Answer:
a(n)= 1/2 * (-8) n-1
Step-by-step explanation:
In a geometric sequence, the ratio between successive terms is constant. This means that we can move from any term to the next one by multiplying by a constant value. Let's calculate this ratio over the first few terms:
\dfrac{-256}{32}=\dfrac{32}{-4}=\dfrac{-4}{\frac12}=\blue{-8}
32
−256
=
−4
32
=
2
1
−4
=−8start fraction, minus, 256, divided by, 32, end fraction, equals, start fraction, 32, divided by, minus, 4, end fraction, equals, start fraction, minus, 4, divided by, start fraction, 1, divided by, 2, end fraction, end fraction, equals, start color #6495ed, minus, 8, end color #6495ed
We see that the constant ratio between successive terms is \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. In other words, we can find any term by starting with the first term and multiplying by \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed repeatedly until we get to the desired term.
Let's look at the first few terms expressed as products:
nn 111 222 333 444
h(n)\!\!\!\!\!h(n)h, left parenthesis, n, right parenthesis \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large0}\!\!\!\!\!\!
2
1
⋅(−8)
0
start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 0, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large1}\!\!\!\!\!\!
2
1
⋅(−8)
1
start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 1, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large2}\!\!\!\!\!\!
2
1
⋅(−8)
2
start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, squared \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large3}
2
1
⋅(−8)
3
start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, cubed
We can see that every term is the product of the first term, \red{\dfrac12}
2
1
start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, and a power of the constant ratio, \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. Note that this power is always one less than the term number nnn. This is because the first term is the product of itself and plainly 111, which is like taking the constant ratio to the zeroth power.
Thus, we arrive at the following explicit formula (Note that \red{\dfrac12}
2
1
start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030 is the first term and \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed is the constant ratio):
a(n)=\red{\dfrac12}\cdot\left(\blue{-8}\right)^{\large{\,n-1}}a(n)=
2
1
⋅(−8)
n−1
a, left parenthesis, n, right parenthesis, equals, start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, n, minus, 1, end superscript
Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.
At Tubman Middle School, there are 6 English teachers and 5 science teachers. If each
student takes one English class and one science class how many possible combinations of
teachers are there?
There are 30 possible combinations of teachers.
Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:
To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.
6 x 5 = X30 = XTherefore, there are 30 possible combinations of teachers.
Learn more about combinations in https://brainly.com/question/24180105.
This year, a small business had a total revenue of $42,900 . If this is 35% less than their total revenue the previous year, what was their total revenue the previous year?
if this value 35% less than the total, we conclude that:
42,900 = 65%
1% = 660
100% = 66,000
if you want to check the value, just do 65% of 66000, which equals to 42,900
hope it helps :)
The number of bags of Brand Y dog food sold on these five days was 175. Which bar represents the data for Day 5 for Brand Y?
Answer:
30
Step-by-step explanation:
Which points are possible approximations for this system? Select two options.
Step-by-step explanation:
second: (2.2,-1.4)
third: (2.2,-1.35)
Step-by-step explanation:
hope it helps✨
Find the values of the missing sides. You must use exact answers! PLEASE HURRY AND HELP
Answer:
x=4sqrt3 a=4 b=3 ,y=8sqrt3 c=8 d=3
Step-by-step explanation:
because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)
Express 1.2, 2.25, 3.5, 4.06 as a fraction in its simplest form
Answer:
1.2 = 12/10 = 6/5
2.25 = 225/100 = 9/4
3.5 = 35/10 = 7/2
4.06 = 406/100 = 203/50
The vertex is 2,-4 what is the parabola equation
Answer:
y + 4 = (x - 2)^2
Step-by-step explanation:
The vertex form of the equation of a vertical parabola is
y - k = a(x - h)^2, where (h, k) represents the vertex and a is a scaling factor which stretches or compresses the parabola vertically. If all we know is the vertex (2, -4), then the desired equation is:
y + 4 = a(x - 2)^2
If there is no vertical stretching or compression, then the equation becomes:
y + 4 = (x - 2)^2
Answer:
y = x² - 4x
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (2, - 4) , with a = 1 , the equation is
y = (x - 2)² - 4 ← expand using FOIL
= x² - 4x + 4 - 4
y = x² - 4x ← equation of parabola
Answer ASAP please!
