given the following geometric sequence: 1,3,9,27,81,...
Write an explicit formula that describes this sequence.
Using the formula, find the 18th term of the sequence
Answer:
The 18th term of the geometric sequence is [tex]a_{18}=129140163[/tex]
Step-by-step explanation:
[tex]a_n=a_1(r)^{n-1}\\\\a_{18}=1(3)^{18-1}\\\\a_{18}=3^{17}\\\\a_{18}=129140163[/tex]
what is 36:52 simplest form
Answer:
9:13
Step-by-step explanation:
36:52
divide both by two
18:26
divide both by 2
9:13
Find an equation for the perpendicular bisector of the line segment whose endpoints are (5, 5) and ( 7, 1).
Answer:
x -2y = 0
Step-by-step explanation:
A perpendicular bisector is a line perpendicular to a given line or segment that goes through the midpoint between given points. The perpendicular line will have a slope that is the opposite reciprocal of the slope of the segment between the given points.
__
The midpoint between A and B is ...
M = (A +B)/2
M = ((5, 5) +(7, 1))/2 = (12, 6)/2 = (6, 3)
The slope of the line between A and B is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -5)/(7 -5) = -4/2 = -2
__
The opposite reciprocal of the slope of the given segment is ...
m' = -1/-2 = 1/2
The point-slope form of the equation of the perpendicular bisector can be written as ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -3 = 1/2(x -6) . . . . line with slope 1/2 through point (6, 3)
Multiplying by 2 gives ...
2y -6 = x -6
Subtracting (2y -6) gives the standard-form equation ...
x -2y = 0
Select the correct answer.
Which American sociologist strongly criticized the structural functionalism approach to sociology?
O A Lester Ward
ОВ.
Robert Nisbet
OC. C. Wright Mills
OD. Julian Samora
Answer:
C. Wright Mills
Step-by-step explanation:
was the American sociologist who strongly criticized the structural functionalist approach to sociology.
A new fitness center opens with 120 members. Every month the fitness center increases the number of members by 40 members. How many members will the fitness center have after being open for 3 months?
Answer:
240 members
Step-by-step explanation:
Let y = total and x = no. of months
y = 40x + 120
= 40(3) + 120
= 120 + 120
= 240 members
Does anyone know the correct answer?
Answer:
A)
Step-by-step explanation:
area of triangle is base x height divided by two
Answer:
Option A is the correct answer
Step-by-step explanation:
[tex]Area \:of \triangle =\frac{(Height)(Base)}{2}=\frac{(6)(7)}{2}[/tex]
Hope it helps you in your learning process.
f(x) = (2x − 3)(x + 6)(5x + 6) has zeros at x = -6, x = -6/5 and x =3/2.
What is the sign of f on the interval - 6
Answer:
Step-by-step explanation:
f ( - 7 ) = [ 2 ( - 7 ) - 3]( - 7 + 6 )[ 5 ( - 7 ) + 6 ] = ( - 17 )( - 1 )( - 29 ) < 0 , Negative
f ( - 5 ) = [ 2 ( - 5 ) - 3]( - 5 + 6 )[ 5 ( - 5 ) + 6 ] = ( - 13 )( + 1 )( - 19 ) > 0 , Positive
f ( - 1 ) = [ 2 ( - 1 ) - 3]( - 1 + 6 )[ 5 ( - 1 ) + 6 ] = ( - 5 )( + 5 )( + 1 ) < 0 , Negative
The answer is (A) " f " is always POSITIVE
Write a function rule for the table.
f(x) = 4 – x
f(x) = –4x
f(x) = x + 4
f(x) = x – 4
Answer:
f(x) = x – 4
checking for all the functions by replacing x as 3
f(x) = 4 – x
f(3) = 4 - 3
f(3) = 1
does not match
f(x) = –4x
f(3) = -4(3)
f(3) = -12
does not match
f(x) = x + 4
f(3) = 3 + 4
f(3) = 7
does not match
f(x) = x – 4
f(3) = 3 - 4
f(3) = -1
matches
Answer:
f(x) = x - 4
Step-by-step explanation:
The options are:
f(x) = 4 – x
f(x) = –4x
f(x) = x + 4
f(x) = x – 4
For f(x) = 4 – x, when x=3, f(x)=1 so it cannot be right.
For f(x) = –4x, when x=3, f(x)=-12 so it cannot be right either.
f(x) = x + 4, when x=3, f(x)=7 so it cannot be right.
The only choice left which is also the right answer is f(x) = x – 4
Mike’s wooden storage box is 25 inches by 36 inches by 39 inches what is the volume of mike’s box
Answer:
It would be 35100.
please help with this and solve it using the equation
Answer:
E
Step-by-step explanation:
17-9=8 so the answer is 8
Please help with these 2 questions
Write the equation in slope-intercept form of the line parallel to y=4x-2 and passes through (4,6).
