What is the 7th term of the geometric sequence 4, −20, 100, …? −312,500 −12,500 62,500 1,562,500?

Answers

Answer 1

The n-th term a[n] is given by
.. a[n] = 4*(-5)^(n -1)
Then
.. a[7] = 4*(-5)^6 = 62,500

The 3rd selection is appropriate.

Answer 2

Answer: The correct option is (C) 62500.

Step-by-step explanation: We are given to find the 7-th term of the following geometric sequence :

4, −20, 100, . . .

We know that

the n-th term of a geometric sequence with first term a and common ratio r is given by

[tex]a_n=ar^{n-1}.[/tex]

For the given geometric sequence, we have

first term, a = 4

and common ratio r is given by

[tex]r=\dfrac{-20}{4}=\dfrac{100}{-20}=~~.~~.~~.~~=-5.[/tex]

Therefore, the 7-th term of the given geometric sequence is

[tex]a_7=ar^{7-1}=4\times(-5)^6=4\times 15625=62500.[/tex]

Thus, the required 7-th term is 62500.

Option (C) is CORRECT.

Related Questions

twelve inches longer than width

Answers

let w=width

w+12

*longer indicates addition

help:

quadrilateral ABCD is located at A(-2,2) B(-2,4) G(2,4) D(2,2). the quadrilateral is then transformed using the rule (x+2,y-3) to form the image A'B'C'D'. what are the new coordinates of of A'B'C'D'? describe what characteristics you would find if the corresponding vertices were connected with line segments.

Answers

The given rule is a translation to the right (2 steps) and down (3 steps).
In order to find the new coordinates, you need to take the given x and add 2 and the given y and subtract 3.
Therefore:
A' (-2+2 , 2-3) --> (0,-1)
B' (-2+2 , 4-3) --> (0,1)
C' (2+2 , 4-3) --> (4,1)
D' (2+2, 2-3) --> (4,-1)

Since the quadrilaterals ABCD and A'B'C'D' are rectangles, connecting the corresponding vertices would give you a parallelepiped, which means that AA', BB', CC', DD' are parallel and congruent segments.

PLEASE HELP
Use the domain {½ , 1, 2, 4, 8} to plot the points on the graph for the given equation.
[tex]y=log_{2}x[/tex]

WILL MARK AS BRAINLIEST

Answers

Since the domain are the x-values of the function, we need to find the y-values using those x-values.
- for x=[tex] \frac{1}{2} [/tex], [tex]log x_{2} ( \frac{1}{2} )=-1[/tex]. Now we have our first ordered pair: [tex]( \frac{1}{2} ,-1)[/tex]
- for [tex]x=1[/tex], [tex]log_{2} (1)=0[/tex] which gives us our next ordered pair: [tex](1,0)[/tex]
- for x=2, [tex]log_{2} (2)=1[/tex], so (2,1)
- for x=4, [tex]log_{2} (4)=2[/tex], so (4,2)
- for x=8, [tex]log_{2} (8)=3[/tex], so our last order pair is (8,3)

Finally we can plug the points and joint them to create our graph:

Answer:

Warning the guy above is correct just make sure you count each line as 1,2,4,8. On the graph if you count the bold big lines for the domain you will run out of room for the last domain for 8. Like the person above did.

Step-by-step explanation:

Determine whether the equation defines y as a function of x. y = 2x + 8

Answers

we have that
y = 2x + 8
for x=1-----------> y=2*1+8=10
for x=2-----------> y=2*2+8=12
for x=3-----------> y=2*3+8=14
.
.
.

the equation y = 2x + 8 ----------- > defines y as a function of x, because for each x there is only one value of y.

the answer is
yes, the equation y = 2x + 8 defines y as a function of x

hello please help me with this quick

Answers

the first option

hope this helps<3

My teacher says everything is there to answer this question but I don't know. Someone please explain.

Two travellers spend from 12 o'clock to 6 o'clock walking along a level road, up a hill and back again. Their pace is 4 mph on the level, 3 mph uphill, and 6 mph downhill.

