a bearing upper n 75 degrees upper e at 12 miles per hour. how far apart will the ships be after 2 ​hours?

Answers

Between N75E and E there are (90-75)=15°
Between E and S there are 90°
Between South and S12°W there 12°
Applying cosine rule 
Another way is to measure all angles clockwise from north (called azimuth) The ship at S12°W is at 180+12 = 192° 
The ship at N75°E is at 75° 
Angle between them is 192-75 = 117°

Applying cosine rule:
c=√(36²+24²-2×36×24cos117)
c=√2656.496
c=51.54 mi

Anyone know? Will give brainiest

Answers

By using the process of elimination, the answer is A.
The answer is going to be A because if you flip the shapes the angles do not meet each other.

A , O and B lie on a straight line segment

Evaluate x the diagram is not drawn to scale

Answers

we know that
if A , O and B lie on a straight line segment
then
∡AOY+∡YOZ+∡ZOB=180°
so
3x+x+x=180-----> 5x=180--------> x=180/5--------> x=36°

the answer is
x=36°

The value of x from the given diagram is; 36°

Sum of angles on a straight line.

The sum of angles on a straight line is 180°.

In this scenario, the sum of angles on the straight line: AOB is 180°.

Therefore, we have

3x + x + x = 180°

5x = 180

x = 36°

Read more on sum of angles on a straight line:

https://brainly.com/question/24024505

A researcher reports that mean ratings of liking for some food are m = 0.8, sd = 2.4. if the null hypothesis was that the mean equals 0, then what is the effect size for this test using estimated cohen's d?

Answers

cohen's d is a rathe rwrong way to word things so i suggest you rerun your Claulctaion

Consider the square root of 25. Is it rational or irrational? Explain your reasoning.

Answers

Hi there!

The square root of 25 is rational. This is because it is equal to the product of 5 x 5. Since 5 is a rational number and 25 is equal to 5 x 5, the square root of 25 is rational.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
 yes, 25 is a rational number because it can be expressed as the quotient of twointegers: 25÷ 1.

the perimeter of a rectangular parking lot is 190 meters. the width is one fourth the length. write a system of equation for this scenario

Answers

Hello!

You can make 2 equations based on what you know

2l + 2w = 190

w = 0.25l

Put w into the first equation

2l + 2(0.25l) = 190

Distribute the 2

2l + 0.5l = 190

Combine like terms

2.5l = 190

Divide both sides by 2.5

l = 76

Put l into the second equation

w = 0.25(76)

Multiply

w = 19

The length is 76 and the width is 19

The answer is

2l + 2w =190
w = 0.25l

Hope this helps!

Final answer:

To write a system of equations for the scenario, assign variables to the length and width of the rectangular parking lot. Use the information given to create two equations.

Explanation:

To write a system of equations for this scenario, let's start by assigning variables to the length and width of the rectangular parking lot. Let's say the length is represented by 'L' and the width is represented by 'W'. According to the given information, the width is one fourth the length, so we can write the equation:

W = (1/4)L

The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter is given as 190 meters, so we can write the equation:

2L + 2W = 190

Now we have a system of equations:

W = (1/4)L

2L + 2W = 190

These are the equations that represent the given scenario.

Two jets leave Dallas at the same time and fly in opposite directions one is flying west 50 mph faster than the other another two hours the Jets are 2500 miles apart find the speed of the jet

Answers

hope this helps............

Could someone please help with this question!

