Answer:
[tex]4 \sqrt{122} \sqrt{12} \\ (4 \times 2) \times ( \sqrt{12} \times \sqrt{12} ) \\ (4 \times 2) \times 12 \\ 8 \times 12 \\ 96[/tex]
Find an explicit formula for the geometric sequence \dfrac12\,,-4\,,\,32\,,-256,.. 2 1 ,−4,32,−256,..start fraction, 1, divided by, 2, end fraction, comma, minus, 4, comma, 32, comma, minus, 256, comma, point, point. Note: the first term should be \textit{a(1)}a(1)start text, a, left parenthesis, 1, right parenthesis, end text. a(n)=a(n)=a, left parenthesis, n, right parenthesis, equals
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.
Solving Functions. Julio is paid 1.4 times his normal hourly rate for each hour he works over 29 hours in a week. Last week he worked 44 hours and earned $560.00.
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART
2 QUESTIONS
Hi, Laura! ;)
The answer to the first question is 5,62.Here is the step by step solution:They want to know the center of a distribution. Another word for center is middle. When you have a set of numbers, you can find the middle by calculating the mean, the "average" of the data set.
1) Add all the numbers: 12,8 + 5,7 + 7,9 + 1,3 + 3,2 + 2,8 = 33,7
2) Divide the sum by the quantity of numbers, which is 6: 33,7 / 6 = 5,616
The closest number to 5,616 is 5,62.
==========================================================
Now let's answer your second question.
The correct answer is, indeed, 0,14.How do we get to this number? Here is the step by step solution:1) First step is to find out how many possible outcomes you have. It is the
number of raffle tickets in the box: 200.
2) Then, let's define the number of tickets that are prizes: 4 + 8 + 16 = 28.
The probability of selecting a prize ticket is the number of prize tickets divided by all the raffle tickets in the box: 28 / 200 = 0,14.
Now, let's practice Probability with another Brainly problem:
https://brainly.com/question/16447117
Good luck, Laura! :)
What is the period of the function y=3/2con(3/5x)+5
Answer:
[tex]y = \frac{3}{2} cot( \frac{3x}{5} ) + 5 \\ \\ \pi \div \frac{3}{5} \\ \ \\ = \frac{5\pi}{3} is \: period[/tex]
whats 5867 times 382
Answer: 2,241,194
Step-by-step explanation:
5867 times 382 is 2,241,194
if 5|x − 1| = 20, then x =
1 or 5
6 or –8
–2 or 4
5 or –3
Please help
Answer:
Step-by-step explanation:
I need help ASAP!!Please explain how to do the problem
Answer:
(x-2)^2 + (y-1)^ = 1
Step-by-step explanation:
First, we take the circle graphing formula, which is (x-h)^2 + (y-v)^2 = r^2 and plug in the values on the graph with the center of the circle being (h,v) and the radius being r. h = 2, v = 1, and r = 1, so we get (x-2)^2 + (y-1)^2 = 1!
I hope this helped! :D
which is odd one out 4:10 12:25 20:50 8:20
Answer:
All of them except 12:25 simply to 2:5. So 12:25 is the odd one out.
in another baseball division one team had a winning of 0.444 what fraction of their team did this team win
QUESTION: Josephine put a frame round his picture which measured 36 cm by 34 cm. A margin 4cm wide was left all the way round. What was the area of the margin ?
(NOTE:SORRY BUT UNFORTUNATELY THERE ISN`T A DIAGRAM)
[tex](4v^{-3} )^3/3v^{-8}[/tex]
Answer:
[tex]=\frac{64}{3v}[/tex]
Step-by-step explanation:
One is given the following equation:
[tex]\frac{(4v^-^3)^3}{3v^-^8}[/tex]
Simplify the numerator, remember to raise every number inside the parenthesis to the exponent outside of the parenthesis. Bear in mind, an exponent raised to another exponent is equal to the exponent times the exponent it is raised to. Then simplify by multiplying the number by itself the number of times that the exponent indicates.
[tex]\frac{(4v^-^3)^3}{3v^-^8}[/tex]
[tex]=\frac{4^3(v^-^3)^3}{3v^-^8}[/tex]
[tex]=\frac{4^3v^-^9}{3v^-^8}[/tex]
[tex]=\frac{64v^-^9}{3v^-^8}[/tex]
Bring the variable (v) in the denominator (value under the fraction bar) to the numerator (value ontop of the fraction bar) by multiplying its exponent by (-1). This can be done simply because all operations in this equation are multiplication or division, remember, an exponent is another form of multiplication.