How far do they walk and at what time do they reach the top of the hill?

Answers

We can start with the basics. What we know is that this entire trip took 6 hours. So the travelers were able to walk on the level, uphill, and downhill in a total of 6 hours.

A level mile takes 1/4 of an hour (15 minutes). An uphill mile takes 1/3 of an hour (20 minutes). A downhill mile takes 1/6 of an hour (10 minutes). So, to go and return over the same mile takes half an hour. This means that in 6 hours, they went 12 miles and came 12 miles back. So they went a total of 24 hours.

If the 12 miles had been all level, it would have taken approximately 3 hours. It the 12 miles had been all uphill, it would have taken approximately 4 hours. When reaching the peak, 3.5 hours would have been the approximate time it took them to reach the top since it is in between.

I will go to the mall if and only if I get paid today.

Determine the conditions that will make the biconditional true.

A. It is true if I go to the mall and I get paid. It is true if I go to the mall and I don’t get paid.
B. It is true if I go to the mall and I get paid. It is true if I don’t go to the mall and I don’t get paid.
C. It is true if I go to the mall and I don’t get paid. It is true if I don’t go to the mall and I don’t get paid.
D. It is true if I go to the mall and I get paid. It is true if I don’t go to the mall and I get paid.

Answers

I would say it would be B.

Final answer:

The correct answer is Option B, covering both true-true and false-false scenarios.

Explanation:

To determine the conditions that make the biconditional statement true, let's analyze it step by step. The statement in question is: "I will go to the mall if and only if I get paid today." A biconditional statement is true in two scenarios: both parts are true or both parts are false.

Looking at the options provided:

Option A is incorrect because if the statement is true, I cannot go to the mall without getting paid.Option B is correct because it encompasses both scenarios where the biconditional statement holds true: If I go to the mall, then I must have gotten paid, and if I don’t go to the mall, then I must not have gotten paid.Option C is incorrect because according to the biconditional, I cannot go to the mall unless I have been paid.Option D is incorrect because if I don’t go to the mall, it must mean that I didn't get paid, which is not covered in this option.

Therefore, the correct answer is Option B: It is true if I go to the mall and I get paid today. It is also true if I don't go to the mall and I don't get paid today. This matches the requirements of a biconditional statement where either both conditions are true or both are false.

30 POINTS + BRAINLIEST.. PLEASE CHECK MY ANSWER

Answers

You are correct.
Good job!

Answer:

you are correct good job

Write the polynomial −11x^3 − 2 − 9x^5 − 4x^2 − 6x^4 − 14x in standard form. Then give the leading coefficient. HELP ASAP!

Answers

to write it in standard form, you line up the terms from the highest degree (exponent) to the lowerest
− 9x^5− 6x^4 −11x^3− 4x^2− 14x − 2
the leading coefficient refers to the coefficient of the highest degree, which is -9 in this case.

Lets get started :)

Writing a polynomial is standard form means arranging them accordingly, in descending power form:

-11x³ - 2 - 9x⁵ - 4x² - 6x⁴ - 14x

The highest power is 5, now we should arrange in decreasing manner
-9x⁵ - 6x⁴ - 11x³ - 4x² - 14x - 2

The leading coefficient is -9

if a and b are independent events then it must be true that P(A|B)=P(A) TRUE OR FALE

Answers

True.
Because two events A and B are called independent if P(A|B)= P(A), i.e., if conditioning on one does not effect the probability of the other.

et f(x) = x2 + 6 and g(x) g(x) x+8/x . Find ( g o f)( -7)

a.63/55

b.259/49

c.-57/7

d.384/7

Answers

Answer:

Step-by-step explanation:

A function composition is where one function is substituted within another function and is written g(f(x)). Here we will substitute f(x) into g(x). For g(f(-7)), we substitute -7 for x.

[tex] \frac{x^2+6+8}{x^2+6}[/tex]

Now substitute -7 for x.