Write the equation in slope-intercept form of the line perpendicular to 2x-7y=1 and passes through (0,-4)
Answer:
Step-by-step explanation:
Micha works at a sporting goods store. He is paid $8.25 per hour plus double time on holidays and makes an average of 8% commission on all golfing equipment sales. This is modeled by the expression 8.25(x) + 8.25(2)(y) + 0.08(z). What is Micha's gross pay if he worked 15 regular hours and 4 holiday hours and had $562.00 in golf equipment sales.
$153.00
$229.75
$234.71
$361.06
Answer:
C
Step-by-step explanation:
took test
An expression is defined as a set of numbers, variables, and mathematical operations. The gross pay of Micha for the given month is $234.71. The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that Micha is paid $8.25 per hour plus double time on holidays and makes an average of 8% commission on all golfing equipment sales, which is modeled by the expression 8.25(x) + 8.25(2)(y) + 0.08(z).
Now, if Micha worked 15 regular hours and 4 holiday hours and had $562.00 in golf equipment sales. Therefore, the value of x, y, and z is,
Regular hours, x = 15
Holiday hours, y = 4
Sales made in dollars, z = 562
Substitute the values in the given expression to get the gross pay of Micha in the given year,
Gross pay = 8.25(x) + 8.25(2)(y) + 0.08(z)
= 8.25(15) + 8.25(2)(4) + 0.08(562)
= $123.75 + $66 + $44.96
= $234.71
Hence, the gross pay of Micha for the given month is $234.71.
Learn more about Expression here:
https://brainly.com/question/13947055
#SPJ2
x2-4x=-4 Solve using quadratic formula (find x)
Answer:
x=2
Step-by-step explanation:
[tex]x^2-4x=-4[/tex]
[tex]x^2-4x+4=-4+4[/tex] (Add 4 to both sides)
[tex]x^2-4x+4=0[/tex]
Now, we can solve it using quadratic formula
[tex]x_{1,\:2}=\cfrac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4* \:1* \:4}}{2* \:1}[/tex]
[tex]x_{1,\:2}=\cfrac{-\left(-4\right)\pm \sqrt{0}}{2* \:1}[/tex]
[tex]x=\cfrac{-\left(-4\right)}{2* \:1}[/tex]
[tex]x=2[/tex]
~
(Hello, I have been having problems with this one. That 3 am studying can really hit you lol.)
Two companies build houses.
Company M builds half as many brick houses as wood houses.
The table below shows the relationship between the number of brick houses and wood houses that Company N builds.
Wood Houses: 5, 10, 15, 20
Brick Houses: 3, 6, 9, 12
Each company built 100 wood houses. How many more brick houses did Company N build than Company M?
Answer:
10
Step-by-step explanation:
company N builds 100 wooden houses cut in half which is 50 brick houses, the ratio for company M is 5:3, 5x20=100 3x20=60. 60-50=10
You flip a coin and spin the spinner below. What is the probability that you flip heads and spin a number greater than 2?The spinner has 4 sides and 1-4
Answer:
1/2
Step-by-step explanation:
x/6=67 whats the answer?
Answer:
x would be equal to 11.66 you get this when you divide 67 by 6.
Step-by-step explanation:
Tim made 10 baskets during a basketball game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by Jordan? What's the answer?
The total point is an illustration of arrangements
There are 6 different numbers that could the total points scored by Tim
How to determine the number of total points?The different number (n) that can represent the total point is calculated as:
n = 2 points + 3 points + 1
Remove the units
n = 2 + 3 + 1
Evaluate the sum
n = 6
Hence, there are 6 different numbers that could the total points scored by Tim
Read more about arrangements at:
brainly.com/question/6032811
Please help, I’ll mark your answer as brainliest.
Answer:
Step-by-step explanation:
What region of the graph would satisfy the following system?
y < 2 + 3
3
--
2
2.
Answer:
Step-by-step explanation:
y < 2 + 3
2 < 5
This statement is correct
There are 72 birds and I need them to be in group of 8 how many group would I have.
Answer:
you would have 9 groups!!!!
Answer:
9 brainliest pls
Step-by-step explanation:
I need help with these problems can anyone explain this to me?
I'd love to help!
What's your question?
Brainliest
ABC is a triangle and PQ is parallel to BC.
BC = 12.6 cm, PQ = 8.4cm and AQ = 7.2 cm.
Find AC.
(i know that parallel lines divide triangle sides proportionally, but can someone do a detailed step on AC)
What is the value of p in this proportion? 5/6/p=2/3/1/2 Enter your answer as a simplified fraction in the box. p =
Answer:
5/8
Step-by-step explanation:
2 people can paint a fence in one hour.how long would it take 10 people
Answer: the is the best i could do
its in the image
Answer:
It would take 5 hours for 10 people to paint the fence.
If every hour 2 people paint the fence, keep counting by two's till you get to 10. You get 5. Hope this helps. :)
Simplify the expression.
