Answer:
[tex]f(n)=f(n-1) + 4(3)^{n-2}[/tex]
[tex]\textsf{where}\quad f(1)=4[/tex]
Step-by-step explanation:
Given sequence: 4, 8, 20, 56, 164
First, work out the difference in the terms:
[tex]4 \underset{+4}{\longrightarrow} 8 \underset{+12}{\longrightarrow} 20 \underset{+36}{\longrightarrow} 56 \underset{+108}{\longrightarrow} 164[/tex]
As the first differences are not the same, work out the second differences:
[tex]4 \underset{\times 3}{\longrightarrow} 12 \underset{\times 3}{\longrightarrow} 36 \underset{\times 3}{\longrightarrow} 108[/tex]
Therefore, the term-to-term rule is:
[tex]f(n)=f(n-1) + 4(3)^{n-2}[/tex]
[tex]\textsf{where}\quad f(1)=4[/tex]
[tex]f(2)=f(1) + 4(3)^{2-2}=4+ 4(3)^{0}=4+4=8[/tex]
[tex]f(3)=f(2)+4(3)^{3-2}=8+4(3)^1=8+12=20[/tex]
[tex]f(4)=f(3) + 4(3)^{4-2}=20+4(3)^2=20+36=56[/tex]
[tex]f(5)=f(4) + 4(3)^{5-2}=56+4(3)^3=56+108=164[/tex]
Determine the equation of the parabola that opens up, has focus (−2,7), and a focal diameter of 24.
Answer:
[tex] \sf{(x + 2)}^{2} = 24(y -1) [/tex]
Step-by-step explanation:
Given:
focus(h,k)= (−2,7)
Focal Diameter (Latus rectum) = 24
To find:
Equation of parabola= ?
Solution:
Focal Diameter also known as letus rectum is the segment which passes through Focus and intersects the Axis of parabola having end point at the wall of of parabola.
Focal Diameter = 24
[tex]4p = 24 \\ p = \cancel\frac{ 24}{ 4} = 6 \\ \fbox{p = a = 6}[/tex]
Now to find the equation of parabola we need the vertex(h,v).
Vertex is a point on parabola which lies in same axis of symmetry at equidistant from the directrix and Focus and the distance is one fourth of letus rectum.
Now,
[tex] \sf \: (h,v) = (h,k-p) \\ \sf \: (h,v)= (-2,7-6) \\\sf \: \fbox{ (h,v) = (-2,1)}[/tex]
Equation of parabola
[tex]\sf{(x-h)}^{2} = 4a(y - v)[/tex]
Substituting the cordinate of vertex in above equation,
[tex] \sf{(x - (-2)}^{2} = 4 \times ( 6)(y-1 ) \\ \sf{(x + 2)}^{2} = 24(y -1)[/tex]
This is the final answer.
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Find the missing side lengths. Round decimals to the nearest tenth.
Answer: 36.2
Step-by-step explanation:
All the line segments of this 22-gon meet at right angles. The radius of the smallest circle that will completely surround the polygon is
Answer:
√61 ≈ 7.81
Step-by-step explanation:
It appears that the polygon can be enclosed by a rectangle that is 12 units wide and 10 units high. The enclosing circle is the one that will circumscribe that rectange. Its radius is half the length of the diagonal, so is ...
(1/2)√(12² +10²) = 1/2√244 = √61
The smallest circle that will surround the polygon will have a radius of √61 ≈ 7.81 units.
_____
The Pythagorean theorem is used to find the length of the diagonal. It tells you the square of the diagonal is the sum of the squares of the sides of the rectangle. Our radius is half the diagonal, so is half the square root of the sum of the squares of the side lengths.
Trying to finish khan academy. I need to simplify. How do I do it?
Answer:
-5+5k-8k-20
-3k-25
-(3k+25)
Answer:
Step-by-step explanation:
(-5 - -25k) - (8k + 20) =
-(18k - 15)
A robot can complete 7 tasks in 2/3
hour. What is the unit rate for hours per task
Answer:
2/21 hours per task.
Step-by-step explanation:
2/3 / 7 hours per task
= 2/21.
convert 17/4 to a mixed
Answer:
17/4 is 4 ¼ as a mixed fraction
Step-by-step explanation:
hope this helps
Question 2
Which function is equivalent to f(x) = -5(x + 4)2 + 8?