[tex]\frac{x^2+6+8}{x^2+6} = \frac{(-7)^2+6+8}{(-7)^2+6}=\frac{49+6+8}{49+6}=\frac{63}{55}[/tex]

answer asap which equation could have been used to create this function table?
A. y = x + 5
B. y = 5x
C. y = x + 4
D. y = 4x

Answers

C. y= x + 4
If you plug it in
1 + 4=5
6 + 4 = 10
8 + 4 = 12
and so forth

A polygon has 8 sides. What is the sum of its interior angles? use formula
s = ( n - 2 ) (180°)
A. 1260°
B. 720°
C. 1620°
D. 1080°

Correct answer will be rewarded with full points as well as the mark of the brainliest

Answers

The sum s for n=8 is
.. s = (8 -2)(180°)
.. s = 1080°

Selection D is appropriate.

_____
Put the number into the formula where the corresponding variable is, then do the arithmetic. A calculator can do the arithmetic for you, if necessary.

S= (8-2) (180°)= (8-2)=6×180=1080 the answer is D.

The cost for three packages of moving boxes is modeled by the system of equations below. let s represent small boxes, m represent medium boxes, and l represent large boxes. which ordered pair (s, m, l) represents the costs of the three boxes?

Answers

i would go with m looks more reasonable

find the circumferences

Answers

check the picture below.

so... notice, the larger green circle, has a radius of 22.

now, the blue smaller circle, is taking up half of the diameter of the green one, so, the diameter for the small one is 22, and its radius is half that, or 11.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\\\\ -------------------------------\\\\ \stackrel{\textit{large green circle}}{C=2\cdot \pi \cdot 22}\implies C=44\pi \qquad\qquad \qquad \stackrel{\textit{small blue circle}}{C=2\cdot \pi \cdot 11}\implies C=22\pi [/tex]

if a sample of 21 runners were taken from a population of 580 runners, μ could refer to the mean of how many runners times?

Answers

21 because that's the only people that you have information on.

Answer:

the answers is 580

which of the numbers below could be terms in the sequence an=4n-7 A)29 B)21 C)20 D)28

Answers

Answer:

A)29 and B) 21,

Step-by-step explanation:

First,in the sequence[tex]a_n=4n-7[/tex] , the parameter [tex]n[/tex] must to be a integer.

Second, we need to solve the equations by [tex]n[/tex].

[tex]n=(a_n+7)/4[/tex]

All the option in the problem represent an [tex]a_n[/tex]

Then, we need to prove all number in the options, if the result is a integer number, this option can be part of the sequence.

For A)

[tex]n=(29+7)/4=9\\[/tex]

For B)

[tex]n=(21+7)/4=7\\[/tex]

For C)

[tex]n=(20+7)/4=6.75\\[/tex]

For D)

[tex]n=(28+7)/4=8.75\\[/tex]

Only A) and B) only A and B meet the requirement

How was his payment

Answers

Subtract off the down payment: 880 - 250 = 630

So he'll pay 630 over 8 equal payments
Divide: 630/8 = 78.75

His monthly payment is $78.75

A triangle has an area of 40 square units. Its height is 8 units. What is the length of its base?

Answers

Area = (1/2)bh
h = 8 units

(1/2)b·8 = 40
4b = 40
b = 40/4
b = 10 units

Ann buys a dress in a sale. The normal price of the dress is reduced by 20%. The normal price is £36.80. Work out the sale price!

Also explain how you calculated it ...

Answers

Hello!

Let's do this step by step!

#1

"Reducing" means to make something smaller, like a discount. So we are reducing the price of the dress by 20%. This means we must first find what 20% of the dress's price is and then subtract that from the price.

#2

36.80 * 20% = 7.36

So, 20% of 36.80 is 7.36. Subtract that:

#3

36.80 - 7.36 = 29.44

Answer:

The sale price of the dress is $29.44.

Good day!

Patrick is constructing the circumscribed circle for △RST.

Which construction could be his first step?

Construct the perpendicular bisector of ST¯¯¯¯¯ .

Construct the angle bisector of ∠T .

