Answer:
The series has 7 terms
[tex]\displaystyle S_7=\frac{4372}{243}[/tex]
Step-by-step explanation:
Geometric Series
In the geometric series, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the series:
-12, -4, -4/3, ..., -4/243
We can find the common ratio by dividing one term by the previous term:
[tex]\displaystyle r=\frac{-4}{-12}[/tex]
Simplifying:
[tex]\displaystyle r=\frac{1}{3}[/tex]
Sum of terms: Given a geometric series with first term a1 and common ratio r, the sum of n terms is:
[tex]\displaystyle S_n=a_1\frac{1-r^n}{1-r}[/tex]
We need to find how many terms the series has. Using the explicit formula of a geometric series:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
The last term is an=-4/243 and the first term is a1=-12. Solving for n:
[tex]\displaystyle n= \frac{\log(a_n/a_1)}{\log r}+1[/tex]
[tex]\displaystyle \frac{\log(-4/243/-12)}{\log 1/3}+1[/tex]
[tex]\displaystyle \frac{\log(1/729)}{\log 1/3}+1[/tex]
n=7
The series has 7 terms
Thus, the sum of the 7 terms of the series is:
[tex]\displaystyle S_7=-12\frac{1-(1/3)^7}{1-(1/3)}[/tex]
[tex]\mathbf{\displaystyle S_7=\frac{4372}{243}}[/tex]
Please help me with this
Answer:
x = 19 degrees
y = 84 degrees
Step-by-step explanation:
recall that for an isosceles triangle (which is pictured), the base angles have the same value.
In our case, we can see that the base angles are 48 deg and (3x-9) deg
if they are equal, we can equate them like this:
48 = 3x-9 (add 9 to each side)
48 + 9 = 3x
57 = 3x (divide both sides by 3)
x = 57/3
x = 19 degrees (answer)
also recall that the sum of the interior angles of a triangle add up to 180 deg, hence
48 deg + 48 deg + y deg = 180 deg
2(48) + y = 180
96 + y = 180
y = 180 - 96
y = 84 deg
Can anyone tell me what this graph is in slope intercept form?
Answer:
the standard form equation is 1/2x^2-x-3/2=0
the vertex form equation is 1/2(x-1)^2-2=0
Step-by-step explanation:
Unfortunately, this can't be written in slope intercept form but I can write it in standard form(ax^2+bx+c) or vertex form (a(x-h)+k)
The vertex is (1,-2)
I estimate a=1/2 because the graph was widened and that can only be done by a fraction.
So, 1/2(x-1)^2-2=0
To find it in standard form
foil (x-1)(x-1)= x^2-2x+1
Then multiply by 1/2(x^2-2x+1)= 1/2x^2-x+1/2-2
To add 1/2-2. You mulitply -2 by 2/2 which equals 1/2-4/2 which equals -3/2
So the standard form equation is 1/2x^2-x-3/2=0
Please help:
Erin had 3 1/9 boxes of granola bras. She gave 1 3/4 of the boxes to her friends. How much did Erin have left for herself?
Answer:
1 13/36
Step-by-step explanation:
i just subtracted 1 3/4 from 3 1/9
What is (8 × 10 -3 )(.0003) in scientific form.
Answer:
2.31 ×10 ^− 2
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
HELP ME!! please help me
Answer:
7xy + 2x^2t
Step by step explanation:
You just group the like terms and simplify (pay attention to the signs)
5xy + 2xy = 7xy
-1x^2t + 3x^2t = 2x^2t
So the answer is : 7xy + 2x^2t
1. Given f(x) = 3x – 4 and g(x)=–2x+7 evaluate:
(fog)(5)
Answer:
(f o g)(5) = -13
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlgebra I
Composition of functionsStep-by-step explanation:
Step 1: Define
f(x) = 3x - 4
g(x) = -2x + 7
(f o g)(5) is f(g(5))
Step 2: Find composite function
Substitute: (f o g)(x) = 3(-2x + 7) - 4Distribute: (f o g)(x) = -6x + 21 - 4Combine like terms: (f o g)(x) = -6x + 17Step 3: Solve
Substitute: (f o g)(5) = -6(5) + 17Multiply: (f o g)(5) = -30 + 17Add: (f o g)(5) = -132. What are the slope and y-intercept of the
line described by y = 3x - 6?