Answers

I added a screenshot of the question

Part (A):
Since the two figure are similar, therefore, we will use the similarity proportionality to get the unknown side as follows:
[tex] \frac{16}{8} = \frac{x}{2} [/tex]

x = [tex] \frac{2*16}{8} = 4 units[/tex]

Part (B):
Since the two figures are similar, therefore, we will use similarity proportionality to get the unknown sides as follows:
[tex] \frac{y}{8} = \frac{12}{4} = \frac{18}{x} [/tex]

x = [tex] \frac{18*4}{12} = 6 units[/tex]

y = [tex] \frac{12*8}{4} = 24 units[/tex]

Hope this helps :)

Use the difference of squares theorem to find the solution of the following equation:

v^2 = 252

Answers

v^2 = 252
v^2 - 252 = 0
(v - sqrt252)(v + sqrt252) = 0

so the 2 solutions are sqrt252 and - sqrt252

=  15.87 and -15.87   to nearest hundredth.

write the standard form of the line that passes through the given point. include your work in your final answer. (-8,0) and (1,5)

Answers

We are given two points on the line. Using these points first we need to find the slope of the line.

The points are (-8,0) and (1,5). The slope(m) of the line will be:

[tex]m= \frac{5-0}{1+8} = \frac{5}{9} [/tex]

Using the slope and a point (-8,0) we can write the equation in point slope form as:

[tex]y-0= \frac{5}{9}(x+8) \\ \\ y= \frac{5x}{9} + \frac{40}{9} \\ \\ 9y=5x+40[/tex]

In standard form, the equation will be:

5x - 9y = - 40

20 POINTS!
Find P(4).
I don't know or understand how to do this.

Answers

its a 1 out of 8 chance to get 4 or a 0.125 chance in landing on it

The calculated value of the probability of 4

How to determine the probability of 4

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

The spinner

Where, we have

Sections = 8

Also, we have

Sections that read 4 = 1

Using the above as a guide, we have the following:

P(4) = 1/8

Hence, the probability of 4 is 1/8

Read more about probability at

https://brainly.com/question/31895366

#SPJ3

find the surface area of a sphere with a radius of 0.8 ft

Answers

Sphere Surface Area     =     4 • π • r²
Sphere Surface Area     = 4 * PI * .8^2
Sphere Surface Area     = 8.0424771932 square feet
 



The scatterplot shows a linear relationship between the distance traveled and the time elapsed. What is the rate of change of the linear relationship?
For every increase in time by 1 hour, the distance increases
36 miles.
54 miles.
72 miles.
90 miles.

Answers

To solve the question we get the slope for the given  graph. This is given by:
slope,m=(change in y-values)/(change in x-values)
taking 2 points (1.25, 90) and (0.75,54) we get:
slope,m=(90-54)/(1.25-0.75)=36/0.5=72
The answer is:
72 miles

Answer:

The answer is C. 72 miles.

Step-by-step explanation:

A total of 327 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?

Answers

218 Students
109 Adults

Let x = adults
Let 2x = students

Add together and set equal to the total number. 
Final answer:

109 adult tickets were sold for the school play.

Explanation:

Let's assume the number of adult tickets sold is x.

According to the given information, the number of student tickets sold is 2 times the number of adult tickets sold. So, the number of student tickets sold is 2x.

Since the total number of tickets sold is 327, we can write the equation x + 2x = 327. Simplifying this equation gives us 3x = 327. Dividing both sides by 3, we get x = 109.

Therefore, 109 adult tickets were sold.

Learn more about number of adult tickets sold here:

https://brainly.com/question/19426877

#SPJ11

Jason eats 10 ounces of candy in 5 days. a. How many pounds does he eat per day?
b. How long will it take Jason to eat 1 pound of candy?

Answers

A. He eats 1/8 a pound of candy each day.
B. It would take him a total of 8 days to eat a pound of candy.

A. Since he ate 10 ounces in 5 days, you divide 10 by 5 to find he ate 2 ounces per day. Since there are 16 ounces in a pound that would be your denominator (bottom of fraction) and 2 would be the numerator (top of your fraction). You will get 2/16 which if you simplify (divide by 2) you get 1/8.

B. Knowing that there are 16 ounces per pound and he ate 1/8 pound ( 2/16 pound or 2 ounces) a day, you can either look at the simplified denominator to get the answer, or, divide 16 by 2 to get your answer.

I hope this helps!

please help but only answer if you're going to show work please!!!!