………
Answer:
47.746, answer choice C
Step-by-step explanation:
47.746
Two similar polygons have areas of 4 square inches and 64 square inches.
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
Answer:
4
Step-by-step explanation:
The ratio of the area of similar figures is the ratio between corresponding sides squared. This means that 64/4 or 16 is the square of the ratio of corresponding sides. By taking the square root of 16, we get that ratio is 4.
Can someone help me on any of the problems that are circled
HELP PLEASE !!
find the surface area of the cylinder and round it to the nearest tenth.
Answer:
18.8
Step-by-step explanation:
Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8
Ken needs a surgery on his foot. The estimated cost of the surgery is $5,000. The insurance policy provided by Ken's company has $500 deductible and 20% co-pay. How much will Ken have to pay for foot surgery?
9514 1404 393
Answer:
$1400
Step-by-step explanation:
Ken will be required to pay the deductible and 20% of the remaining amount.
Ken pays $500 + 0.20(5000 -500) = $500 +900
Ken pays $1400
(y+2)(y^2-2y+4) ..........................
You can use the distributive property to multiply:
( y )( y² - 2y + 4 ) + ( 2 )( y² - 2y + 4) =
y³ - 2y² + 4y + 2y² - 4y + 8 =
y³ + 8
The -2y² and the 2y² cancel each other, and the 4y and -4y cancel each other out!
ac circular runway has a radius of 100 m.Find the distance covered by a person in one complete rotation .
Answer:
628m
Step-by-step explanation:
Given radius=100m
distance=circumference
=2pie r
=2×22/7×100
=628m
please mark me brainliest
if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and y
plz help me
The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
Question 4 options:
A)
A = (45,000)e–0.02t
B)
A = 45,000 + e–0.02t
C)
A = (45,000)e0.02t
D)
A = 45,000 + e0.02t
Answer:
Step-by-step explanation:
The general form of this equation is
[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.
Therefore, filling in:
[tex]A=45000e^{-.02t[/tex]
Y'ALL PLEASE HELP ME I WOULD GREATLY APPRECIATE IT!!!!!:)!!!!!!
Find the measure of angle TOS in the figure below. SHOW YOUR WORK SO I CAN SEE HOW YoU GOT IT!!!!
Step-by-step explanation:
<TOS=122° [being vertically opposite angle]
Answer:
angleTOS =122°
EXPLANATION:
[ If two straight lines intersect at point O, vertically opposite angles are equal]As vertically opposite angles are equal; Hence AngleTOS=QOR=122°
3. Find the product, using suitable properties :
a) 26 x (-48) + (-48) x (-36)
b) 625 x (-35) + (-625) x 65
please answer fast 10 marks
a) 26 x (-48) + (-48) x (-36) = ( –1248) + ( + 1728) = – 1248+ 1728 = 480
b) 625 x (-35) + (-625) x 65 = ( –21875) + ( –40625) = – 21875 –40625 = –62500
I hope I helped you^_^
4.
Find the inverse of A if it has one, or state that the inverse does not exist.
Answer:
Hello,
[tex]\begin{bmatrix}\dfrac{-1}{5} &0\\\dfrac{-1}{10}&\dfrac{1}{4}\end{bmatrix}[/tex]
Step-by-step explanation:
See jointed file
The inverse of the matrix A is
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
[tex]A = \left[\begin{array}{cc}-5&0\\-2&4\end{array}\right][/tex]
The matrix A is a square matrix and its determinant is not zero.
So the inverse exist.
The inverse of matrix A.
We will change the rows into columns and columns into rows.
So,
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
Thus,
The inverse of the matrix A is given above.
