What is the recursive formula for the sequence 3, 12, 48, 192, 768...?

Answers

Answer 1

Final answer:

The given sequence is a geometric sequence. Each term in the sequence multiplies by 4 to obtain the next. Therefore, the recursive formula for the sequence is an = 4 * an-1.

Explanation:

The given sequence is: 3, 12, 48, 192, 768, and so on. Looking at the sequence, we can see that each term is multiplied by 4 to get the next term. So, the sequence is a geometric sequence. The recursive formula for a geometric sequence is given by: an = r * an-1, where an is the nth term, r is the common ratio, and an-1 is the previous term. In this case, r equals 4 (since we are multiplying each term by 4 to get the next term). Thus, "the recursive formula for this geometric sequence is: an = 4 * an-1".

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Related Questions

3 problems, 50 points

Answers

1is 6/13 2is5/x-m h

1. m=9

2.vertical: x=4, horizontal y=1

3.So if y = 3 and x = 5 then we have
3= y(1/6)
Solve for y
y= 24

Therefore the equation should be
y = 24/x

So when x = 3
y = 24/3
y = 8
hope this helps and sorry if I'm wrong

answer this question please and right

Answers

Formula : (x - x1)² + (y - y1)² = r²

Given center of the circle at (-10,6) and radius 4,

(x + 10)² + (y - 6)² = 4²

(x + 10)² + (y - 6)² = 16

Answer: (x + 10)² + (y - 6)² = 16

Use the formula (x - x1)² + (y - y1)² = r².

Center of circle: (-10, 6)
Radius: 4

(x - -10)² + (y - 6)² = 4²
Equation: (x + 10)² + (y - 6)² = 16

If sin x =1/2 what
is cos x

Answers

[tex]\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\to\cos x=\sqrt{1-\sin^2x}\\\\\sin x=\dfrac{1}{2}\\\\\text{substitute}\\\\\cos x=\sqrt{1-\left(\dfrac{1}{2}\right)^2}=\sqrt{1-\dfrac{1}{4}}=\sqrt{\dfrac{3}{4}}=\dfrac{\sqrt3}{\sqrt4}=\dfrac{\sqrt3}{2}[/tex]

Triangle rst is circumscribed about the circle below. What is the perimeter of the triangle?

Answers

I have attached the diagram that is related to this question.

Answer:
perimeter of the triangle = 24 units

Explanation:
Using the grid, we can note that:
RS = 6 units
ST = 8 units

We know that the triangle inscribed in a circle is a right-angled triangle. Therefore, we can use the Pythagorean theorem to get the third side as follows:
(RT)² = (RS)² + (ST)²
(RT)² = (6)² + (8)²
(RT)² = 100
RT = 10 units

Now, we can get the perimeter as follows:
perimeter = RS + ST + RT
perimeter = 6 + 8 + 10
perimeter = 24 units

Hope this helps :)

Not sure what the answer is but this guy didnt attach the dang picture so here.

Help please? what is the length of side x?
Triangle AAS use sine rule

Answers

check the picture below.

make sure your calculator is in Degree mode.

The measure of an angle is two times the measure of a supplementary angle. what is the measure of each angle

Answers

Let the angles be x and (180-x).

Let 2x = 180-x.

Then 3x = 180, and x = 60. One angle is 60 degrees and the other is 180-60, or 120, degrees.

Answer:

60 and 120 have a good day!

Step-by-step explanation:

Find the following measure for this figure.
Volume =
18 cubic units
24 cubic units
36 cubic units

Answers

The figure on the picture is parallelepiped (or right rectangular prism), whose volume is icalculated as V=lwh, where l measures the length, w measures the width and measures the altitude of parallelepiped.

In your case, l=4 units, w=2 units, h=3 units and V=4×2×3=24 cubic units.

Answer:

So the answer is 24 cubic units

Step-by-step explanation:

l=4 units,

w=2 units,

h=3 units and

V=4×2×3=24 cubic units.

Find the price per ounce rounded to the nearest cent: 1 lb 10 oz for $10.98.

A.) 0.5
B.) 1.98
C.) 0.42
D.) 0.9

Answers

Answer is C.) $0.42/oz

Which expression is equivalent to 3(4m − 5)?