Construct a copy of ∠S that is adjacent to ∠R .

Construct the angle bisector of ∠R .

Answers

To me, the answer would be the option A :
Construct the perpendicular bisector of ST¯¯¯¯¯ .

Hope this helps !

Photon

The first step Patrick will take in the construction of a circumscribed circle for △RST is: Construct the perpendicular bisector of line segment ST.

What is a Circumscribed Circle of a Triangle?

A circumscribed circle for a triangle can be defined as a circle is placed inside a polygon or triangle such that it touches all the sides of the triangle.

An example of a circumscribed circle of a triangle is shown in the image attached below.

Therefore, the first step Patrick will take in the construction of a circumscribed circle for △RST is: Construct the perpendicular bisector of line segment ST.

Learn more about circumscribed circle on:

https://brainly.com/question/15605172

evaluate j/4 when j=12

Answers

the answer is three because you are dividing 12 and 4 =3

These types of questions look weird, but when they give you the variable or "j", it is quite nice. The word "evaluate" is used when the expression does not have an equal sign. All you really have to do is simplify it.

J=12 means "the letter "J" is representing 12. The letter "J" could represent anything in this question, but for this question we are told that "j' equals the number 12.

Simply substitute 12 for "J" in the expression and now you have 12 divided by 4. Then you could say the expression becomes 3 if you simplify 12 over 4 which is the same as 12 divided by 4.

A real life example of this question could be, "4 packs of jewels on a game cost $12.

Not the best explanation, but I hope it helps.

Can someone explain to me how this problem is solved? Thanks.

The height of a coconut falling from a tree is represented by the function h(t)=-16t^2+24 where h(t) is the height of the coconut, in feet, and t is time, in seconds

what is the initial height, in feet, of the coconut?

Answers

If the function is h(t)=-16t^2+24, where h(t) is the height of the coconut in feet, then we can figure out the initial height (in feet) based on something called initial conditions. Initially, time is 0 seconds. Plugging that number into the equation results in:
h(0)=-16(0)^2+24 = 24 feet. Therefore, the initial height of the coconut is 24 feet

PLEASE HELP ME WITH THIS

Answers

Pythagorean Theorem:

states a^2 + b^2 = c^2

given triangle:
5^2 + 13^2 = 14^2

25 + 169 = 196

194 = 196 False so it isn't a right triangle
since C^2 (196) is greater than a^2 +b^2 (194)
the triangle would be Obtuse

this property says that xa divided by xb equals xa-b

Answers

That is the quotient of powers property.

Answer: Quotient rule of division

Explanation:

In this question, a & b are the exponent of the x.

We know that division is the opposite operation of the multiplication.

Quotient rule division: We subtract the exponent (power) when we dividing the numbers with same base..

Here same base means numerator (top) and denominator (bottom) contain same number and exponent (power) of both numerator and denominator are same or different.

For example: [tex] \frac{5x^{8}}{5x^{6}} [/tex]

Here base 5 is same and exponent are different.

It is same as 5⁸⁻⁶ = 5³ = 125

Now given that,

[tex] \frac{x^{a}}{x^{b}} [/tex] = [tex] x^{a-b} [/tex]

A homeowner has 60 feet of fencing material to enclose a rectangular area for his pets to play in. One side of the house will be used as a side of the play area. What deminsions should be used in order to maximize the play area?

Answers

Let the length of the side that would be a house be l. Given that the total length of the fencing material is 60 and the other side is x, then:
2x+l=60
⇒l=60-2x
The area of the house will therefore be:
A=length*width
A=x(60-2x)
A=60x-2x²
differentiating A w.r.t x we get
dA/dx=60-4x

equating the above to zero and solving for x we get
60-4x=0
hence
4x=60
⇒x=60/4
x=15
this implies that one of the sides of the area is 15 ft and the other is 30 ft

Answer:

i just want to say that the answer above is correct 15 ft by 30 ft is the write answer

Step-by-step explanation:

i just took my test and got it right

A 1.6km road rises vertically 400m. what is the angle of elevation of the road? angle of elevation = _ degree

Answers

tan x = 0.4/1.6
x = 14.04°

Final answer:

To determine the angle of elevation of the road, we use the tangent ratio of rise (400m) to run (1600m), resulting in an angle of approximately 14 degrees.