Learn more about matrix here:
https://brainly.com/question/28180105
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The area CA) of a Parallelogram is found by using this formula A = BH What is the area when b is 7cm and h is 3cm?
Answer:
Area of parallelogram = 21
Step-by-step explanation:
A = BH
Plug in
A = 7×3
Solve
A = 21
The answer will be 21.
Algebra 1 need help ASAP
Answer:
Step 1: 12-2a=3a-18
Step 2: 12-5a=-18
Step 3: -5a=-30
Step 4: a=6
I hope this helps!
pls ❤ and give brainliest pls
Independent Practice
Which model is most appropriate for the set of points?
(–2, 5), (–1, –1), (0, –3), (1, –1), (2, 5)
A.
exponential
B.
linear
C.
quadratic
Tuto
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
8r + 9pg - pg - pq
Answer:
8r+8pg-pq
Step-by-step explanation:
The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg
Hope this helps!
Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
Find all three distinct roots for X³ =1. (two of them are complex mumber). And show that sum of all roots is zero.
x ³ = 1
x ³ - 1 = 0
x ³ - 1³ = 0
Factorize the right side as a difference of cubes:
(x - 1) (x ² + x + 1) = 0
Then
x - 1 = 0 or x ² + x + 1 = 0
The first equation yields x = 1 as a root.
For the other equation, rearrange and complete the square to get the other two roots,
x ² + x + 1/4 = -3/4
(x + 1/2)² = -3/4
x + 1/2 = ±√(-3/4) = ± i √3/2
x = -1/2 ± i √3/2
x = (-1 ± i √3)/2
Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:
(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1
and adding to 1 indeed shows that the sum of roots is zero.
Please help me find x
Need help fast!!
Answer:
x = 100°
Step-by-step explanation:
p and q are parallel lines. Construct line 'l' parallel to p and q
a = 30° {p// l when parallel lines are intersected by transversal alternate interior angles are congruent}
c +110 = 180 {linear pair}
c = 180 - 110
c = 70°
b= c {q // l when parallel lines are intersected by transversal alternate interior angles are congruent}
b = 70°
x = a + b
x = 30° + 70°
x = 100°
The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?
Answer:
9 years older
Step-by-step explanation:
The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )
In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so
[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides
40x + 150 = 30x + 180 ( subtract 30x from both sides )
10x + 150 = 180 ( subtract 150 from both sides )
10x = 30 ( divide both sides by 10 )
x = 3
Then
Michell is 8x = 8 × 3 = 24 years old
Connor is 5x = 5 × 3 = 15 years old
Mitchell is 24 - 15 = 9 years older than Connor
Find the image of the given point
under the given translation.
P(-7,1) T(x,y) = (x + 9, y-3)
P' = ([?], []).
Answer:
P' = (2, -2)
Step-by-step explanation:
You have the x-value and the y-value of the pre-image, so all you have to do is plug that into the translation statement (x + 9 , y - 3).
Since x = -7 and y = 1 that would be (-7 + 9, 1 - 3), or (2, -2).
What is the value of a? Round to the nearest tenth.
Answer:
50 percent?
Step-by-step explanation:
The total cost of 2 bracelets and 3 necklaces is $15.50. The total cost of 4 bracelets and 1 necklace is $13.50. Let b represent the cost of each bracelet and n represent the cost of each necklace. This situation can be represented by the following system of equations.
{2b+3n=15.504b+n=13.50
What is the cost of one bracelet?
A
$2.50
B
$7.75
C
$5.00
D
$3.50
Answer:
A
$2.50
Step-by-step explanation:
b = cost of bracelet
n = cost of necklace
2b+3n = 15.50
4b+1n = 13.50
Multiply the first equation by -2
-4b -6n = -31
4b +n = 13.50
---------------------------
-5n = -17.50
Divide each side by -5
-5n/-5 = -17.5/-5
n = 3.50
Now we can find b
4b+n = 13.50
4b+3.50 = 13.50
4b+3.50-3.50 = 13.50 -3.50
4b = 10
Divide by 4
4b/4 = 10/4
b = 2.50