Answers

Hello!

your answer is:
using the distributive property of multiplication, the equivalent expression is:
12m-15

I hope this helps, and have a nice day!

The equivalent expression for the given expression is 12m-15.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 3(4m-5).

Using distributive property A(B+C)=AB+AC, we get

3×4m-3×5

= 12m-15

Therefore, the equivalent expression for the given expression is 12m-15.

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A pet store is selling a new dog collar for $12.00. If there is a sales tax of 10 percent, what is the actual cost of the collar

Answers

Price of the collar = $12.00

Sales Tax = 10% x $12 = 0.1 x 12 = $1.20

Total Cost = $12.00 + $1.20 = $13.20

Answer: $13.20

PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Find the value of x and y.

Answers

[tex]180^o-112^o=68^o[/tex]

[tex]\left\{\begin{array}{ccc}2x+3y=68&|\cdot(-15)\\30x+11y=112\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-30x-45y=-1020\\30x+11y=112\end{array}\right}\\.\ \ \ \ \ \ \ -34y=-908\ \ \ |:(-34)\\\\.\ \ \ \ \ \ \ \ \ \ \ y=\dfrac{908}{34}\to y=\dfrac{454}{17}\\\\2x+3\cdot\dfrac{454}{17}=68\ \ \ \ |\cdot17\\\\34x+1362=1156\ \ \ \ |-1362\\34x=-206\ \ \ \ |:34\\\\x=-\dfrac{206}{34}\to x=-\dfrac{103}{17}\\\\ \left\{\begin{array}{ccc}x=-\dfrac{103}{17}\\\\y=\dfrac{454}{17}\end{array}\right[/tex]

Solve the inequality. Graph the solution set.

2r−9≤−6

Answers

we have that

2r−9≤−6------> 2r ≤ -6+9-------> 2r ≤ 3-----> r ≤ 1.5

the solution is the interval (-∞, 1.5]

using a graph tool
see the attached figure

Hey!

The first step to solving this inequality is to change the equation. We'll change the equation by adding plus nine to both sides of the equation. This will help us get 2r on its own.

Original Equation :
2r - 9 ≤ -6

New Equation {Added Plus 9 to Both Sides} :
2r - 9 + 9 ≤ -6 + 9

Now we'll simplify the equation by solving -9 + 9 and -6 + 9.

Old Equation :
2r - 9 + 9 ≤ -6 + 9

New Equation {Old Equation Simplified} :
2r ≤ 3

Once again we'll have to change the equation. We'll do this by adding divide both sides by two. This will give us the variable ( r ) on its own.

Old Equation :
2r ≤ 3

New Equation {Added Divide 2 to Both Sides} :
[tex] \frac{2r}{2} [/tex]  ≤  [tex] \frac{3}{2} [/tex]

Now we simplify.

Old Equation :
[tex]\frac{2r}{2}[/tex] ≤  [tex]\frac{3}{2}[/tex]

New Equation {Old Equation Simplified} :
r ≤  [tex] \frac{3}{2} [/tex]

Now, that is, in fact, the solution but since I'm not sure which form you need, I've written it in other forms as well.

Solution →   r ≤  [tex] \frac{3}{2} [/tex]

Decimal → 1.5

Interval Notation → [tex](-[/tex] ∞[tex], \frac{3}{2} )[/tex]

Below, I have also attached a graph that shows how this inequality should be graphed.

Hope this helps!

- Lindsey Frazier ♥

20 PTS AND I'LL MARK BRAINLIEST

∠1 and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠2=(5+4y)∘ and m∠3=(6y−25)∘ . What is m∠1 ?

Answers

Since m∠2 and m∠3 are vertical angles, they are congruent. Knowing this, we can form this equation:
5+4y=6y-25 (We'll add the degrees symbol later)
5 = 2y - 25
30 = 2y
y = 15°
We can plug the y-value into the value for m∠2.
5 + 4(15) = 65°

Now, we can easily find m∠1, since they are a linear pair.
m∠1 + m∠2 = 180
m∠1 + 65 = 180
m∠1 = 115°.
m∠1 equals 115°.