Answers

input h = - 2 into the expression

4[3(-2)  - 6]
---------------
  1 + (-2)

     4[-6  - 6]
= ---------------
      -1

     4[-12]
= ---------------
      -1

     -48
= ----------
      -1
= 48
To solve this problem you must apply the proccedure shown below:

 1. You have the following expression given in the problem above:

 4(3h-6)/(1+h)

 2. Then, if h is h=-2, you have to substitute this value into the expression given above, as below:

 4(3h-6)/(1+h)
 4(3(-2)-6)/(1+(-2))

 3. Then, you have
 4(-6-6)/(1-2)
 4(-12)/-1
 -48/-1
 48

The cost of gasoline is expected to increase by 2.5% next year. If p represents the current cost of gasoline, which experession represents the expected gasoline price next year?

Answers


[tex]y = x \times 0.025[/tex]

Solve the polynomial equation. state the multiplicity of each root. 8x3 - 12x2 + 6x - 1 = 0

Answers

Factorise to get (x - 0.5)^3 = 0
The equation has root 1/2 with multiplicity 3.

Mike is going to a ball game on saturday. he will pay $8.00 admission, plus $1.50 per item he buys at the concession stand. which of the equations represents this information?

Answers

The first thing you should do for this case is to define a variable:
 x: number of items that he buys at the concession stand
 y: total payment
 We now write the equation that represents this problem.
 We have then:
 y = 1.50x + 8
 Answer:
 An equation that represents this information is:
 y = 1.50x + 8

The equation that represents this information will be y = 1.5x + 8.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mike is going to a ball game on Saturday.

He will pay $8.00 for admission, plus $1.50 per item he buys at the concession stand.

Let x be the number of items and y be the total cost.

Then we have

y = 1.5x + 8

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ5

Other Questions
how do I do this question 4x-2=6 WILL GIVE BRAINLIESTWhich of the following represents the ratio of the hypotenuse to the given side Only 6 of the 75 trees in a park are at least 30 feet tall. What percent of the trees are under 30 feet tall? Two large numbers of the Fibonacci sequence are F61 = 2,504,730,781,961 and F62 = 4,052,739,537,881. If these two numbers are added together, what number results?A.F123B.F60C.F63D.F64 - 1 "when creating specifications to meet your audience's needs" What is the equivalently non equivalent for the function d(x)=7x^3 - 6x^2 what is the vaule of d(4) What is efficiency? in economics ? but only good answers. Who did president Jefferson send to survey the Louisiana territory before the purchase? A rectangular jewelry box costs $125 to gold plate. Calculate the cost of gold plating a box which is similar in shape and that holds 8 times as much.The answer is not $1,000 or $8,000 or $64,000 Reasons for poverty in Brazil include all of these factors except _____.a lack of affordable and available farmlanda scarcity of natural resourcespoor soil and climate in the northeasta lack of well-paying jobs in the cities Sam and Brett share 54 in the ratio of 5:4 how much does each person get A block with mass m =7.4 kg is hung from a vertical spring. when the mass hangs in equilibrium, the spring stretches x = 0.23 m. while at this equilibrium position, the mass is then given an initial push downward at v = 3.9 m/s. the block oscillates on the spring without friction. 1 what is the spring constant of the spring? 10.(3 pt)Which term correctly describes President Abraham Lincoln's attitude toward Reconstruction? A.reconciliation B.retaliation C.retribution D.revenge The concept of the human ecological footprint refers to the impact that humans have had on the environment. today the human ecological footprint is The actions of an employee are not attributable to the employer if the employer has not directly or indirectly encouraged the employee to violate a law and if The equation of a circle is (x2)^2+(y16)^2=169 . What is the circle's radius? Find the length and width of a rectangle that has the given area and a minimum perimeter. area: a square centimeters as other nations moved toward war in the 1930s, on what path did president roosevelt and congress put the united states ? why did they choose this route? (history) How were the "plumbers" connected to president nixon? on?