Answer:
If your trying to find the slope and y-int of that equation:
Slope: 3
y-int: (0, -6)
Which notation best represents the phrase “at least 24”?
Answer:
less than or equal to 24
Step-by-step explanation:
this symbol ≤
7/2X – 19 = -13 + 2x
what is the solution equation?
please help i give brainliest
Answer:
9 cm
Step-by-step explanation:
The standard width of a tennis court is 27 feet. If 1 meter ≈ 3.3 feet, what is the width of the tennis court in meters? Round to the nearest tenth, if necessary.
Answer:
8.2 meters (8.18 without rounding)
Step-by-step explanation:
27 divided by 3.3 = 8.2 meters
ASAP PLEASE!!!
Find the supplementary angle of an angle measuring 183. If the supplementary angle does not exist, explain why. (1 point)
The supplementary angle is 177,
The given angle does not have a supplementary angle because supplementary angles add to the sum of 360'. The supplementary angle would need
to be 177 , and the supplement for it cannot be greater than 90° based on the definition of supplementary angles.
The supplementary angle is 107
The given angle does not have a supplementary angle because supplementary angles add to the sum of 180°. The supplementary angle would then
need to be -3, and negative angles are not allowed based on the definition of supplementary angles.
Answer:
"The given angle does not have a supplementary angle because supplementary angles add to the sum of 180°. The supplementary angle would then need to be -3, and negative angles are not allowed based on the definition of supplementary angles."
Step-by-step explanation:
A supplementary angle completes an angle less than 180 degrees by filling in what's left. Ex. 170 and 10 are supplementary angles because they add up to a straight line, 180.
Since 183 is greater than 180, no angle (a negative angle isn't an angle) can complete it.
The concurrency of which lines create the Centroid?
A. Perpendicular Bisectors B. Medians
C. Angle Bisectors
D. Altitudes
Which of the following isn't true about the graph of a proportional relationship? A. it is a straight line B. it passes through the origin C. it is "U" shape.
Answer:
Its B or it can be A because there both right
Lewis is saving for a down payment of $8,750 on a house. The initial amount of money he has saved is $250, and the amount of money he plans on saving every month is $340. To model the situation, he created this equation, where x represents the number of months and y represents the total amount of savings: y = 250 + 340x. Determine the missing steps and justifications.
Answer:
8,750 = 250 + 340x
I believe he is missing the cost of the house
ok I'm bout to get to the point my mother hates people that don't are not straight and I'm bi so how do I come out to my mom and my BSF
Answer:
you should life make a cake and put frosting words on it that say I'm bi and i'm proud!
You should just sit down with her and talk about it
Fran and Winston have a combined income
of $80 000. One quarter of Winston's income
is the same as one-sixth of Fran's income.
How much does each person earn?
Answer:
Winston:$32,000
Fran:$48,000
1 of 4 parts is equal to 1 of 6 parts so if you add 4 parts to 6 parts you get 10. Divide the total amount by 10 and you get 8000. multiply 8000 to the amount of parts each person gets and you get that.
Plz help guys answer this!!!!
Answer:
Between steps B and C
Step-by-step explanation:
12 × 5 is 60 not 72
and - × -9y = 9y
the answer should be [tex]\frac{-65}{11}[/tex]
Express 345200000 in standard form
Answer:
3.452 × 10^8
Step-by-step explanation:
hope this helps :)
Identify the equation in point-slope form for the perpendicular bisector of the segment with endpoints J(−24,−4) and K(−4,6).