Hope this helps!

Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j

Answers

We are to find the dot product of the given vectors. To find this just multiply the coefficients of i terms(horizontal components) and multiply the coefficients of j terms(vertical components), and add the two products together, as shown below:

a.b = (6i + 5j).(-5i+4j)
a.b = 6(-5)+5(4)
a.b = -30 + 20
a.b = -10

The dot product results in a scalar quantity, so you only get a magnitude not a vector.

Answer:

-10

Step-by-step explanation:

took the test

What is the slope-intercept form equation of the line that passes through (3, 4) and (5, 16)?

Answers

Answer:
y = 6x - 14

Explanation:
The general formula of the linear line is:
y = mx + c
where:
m is the slope and c is the y-intercept

1- getting the slope:
slope is calculated as follows:
m = [tex] \frac{y2-y1}{x2-x1} [/tex] = [tex] \frac{16-4}{5-3} = 6[/tex]

The equation of the line now is:
y = 6x + c

2- getting the y-intercept:
To get the y-intercept, we will use any of the given points, substitute in the equation and solve for c.
I will use the point (3,4) as follows:
y = 6x + c
4 = 6(3) + c
4 = 18 + c
c = -14

Based on the above calculations, the equation of the line is:
y = 6x - 14

Hope this helps :)

does anyone know what the measuure of Ф should be . is so i will mark brainliest.

Answers

Since the triangles are congruent, they should have similar angle measures:

A triangle's angles measure 180°, so we just have to subtract the other two angle measures:

180 - 50 - 70 = Ф
60 = Ф

What is the square root of 325 rounded to two decimal places?

Answers

The square root of 325 is 18.03

Zekia divides of 6 cups of fruit juice equally among 8 friends two of her friends don't drink the juice how much juice is leftover

Answers

6 cups divided by 8 friends is 0.75 cup per friend
if 6 friends drink and 2 dont, then the amount of juice saved is
0.75 cup/friend * 2 friends = 1.5 cup

1.5 cup of juice is left over

Final answer:

Since Zekia has 6 cups of fruit juice to divide among 8 friends, with 2 not drinking, there will be no juice leftover because each of the 6 drinking friends will receive 1 cup each.

Explanation:

Zekia has 6 cups of fruit juice that she wants to divide equally among her 8 friends, but 2 friends don't drink any. Initially, we would divide 6 cups by 8 to find out how much each friend gets. However, since 2 friends aren't drinking, only 6 friends will be actually consuming the juice.

First, let's calculate the amount of juice each of the 6 friends would receive:

Total juice = 6 cups

Number of friends drinking = 8 - 2 = 6

Juice per friend = Total juice ÷ Number of friends drinking = 6 cups ÷ 6 = 1 cup

So, each of the 6 friends will get 1 cup of juice. Since all 6 cups of juice are consumed, there is no juice leftover.

There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How? Give an example to support your answer.

Answers

Final answer:

The phrase 'What you put into it is what you get out of it' applies to functions in mathematics, where given an value x (input) into a function, you get an output y. It also applies to real life examples, like sports practice, where your input of time and effort has a corresponding output of skill level.

Explanation:

Yes, the expression “What you put into it is what you get out of it” can be applied in mathematics, particularly to functions. In mathematical context, this statement represents the fundamental concept of a function, where an input (what you put into it) mapped to an output (what you get out of it). For example, consider a linear function y = 2x + 3. The value of y (output) depends on the value chosen for x (input). Thus, if x = 2 (input), y = 7 (output). The output here is a result of the input 'fed' into the function.

The same idea can be extrapolated to functions in everyday life, such as practicing a sport. The input to the 'function' is the time and effort you put in, and the output is the proficiency you achieve. As with mathematical functions, each 'input' in life tends to have a corresponding 'output', reinforcing the idea of causes having effects.

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Final answer:

The expression 'What you put into it is what you get out of it' applies to functions such that what you put into the function (input) directly influences what you get out of the function (output).

Explanation:

Yes, the expression 'What you put into it is what you get out of it' can indeed be applied to the concept of functions in mathematics. A function is a special relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. The input you 'put into' a function is the independent variable and the output or 'what you get out of' the function is the dependent variable.