F(x)=-5x2-40x-32
F(x)=-5x2+8x+88
F(x)=-5x2-40-72
F(x)=-5x2+8x+24
( the 2 is squared)
Step-by-step explanation:
-5(x + 4)² + 8 = -5(x² + 8x + 16) + 8 =
= -5x² - 40x - 80 + 8 = -5x² - 40x - 72
so, the third answer option must be correct, but you made a mistake there and forgot the "x" as factor of -40.
A customer will choose one card to buy a random. Based on the data in the table, which statement is true? Help!
PLS HELP ME I WiLL MARK THE BRAINLIEST
Answer:
look at analysis
Step-by-step explanation:
1. 152
2. 200
3. 10857
4. 123.4
5. 1848
Angle θ is in standard position. if sin(θ) = − 1 3 , and π < θ < 3π 2 , find cos(θ).
The value of the angle θ is 160.52° then the value of the cosine will be negative 0.9428.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Angle θ is in standard position.
If sin(θ) = − 1/3 , and π < θ < 3π/2
Then the angle will be
[tex]\theta = \sin ^{-1}\dfrac{-1}{3}\\\\\theta = -19.47[/tex]
Then add 180 degrees, then we have
[tex]\theta = -19.47 + 180\\\\\theta = 160.52[/tex]
Then the value of the cosine will be
[tex]\cos 160.52^o=-0.9428[/tex]
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Answer:
-2√2/3
Step-by-step explanation:
edge 22
what is 3 × 2/7 in lowest terms
Answer:
6/7
Step-by-step explanation:
3x2/7 in the same as 3/1x2/7, which is 6/7
(simply multiply the denominator and numerator of the fraction)
Answer: hii <3
Exact Form:
6/7
Decimal Form:
0.857142
Step-by-step explanation:
Simplify the expression.
Hopefully this helps you
- Matthew
Can someone please tell me the rest of the answers?
Answer:
35 miles per hour.
223 minutes to reach destination.
Step-by-step explanation:
It's counting down by 35
35 miles per hour.
260/35=7.42857142857
7.42857142857*30=222.857142857
Rounding to nearest whole number
223
SonicIsCoool
On Scratch you tube, Inst and much more here to help :)
Is FGH ~ JKL? If so, identify the similarity postulate or theorem that applies.
Answer: D
Step-by-step explanation:
There are two pairs of congruent angles.
The two triangles FGH and JKL are similar to each other by Angle-Angle property. Hence, option D is correct.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
In the given figure we can see that the two triangles FGH and JKL have two angles equal that is ∠f =∠J = 30° and ∠L = ∠H =55°. Two angles are similar then the triangles are similar.
Hence, option D is correct.
To know more about similarities follow
https://brainly.com/question/24184322
#SPJ2
The algebraic expression of the SUM is n²+2n. What is the common difference and first term
Answer:
see explanation
Step-by-step explanation:
substitute n = 1, 2 into the sum rule
1² + 2(1) = 1 + 2 = 3 , then
a₁ = 3
2² + 2(2) = 4 + 4 = 8 , then
a₁ + a₂ = 8
3 + a₂ = 8 ( subtract 3 from both sides )
a₂ = 5
then
common difference d = a₂ - a₁ = 5 - 3 = 2
First term is 3 and common difference = 2
Write a two-column proof on a space provided
Answer:
Step-by-step explanation:
I toss a coin more then 60 times and i comes down tails 40% of the time. How many heads did i toss
Answer:
36.
Step-by-step explanation:
100 - 40 = 60% of heads.
60% = 0.60.
60 * 0.60 = 36.
What is the measure of \angle D∠Dangle, D?
Answer:
135⁰
Step-by-step explanation:
As in cyclic quadrilateral sum if opposite angles is equal to 180⁰
help with number one please
Answer:
The solution to the set of linear equations is:
[tex](5,-4)[/tex]
Step-by-step explanation:
Hey there!
In order to solve this system of equations, we can put the equations equal to each other since both equations are equal to y
[tex]6-2x=-4x+16[/tex]
Now we simplify
[tex]2x=10[/tex] ---> [tex]x=5[/tex]
So now that we know that x is equal to 5, we can find the value of y
let's substitute it in one of the equations
[tex]y=6-2(5)[/tex] ---> [tex]y=-4[/tex]
So now we know that the point where the two equations intersect is:
[tex](5,-4)[/tex]
This is going to be our solution
The graph is in an attachment below
im stuck lol i just need a answer
Answer:
131 here is the answer and your welcome
FUN QUESTIONS OF MATHETICS FOR BOREDISH PEOPLE:
3x3?