Option A:
y + 6 = 2(x − 4)
Option B:
y − 6 = 2(x + 4)
Option C:
y + 1 = −2(x − 14)
Option D:
y − 1 = −2(x + 14)
Given:
Endpoints of a segment are J(−24,−4) and K(−4,6).
To find:
The equation in point-slope form for the perpendicular bisector of JK.
Solution:
Slope of JK is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{6-(-4)}{-4-(-24)}[/tex]
[tex]m=\dfrac{6+4}{-4+24}[/tex]
[tex]m=\dfrac{10}{20}[/tex]
[tex]m=\dfrac{1}{2}[/tex]
Product of slopes of two perpendicular lines is -1. So, product of perpendicular line of JK is -2.
Perpendicular bisector of JK passes through the midpoint of JK.
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-24-4}{2},\dfrac{-4+6}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-28}{2},\dfrac{2}{2}\right)[/tex]
[tex]Midpoint=\left(-14,1\right)[/tex]
Point slope form:
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope.
Perpendicular bisector of JK passes through (-14,1) with slope -2. So, the point slope form of JK is
[tex]y-1=-2(x-(-14))[/tex]
[tex]y-1=-2(x+14)[/tex]
Therefore, the correct option is D.
The length of a rectangular park is 20 feet longer than the width of the park. If the length of the park is 36 feet, what is the width of the park?
A.
4 feet
B.
16 feet
C.
42 feet
D.
56 feet
Answer: B. 16 feet
Step-by-step explanation:
We know that the length is 20 feet longer that the width. If the length of the park is 36 feet, the width is 20 feet less.
36 - 20 = 16 feet
So, the width of the park is 16 feet.
hope this helps!
simplify (2x − 5)(3x² + 7x− 8)
Answer:
6x³-x²-51x+40
Step-by-step explanation:
(2x − 5)(3x² + 7x− 8)
vv
6x³ +14x² -16x -15x² -35x +40
add like terms:
6x³ -x² -51x +40
Can someone please help
Answer:
5.6<x<∞
Step-by-step explanation:
x has to be no less than or equal to 2.8+2.8. So, x>5.6
x is less than∞
Kim was walking down a rocky path. For 6 minutes, the elevation
dropped uniformly. Altogether it dropped 12 feet. What was the change in
elevation per minute for the 6 minutes?
Answer:
2 feet
Step-by-step explanation:
12 feet in 6 minutes. 12/6=2
if f(x) = 2(x – 3) + 4, findf (-8).
Answer:
f(-8) = -18
Step-by-step explanation:
given :
f(x) = 2(x – 3) + 4
to find f(-8), simply substitute x= -8 into the function:
f(x) = 2(x – 3) + 4
f(-8) = 2[(-8) – 3] + 4
= 2[-8 – 3] + 4
= 2[-11] + 4
= -22+4
= -18
I need help on this one
(IF YOU HELP ME THANKSSS SO MUCH ❤)
Answer: B
Hope you do well!
Please use y=mx+b form or else it won’t work
Answer:
Y=6/5x+5
Step-by-step explanation:
Graph f(x)=3/2x+2. plz help
Answer:
draw a line trough (2,3) and (0, 2)
Step-by-step explanation:
f(x)=(3/2)x+2
so 3/2 is your slope and 2 is your y coordinate of y-intercept
pick any point to start for example (0, 0) and go slope=rise/run=3/2 and you will end-up at (2,3)
now you have a point (2,3) and a second the y-intercept (0,2)
draw a line trough those points
You bought your friend's bike and owe $60.00 to your friend to finish paying for it. You do chores and earn $4.00 per day (7 days per week). If you give your friend all your money how much money would you have after 3 weeks of working?
Answer:
$24.
Step-by-step explanation:
I multiplied 4 by 7 to get 28. Then I multiplied $28 by three weeks and got $84. Since $84 is more than I owe I subtracted $84 by $60 and got $24. I would give my friend $60 and keep $24. Hope this helps! Have a great day!
30 POINTS!! HELP ME PLS!!!
Answer:
Just kidding
Step-by-step explanation:
I dont know