[tex]=\frac{64v^-^9}{3v^-^8}[/tex]
[tex]=\frac{(64v^-^9)(v^(^-^1^)^(^-^8^))}{3}[/tex]
Simplify, remember, multiplying two numbers with the same base that have an exponent is the same as adding the two exponents,
[tex]=\frac{(64v^-^9)(v^(^-^1^)^(^-^8^))}{3}[/tex]
[tex]=\frac{(64v^-^9)(v^8)}{3}[/tex]
[tex]=\frac{64v^-^9^+^8)}{3}[/tex]
[tex]=\frac{64v^-^1}{3}[/tex]
Now bring the variable to the denominator so that there are no negative exponents. Use a similar technique that was used to bring variables with exponents to the numerator.
[tex]=\frac{64v^-^1}{3}[/tex]
[tex]=\frac{64}{3(v^(^-^1^)^(^-^1^))}[/tex]
[tex]=\frac{64}{3v^1}[/tex]
[tex]=\frac{64}{3v}[/tex]
Write f(x)=5 -(x – 4)2 in the form f(x)= ax+bx+c.
Answer:
[tex]f(x) = 5 - (x - 4)^2[/tex].
Step-by-step explanation:
[tex]f(x) = 5 - (x - 4)^2[/tex]
[tex]f(x) = 5 - (x-4)*(x-4)[/tex]
[tex]f(x) = 5 - (x^2 - 4x - 4x + 16)[/tex]
[tex]f(x) = 5 - (x^2 - 8x + 16)[/tex]
[tex]f(x) = 5 - x^2 + 8x - 16[/tex]
[tex]f(x) = -x^2 + 8x - 11[/tex].
Hope this helps!
giải phương trình x/30-x/40=5/4
Answer:
x=150
Step-by-step explanation:
x/30-x/40=5/4
or, (4x-3x)/120=5/4
or, x/120=5/4
or, x=600/4
or, x=150
What is the slope of line AB
1) A couple is expecting the birth of a baby boy. They will name the child by choosing a first name
and middle name from this list of their favorite boys' names: Jacob, Jonah, Joshua, Jeremy,
James, Joseph. The first name will be different from the middle name.
How many different two-part names are possible? (Example: Joseph Jeremy, Jeremy Joseph,
and Joshua James are three different, valid two-part names; Jacob Jacob is not a valid
possibility.)
a) 36
b) 12
c) 30
d) 11
Answer:
C. 30
Step-by-step explanation:
We have a list of names that need to be sorted in a specific order. For this, we will use a permutation. This can be found on a scientific calculator, however, I'll be using the equation.
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
n = total number of objects
r = number of objects selected
In this instance, n will equal 6 since we have 6 different names to choose from and r will equal 2 since we are picking two names. Enter the values into the equation and evaluate.
[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]
Therefore, there are 30 possible two-part names.
There are 50 teenagers at a swim meet. The ratio of locals to out-of-town
participants is 2:3. How many teenagers travelled from out-of-town to the swim
meet?
Answer:
There are 30 out of towners
Step-by-step explanation:
locals: out of town: total
2 3 2+3 = 5
There are 50 total 50/5 =10 so multiply each term by 10
locals: out of town: total
2*10 3 *10 5*10
20 30 50
There are 30 out of towners
Total teenagers = 50
Ratio = 2:3
Let the ratio people out of town be x
2x + 3x = 50
5x = 50
x = 10
Therefore 3× 10, 30 people out of town travelled to swim meet
Must click thanks and mark brainliest
The midpoint of line segment AB is (-2,1). If the coordinates of B are (0,2) what are the coordinates of A?
The required coordinate of A will be at (-4, 0)
When a point bisects a line, it cuts the line into two equal parts and the point on that line is known as its midpoint. The expression for calculating the midpoint of a line is expressed as;
[tex]M(X, Y)= [{ \frac{x_2+x_1}{2} , \frac{y_2+y_1}{2} ][/tex] where:
[tex]X =\frac{x_2+x_1}{2} \\Y=\frac{y_2+y_1}{2}[/tex]
From the question, we are given the following coordinate points
[tex]X=-2\\x_1=0\\[/tex]
Get x₂;
[tex]X =\frac{x_2+x_1}{2}\\-2 =\frac{x_2+0}{2}\\2 \times -2=x_2+0\\-4=x_2\\ Swap\\x_2=-4\\[/tex]
Get y₂;
[tex]Y =\frac{y_2+y_1}{2}\\1 =\frac{y_2+2}{2}\\2 \times 1=y_2+2\\2=y_2+2\\y_2=2-2\\y_2=0[/tex]
Hence the coordinate of A will be (-4, 0)
Learn more about the midpoint here: https://brainly.com/question/18315903
4. What is the volume of the pyramid?
7 ft
9 ft
10 ft
The perimeter of a rectangular piece of plastic is 30 millimeters. The area is 54 square millimeters. What are the dimensions of the piece of plastic?
Answer:
6 mm and 9 mm are the dimensions of the piece of plastic.