4x5?
8x9?
7x3?
Answer: 3x3=9, 4x5=20, 8x9=72, and 7x3=21!
Step-by-step explanation:
7) There are 260 athletes at a meeting.
How many handshakes were there?
Answer:
130
Step-by-step explanation:
Assuming everyone handshakes at the meeting. There will be 130 handshakes in total.
It takes 2 people to handshake, and thus to find the number of handshakes we need to do 260/2=130
130 total handshakes
Hope this helps ^^
This graph plots the number of wins last year and this year for a sample of professional football teams.
Based on the line of best fit, which is the BEST prediction for wins this year for a team that won 4 games last year?
2
4
5
7
Answer:
5 won 4 games last year . This is the best prediction based on the lime fit
(1+sint)/(cost)-(cost)/(1-sint)
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}[/tex]
Multiply through the second term by [tex]1+\sin(t)[/tex] :
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}\cdot\dfrac{1+\sin(t)}{1+\sin(t)}[/tex]
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{1-\sin^2(t)}[/tex]
Recall that [tex]\cos^2(x)+\sin^2(x)=1[/tex] for all x :
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{\cos^2(t)}[/tex]
If [tex]\cos(t)\neq0[/tex], we can cancel a factor of it in the second fraction.
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{1+\sin(t)}{\cos(t)}[/tex]
and this simplifies to
[tex]\dfrac{(1+\sin(t))-(1+\sin(t))}{\cos(t)} = \boxed{0}[/tex]
first to answer correctly will be marked brainliest
Answer:
16-25y^2
Step-by-step explanation:
Hey there!
As you know, both 16 and 25 are perfect squares
All the other answers don't have both numbers as perfect sqaures
Find the perimeter of the given figure.
Answer:
9.4
Step-by-step explanation:
(rectangle) shape 1: perimeter of rctangle= 2(l b)
=7
(semicircle)shape 2:perimeter of semicirlce=½ñd+d(ñ=pie)
0.5×ñ×1.4+1.4=3.6
add them
7+3.6=10.6
i hope i was helpful
please consider as brainlest
Which of the following is the name for a hollow depression in which drainage collects?(1 point) 1.cave 2.sinkhole 3.v-shaped valley 4.canyon
Answer:
sinkhole valley's typically dont collect water where as sink holes are caused by water displacement of soil
find the value of a and b in parallelogram WXYZ
opposit side of parallelogram are equal and opposit angles are also equal
picture explains
asdasdasd
Answer:
Yes, AB is tangentStep-by-step explanation:
The tangent is perpendicular to the radius. The given triangle is right if AB is tangent.
Use Pythagorean to verify
20² = 16² + 12²400 = 256 + 144400 = 400Confirmed
Answer:
AB is tangent to the circle
Step-by-step explanation:
The tangent of a circle is always perpendicular (at a right angle) to the radius. Therefore, if AB is the tangent to the circle, the angle between the radius and AB will be 90° (and ΔBAO will be a right triangle).
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleGiven:
a = 12b = 16c = 20Substitute the given values into the formula:
[tex]\implies 12^2+16^2=20^2[/tex]
[tex]\implies 144+256=400[/tex]
[tex]\implies 400=400[/tex]
Therefore, as ΔBAO is a right triangle with ∠BAO = 90°, AB is tangent to the circle.
Tickets to the aquarium cost $6 each for children and $16 each for adults. A large group purchased a combination of both tickets. If they purchased c child tickets and a adult tickets, write an expression for the total amount they paid in factored form.
Answer:
6c + 16a = T :)
Step-by-step explanation:
We only know how much the cost for the children is, 6, so we put a variable c after it :)
We only know how much the cost for the adults is, 16, so we put a variable a after it :)
I put T to show a varibale for the total :)
Have an amazing day!!
Please rate and mark brainliest!!
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
12, 10, 8,.........
This is______sequence and the _______is equal to _________.
Answer:
Step-by-step explanation:
This is an arithmetic sequence and the common difference = - 2
You might be a little puzzled by the minus sign in front of the two. You can look at the sequence for the answer. It is going down. A plus 2 would make it go up. Minus signs are always a bit tricky and you have to watch out what you do with them. But the rule is simple
a minus common difference produces a sequence that goes down.a plus common difference produces a squence that goes up.You know that this is an arithmetic sequence because the common difference can be found by adding or subtracting a number from the previous term to get to the next term.
A geometrice sequence would use multiplication or division to get from one term to the next.