As an example, consider an equation of a function like y = 2x. Here, 'x' represents the inputs and 'y' the outputs. If you 'put into' this function x = 3 (input), you 'get out of' the function y = 6 (output). Thus, what you 'put into' the function (input) directly influences what you 'get out of' the function (output), demonstrating the principle of 'What you put into it is what you get out of it'

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help pls!!! 10 points!!!

Answers

1) The angle bisector divides makes the segments on one side proportional to the corresponding segments on the other side.
3/4 = x/7.5
x = (3/4)*7.5 = 5.625

2) There are a number of ways to compute the area of the figure. I choose to divide it into a rectangle 8 units wide by 6 units high and two triangles. One triangle is 3 units wide and 2 high, the other is 6 units wide and 1 high. Then the total area is
(8*6)+(1/2)*(3*2 +6*1)
= 48 +6
= 54 units²

For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. Find the total number of visits when the cost for a member and nonmember will be the same.

Answers

If after x day of their visit, non-member and member pays the same

360+4x=16x
360=12x
x=30

After 30 days they visit, they will spend the same amount.

Final answer:

The cost for a member and a nonmember of a rock-climbing gym will be the same at 30 visits.

Explanation:

To find the total number of visits when the cost for a member and a nonmember will be the same, we need to set up an equation based on the problem statement, which we can then solve.

For the member, the cost is the $360 yearly fee plus $4 per visit (for equipment rental) - so if 'x' represents the number of visits, the total cost for a member would be $360 + 4x.

For a nonmember, the cost is $10 per visit (for gym use) plus $6 per visit (for equipment rental) - so the total cost for a nonmember is $16x.

So, to find the number of visits 'x' where both costs are equal, we need to solve this equation: $360 + 4x = $16x.

Solving the equation gives us $360 = 12x, which simplifies to x = 30.

So, the cost for a member and a nonmember would be the same at 30 visits.

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Help me please.
Luke Skywalker's height is 68 inches. The mean height for all Jedi is 66.5 inches and the standard deviation of the Jedi heights is 2.4 inches. What is the z score for Luke Skywalker's height?
Round to the nearest thousandth

Answers

The z-score is computed as follows.

[tex]z=\frac{x-\mu }{\sigma }=\frac{68-66.5}{2.4}=0.625[/tex].

The z-score is 0.625.

The z-score for Luke Skywalker's height is 0.625, indicating that his height is 0.625 standard deviations above the mean.

Z-score Formula: The z-score for Luke Skywalker's height can be calculated using the formula: z = (x - μ) / σ, where x is the individual's height, μ is the mean height, and σ is the standard deviation.

Plugging in the values, we get z = (68 - 66.5) / 2.4 = 0.625 (rounded to the nearest thousandth).

The height of a triangle is 8 inches more than its base. the area of the triangle is 104.5 square inches. find the base and height.

Answers

let
b------> the base of the triangle
h------> the height of the triangle

we know that
area of the triangle=b*h/2
h=b+8-----> equation 1
area=104.5 in²
104.5=b*h/2-----> 209=b*h-----> equation 2

substitute equation 1 in equation 2
209=b*[b+8]----> 209=b²+8b-----> b²+8b-209=0

using a graph tool---> to resolve the second order equation
see the attache figure

the solution is
b=11 in
h=b+8----> h=19 in

the answer is
the base is 11 in and the height is 19 in

Which ordered pairs are in the solution set of the system of linear inequalities? y > -1/2x y <1/2 x + 1

Answers

Look at the picture.

[tex]y=-\dfrac{1}{2}x\\\\for\ x=0\to y=-\dfrac{1}{2}\cdot0=0\to(0;\ 0)\\\\for\ x=2\to y=-\dfrac{1}{2}\cdot2=-1\to(2;\ -1)\\\\\\y=\dfrac{1}{2}x+1\\\\for\ x=-2\to y=\dfrac{1}{2}\cdot(-2)+1=-1+1=0\to(-2;\ 0)\\\\for\ x=0\to y=\dfrac{1}{2}\cdot0+1=1\to(0;\ 1)[/tex]

Answer: Every points on orange area.