Step-by-step explanation:
Keep in mind the formulas for the area and perimeter of a rectangle:
A = lw
P = 2 (l + w)
List the factors of 54:
1, 2, 3, 6, 9, 18, 27, 54
POSSIBLE DIMENSIONS of the piece of plastic:
1 mm and 54 mm:
Area - 54 mm^2
Perimeter - 110 mm
2 mm and 27 mm
Area - 54 mm^2
Perimeter - 58 mm
3 mm and 18 mm
Area - 54 mm^2
Perimeter - 42 mm
6 mm and 9 mm
Area - 54 mm^2
Perimeter - 30 mm
The rectangular piece of plastic with the dimensions 6mm and 9 mm corresponds with the area and perimeter of the piece of plastic mentioned. So these are the correct dimensions.
Hope this helps!
When a plane lands at the local airport, it touches ground and creates an angle between the ground and the belly of the plane. What is a good estimate of the angle measurement? A.65 B. 50 C.35 D. 20
Answer:
Step-by-step explanation:
D (20 degrees) is the most reasonable estimate. Were the angle 65 degrees, the plane would almost surely crash because the body of the plane could not possibly change direction so quickly.
Answer:
D!!!!!!
Step-by-step explanation:
please help me this is urgent I will mark brainliest
which has a steeper slope y-1/2x or y=2/3x?
Answer:
y=2/3x
Step-by-step explanation:
2/3 is greater than 1/2. It doesn't matter if one of the slopes are negative.
A regular polygon has exterior angles of 60°
What is the sum of the polygon’s interior angles?
Answer:
720°
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Divide by 60 to find number of sides (n)
n = 360° ÷ 60° = 6
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 6 , then
sum = 180° × 4 = 720°
The sum of the exterior angles of a regular polygon is 360º
Each exterior angle of a regular polygon is 60º/n
360º/n=60º
360/60=n
6=n
A polygon with 6 sides is a hexagon.
Use the formula (n-2)×180
(6-2)*180=4*180=720º
another solution...
you have 6 interior angles (hexagon)
if an exterior angle is 60º, the corresponding interior angle is 180-60=120º
you have 6 of these 120º angles
6*120=720º
PLEASE HELP, I'LL MARK BRAINLIEST.. Of the 37 teachers at Francesca's high school, 9 are female. What is the ratio of the number of male teachers to the total number of teachers? Please write in decimal form
Identify the coordinates of the vertices of the polygon.Identify the coordinates of the vertices of the polygon.
A. (3,5), (–6,1), (–3,–4), (0,–5), (7,–3)
B. (–3,5), (–6,1), (–3,–4), (0,–5), (7,–3)
C. (3,5), (–6,1), (–3,–4), (–5,0), (7,–3)
D. (3,5), (6,1), (–3,–4), (0,–5), (7,–3)
Answer:
A
Step-by-step explanation:
The coordinates are (3,5),(7,-3),(0,-5),(-3,-4) and (-6,1). So the correct option is A
If f(x) = 2x - 4, then prove that, (f-1of)(x) is an identify function.
it's a optional mathematics Questions please solve him
Answer:
f(x)=2x-4
f(1)=2(1)-4
=2-4
f(1)=-2
1/5 of a certain number is added to 5½ the same as when ⅙ of the number that is subtracted from 30⅖find the number
Step-by-step explanation:
1%2F5n + 51%2F5 = 302%2F5 - 1%2F6n
make the 3rd term an improper fraction
1%2F5n + 51%2F5 = 152%2F5 - 1%2F6n
multiply equation by 30, cancel the denominators, resulting in:
6n + 6(51) = 6(152) - 5n
6n + 306 = 912 - 5n
6n + 5n = 912 - 306
11n = 606 is the number
n = 606/11
n = 55 1/11
Answer:
68
Step-by-step explanation:
let unknown number be x
⅕x + 5½= 30⅖ - ⅙x
⅕x + 11/2= 152/5 - ⅙x
collect like terms
⅕x+⅙x= 152/5 - 11/2
[tex] \frac{11}{30}x = \frac{249}{10} [/tex]
cross multiply
30 * 249=(11 * 10)x
7470=110x
x=7470/110
x= 68
[tex]( - 72) \div ( + 9) + (16) \div ( - 4)[/tex]
could you help.....
Answer:
-12
Step-by-step explanation:
Use PEMDAS,
doing the division first, then addition to simplify the terms
(-72)/(+9) + 16/(-4)
(-72/9) + (16/-4)
-8+(-4) = -12
Answer:
-12
Step-by-step explanation:
((-72)÷(9))+((16):(4))
= (-8)+(-4)
= -12
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
How the data set rises and drops can best be summarized by the ___________ of the data set.
A. shape
B. values
C. spread
D. center
Answer:
Shape
Step-by-step explanation:
I hope this will help buddy
Subtract. Write the answer as a fraction simplified to lowest terms
Answer:
3/14
Step-by-step explanation:
4/7 - 5/14
Get a common denominator of 14
4/7 *2/2 - 5/14
8/14 - 5/14
3/14