Explanation:

To calculate the angle of elevation of the road, we can use trigonometry. Specifically, we'll use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. In this context, the opposite side is the rise, which is 400 meters (the vertical height the road climbs), and the adjacent side is the run, which is the horizontal distance of the road, 1.6 km or 1600 meters.

We can calculate the angle of elevation, ϴ (theta), using the formula:

tangent(ϴ) = opposite/adjacent

tangent(ϴ) = 400/1600

ϴ = arctangent(400/1600)

ϴ = arctangent(0.25)

After calculating arctangent(0.25), we find the angle of elevation is approximately 14 degrees.

A land mass is roughly in the shape of a rectangle whose perimeter is 1180 miles. the width is 110 miles less than the length. find the length and the width?

Answers

Answer: length = 350 miles, widht = 240 miles

Explanation:

1) Shape: rectangle

2) dimensions:

length = l
width = w

3) Formula of the perimeter of a rectangle, p = 2 * l + 2 * w

4) Data:

p = 1180 miles

length = x

width = x - 110 miles

5) Equation: p = 2x + 2(x - 110)

2x + 2(x - 110) = 1180

2x + 2x - 220 = 1180

4x = 1180 + 220

4x = 1400

x = 1400 / 4

x = 350

=> length = 350

and width = 350 - 110 = 240

6) Verification:

p = 2*length + 2 * width

1180 = 2 * 350 + 2*240

1180 = 700 + 480

1180 = 1180 => check.

Answer: length = 350 miles, widht = 240 miles

The isosceles trapezoid is part of an isosceles triangle with 38 vertex angle. what is the measure of an acute best angle of the trapezoid? what is the measure of an obtuse base angle of the trapezoid?

Answers

The base angle of any isosceles triangle is the complement of half the vertex angle. In this case, that is
.. 90° -(38°/2) = 71°

The obtuse base angle of the isosceles trapezoid is the supplement of this,
.. 180° -71° = 109°.

Final answer:

The acute base angles of the isosceles trapezoid are each 71 degrees, and the obtuse base angles of the trapezoid are each 109 degrees.

Explanation:

The task is to determine the measure of the acute and obtuse base angles of an isosceles trapezoid that is part of an isosceles triangle with a vertex angle of 38 degrees.

By the isosceles triangle theorem, the angles opposite the equal sides are equal. Since the vertex angle of the isosceles triangle is given as 38 degrees, the base angles of this triangle must be equal. Since the sum of the angles in any triangle must be 180 degrees, we could set up the equation:

38 + 2B = 180

where B represents the base angle of the isosceles triangle. Solving for B gives us:

B = (180 - 38) / 2

B = 71 degre

Each base angle of the isosceles triangle is 71 degrees.

The acute base angles of the trapezoid are also the base angles of the isosceles triangle, so they are 71 degrees each. To find the obtuse base angles of the trapezoid, we note that they are supplementary to the acute base angles. Hence:

Obtuse base angle of trapezoid = 180 - 71

= 109 degrees

describe the transformation of the following function y=tan(2x-pi)

Answers

[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \\\\ f(x)=Acos(Bx+C)+D\\\\ f(x)=Atan(Bx+C)+D \\\\ -------------------\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } |A|\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{C}{B}\\ ~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)[/tex]

with that template in mind, let's check this one,

[tex]\bf y=tan(\stackrel{B}{2}x\stackrel{C}{-\pi })\\\\ -------------------------------\\\\ \textit{horizontal shift of }\cfrac{C}{B}\implies \cfrac{-\pi }{2},\textit{ so of }\frac{\pi }{2}\textit{ to the right} \\\\\\ \textit{horizontal shrinkage of }B\implies 2, \textit{so by }\frac{1}{2}[/tex]

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