(In the picture)
Answer:
18x2y^2^3√3xy2 <-- scratch that its D
Step-by-step explanation:
A stone pyramid in Egypt has a square base that measures 149 m on each side. The height is 91 m. What is the volume of the pyramid
Check the picture below.
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} B=\stackrel{base}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{149\times 149}{22201}\\ h=91 \end{cases}\implies V=\cfrac{(22201)(91)}{3}\implies V=673430.\overline{3}~m^3[/tex]
Somebody help me please
Answer:
see explanation
Step-by-step explanation:
given
(2x + 5)(2x - 1) ← expand using FOIL
(a)
= 4x² - 2x + 10x - 5 ← collect like terms
= 4x² + 8x - 5
(b)
using the method of completing the square on
4x² + 8x - 5 ← factor out 4 from the 1st 2 terms
= 4(x² + 2x) - 5
to complete the square
add/ subtract ( half the coefficient of the x- term )² to x² + 2x
= 4(x² + 2(1)x + 1 - 1) - 5
= 4(x + 1)² - 4 - 5
= 4(x + 1)² - 9
Where are all my math nerds and experts at? Help me out!
Triangle ABC has angle measures as shown below. Using the information in the diagram, find the value of x.
In your answer, give the value of x and explain how you calculated it.
Solution:
The interior angles of a triangle sum up to 180°
This means that...
3(x + 2) + 52 + 35 = 180Simplify the distributive property.
3x + 6 + 52 + 35 = 180Combine like terms.
3x + (6 + 52 + 35) = 180=> 3x + (93) = 180Subtract 93 both sides.
3x + (93) = 180=> 3x + 93 - 93 = 180 - 93Simplify both sides.
=> 3x = 87Divide 3 both sides.
=> 3x/3 = 87/3 => x = 87/3 = 29There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 8 meters high, and the hook is 2 meters from its base. How long is the rope? If necessary, round to the nearest tenth.
ASAP Please!
Answer: 8.2m
Step-by-step explanation:
Let the hook that is 2m from the base represent a
Let the height of the flagpole represent b
The length of the rope (hypotenuse) is c
[tex]\begin{aligned}&a^{2}+b^{2}=c^{2} \\&2^{2}+8^{2}=c^{2} \\&4+64=c^{2} \\&\sqrt{68}=\sqrt{c}^{2}\end{aligned}\\c= 8.25m[/tex]
Add or subtract the following polynomials.
1. 7x-(4xy+12xy)-2
2. (5bc)-(5+bc)
3. 7+(2x-5x)+y
4. 6x+10+[3x-6x]
5. 3x²y-(5x²y)
With solutions pls
Answer 1:
7x-16xy-2
Answer 2:
4bc-5
Answer 3:
7-3x+y
Answer 4:
3x+10
Answer 5:
-2x²y
Solving Solutions Question #1
*Remove the parentheses for addition or subtraction*
[tex]7x-\left(4xy+12xy\right)-2[/tex]
*Determine the sign*
[tex]7x-4xy-12xy-2[/tex]
*Reorder and gather like terms*
[tex]7x+\left(-4xy-12xy\right)-2[/tex]
*Collect coefficients of like terms*
[tex]7x+\left(-4-12\right)\timesxy-2[/tex]
*Calculate the sum or difference*
[tex]7x-16xy-2[/tex]
Solving Solutions Question #2*Simplify or expand*
[tex]5bc-\left(5+bc\right)[/tex]
*Remove the parentheses for addition or subtraction*
[tex]5bc-5-bc[/tex]
*Reorder and gather like terms*
[tex]\left(5bc-bc\right)-5[/tex]
*Collect coefficients of like terms*
[tex]\left(5-1\right)[/tex] [tex]\times[/tex] [tex]bc-5[/tex]
*Collect the sum or difference*
[tex]4bc-5[/tex]
Solving Solution Question #3*Simplify or expand*
[tex]7+(2x-5x)+y[/tex]
*Determine the sign*
[tex]7+2x-5x+y[/tex]
*Reorder and gather like terms*
[tex]7+\left(2x-5x\right)+y[/tex]
*Collect coefficients of like terms*
[tex]7+\left(2-5\right)\timesx[/tex] [tex]\times[/tex] [tex]x+y[/tex]
*Calculate the sum or difference*
[tex]7-3x+y[/tex]
Solving Solution Question #4*Simplify or expand*
[tex]6x+10+(3x-6x)[/tex]
*Determine the sign*
[tex]6x+10+3x-6x[/tex]
*Reorder and gather like terms*
[tex](6x+3x-6x)+10[/tex]
*Collect coefficients of like terms*
[tex](6+3-6)[/tex] × [tex]x+10[/tex]
*Apply the Inverse Property of Addition*
[tex]3x+10[/tex]
Solving Solution #5*Simplify or expand*
[tex]3x^{2} y-5x^{2} y[/tex]
*Collect coefficients of like terms*
[tex](3-5)x^{2} y[/tex]
*Calculate the sum or difference*
[tex]-2x^{2} y[/tex]
I hope this helps you:)