Answer: is c on edge (5,-2) , (3,1) ,(4,2)

What is the equation of this circle in general form? x² + y² + 2x + 6y + 4 = 0 x2+y2−2x−6y−26=0 x2+y2−2x−6y+4=0 x2+y2+2x+6y−26=0 a circle on a coordinate plane centered at begin ordered pair 1 comma 3 end ordered pair. the horizontal x-axis ranges from negative 10 to 10 increments of 1. the vertical y-axis ranges from negative 10 to 10 in increments of 1. the circle passes through begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair 1 comma 9 end ordered pair, begin ordered pair 7 comma 3 end ordered pair, and begin ordered pair 1 comma negative 3 end ordered pair?

Answers

A circle on a coordinate plane is centered at the beginning ordered (1, 3). The equation of the circle is x²+y²-2x-6y-26=0

What is the equation of the circle with radius r units, centered at (x,y)?

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

A circle on a coordinate plane is centered at the beginning ordered (1, 3).

The horizontal x-axis ranges from negative 10 to 10 increments of 1. and the vertical y-axis ranges from negative 10 to 10 in increments of 1.

The equation of the circle is

[tex]x^2+y^2-2x-6y-26=0[/tex]

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By dividing the number of houses in antonio's subdivision by 4 and adding 15, you can find the number of houses in hector's subdivision. if hector has 47 houses in his subdivision, how many houses are in antonio's subdivision?

Answers

let
x--------> the number of houses in antonio's subdivision
y-------> the number of houses in hector's subdivision

we know that
(x/4)+15=y----> equation 1
y=47-----> equation 2

substitute equation 2 in equation 1
(x/4)+15=47-----> multiply by 4----> x+60=188-----> x=128

the answer is
the number of houses in antonio's subdivision are 128

The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D.(-9,8)

Answers

Look at the picture.

[tex]E\left(\dfrac{-5+1}{2};\ \dfrac{2+6}{2}\right)\to E\left(\dfrac{-4}{2};\ \dfrac{8}{2}\right)\to E(-2;\ 4)[/tex]

[tex]\vec{BE}=[-2-(-6);\ 4-10]=[4;\ -6][/tex]

[tex]D(x;\ y)\\\\\vec{ED}=[x-(-2);\ y-4]=[x+2;\ y-4]\\\\\vec{ED}=\vec{BE}\ therefore\\\\ \ [x+2;\ y-4]=[4;\ -6]\to x+2=4\ and\ y-4=-6\\\\x=2\ and\ y=-2\\\\Answer:\ \boxed{A.\ (2;\ -2)}[/tex]

Answer:

A. (2,-2)

Step-by-step explanation:

That is the right answer. Hope this helps!!!

License plates are made using 2 letters followed by 3 digits. how many plates can be made ifrepetition of letters and digits is allowed

Answers

26×26×10×10×10= 676 000

Suppose two fair six-sided dice are rolled. what is the probability that they will both come up with the same number?

Answers

You have a 16.7% chance of rolling doubles

Show work please (6th grade math)

Answers

A rate is a special ratio in which the two terms are in different units. A rate is a little bit different than the ratio, it is a special ratio. For this case, the rate would have units of miles per minutes. We calculate as follows:
rate = 36 miles / 45 min = 0.8 miles per mindistance traveled = 0.8 miles per min ( 60 min ) = 48 miles
Hope this answers the question. Have a nice day.

The answer is 48 miles.

To find how long the bus travels in 60 minutes, we need to find a ratio of how long the bus travels every 15 minutes.

We do this by dividing 45 minutes by 3. We now have 15 minutes.
You then divide the miles by 3 as well. 36 divided by 3 is 12.

A bus travels 12 miles every 15 minutes.

Now, this still isn't the answer. We need to find how many miles the bus travels in 60 minutes.

To find this, we need to find how many 15 minute intervals are in 60 minutes. To do this, we divide 60 by 15 to get 4. We use this 4 to multiply it by 12 to find the total number of miles in 60 minutes.

12 times 4 is 48 miles.

Therefore, the bus travels 48 miles in 60 minutes.

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