Find the 8th term of the geometric sequence 7,−21,63,
Answer:
8th term is -15309
Step-by-step explanation:
[tex]{ \boxed{ \bf{u_{n} = a( {r}^{n - 1} ) }}} \\ { \tt{u_{8} = 7( {( - 3)}^{8 - 1}) }} \\ { \tt{u_{8} = 7( - 2187)}} \\ { \tt{u _{8} = - 15309}}[/tex]
r is the common difference, r = -21/7 = -3
Answer:
a₈ = - 15309
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{7}[/tex] = - 3 , then
a₈ = 7 × [tex](-3)^{7}[/tex] = 7 × - 2187 = - 15309
An investor has an account with stock from two different companies. Last year, his
stock in Company A was worth $6600 and his stock in Company B was worth $3500.
The stock in Company A has increased 7% since last year and the stock in Company B
has increased 1%. What was the total percentage increase in the investor's stock
account? Round your answer to the nearest tenth (if necessary).
Simplify and find the perimeter of the triangle
Answer:
2x - 19
Step-by-step explanation:
Perimeter = sum of sides
First let's simplify each side
We can simplify each side by using distributive property. Distributive property is where you multiply the number on the outside of the parenthesis by the numbers on the inside of the parenthesis.
2(x + 5)
Distribute by multiplying x and 5 by 2
2 * x = 2x and 2 * 5 = 10
2x + 10
1/2(4x + 8)
Distribute by multiplying 4x and 8 by 1/2
1/2 * 4x = 2x and 1/2 * 8 = 4
2x + 4
-3(2x + 11)
Distribute by multiplying 2x and 11 by -3
-3 * 2x = -6x
-3 * -33
-6x - 33
Finally add all the simplified expressions ( remember that they represent the side lengths of the triangle )
2x + 10 + 2x + 4 - 6x - 33
Combine like terms
2x + 2x - 6x = -2x
10 + 4 - 33 = -19
Perimeter: -2x - 19
Answer:
Perimeter = - 2x - 19
Step-by-step explanation:
[tex]Perimeter \: of \: a \: triangle \\ = Sum \: of \: the \: length \: of \: all \: sides \\ = [2(x+5)]+[-3(2x+11)]+[ \frac{1}{2} (4x+8)] \\ = [(2 \times x)+(2 \times 5)]+[(-3 \times 2x)+( - 3 \times 11)]+[ (\frac{1}{2} \times 4x) + ( \frac{1}{2} \times 8)] \\ = (2x + 10) + ( - 6x - 33) + (2x + 4) \\ = 2x + 10 - 6x - 33 + 2x + 4 \\ = 2x - 6x + 2x + 10 - 33 + 4 \\ = - 2x - 19[/tex]
So, the perimeter is - 2x - 19.
factor: 3x^(2)-16x+16
Answer:
[tex]3 {x}^{2} - 16x + 16 \\ 3 {x}^{2} - 12x - 4x + 16 \\ 3x(x - 4) - 4(x - 4) \\ (3x - 4)(x - 4)[/tex]
Step-by-step explanation:
I hope it helped U
stay safe stay happy
31. Which choice describes the value of m when -5(m + 1) = 23?
А
B.
m 2-3
ms-
6 m2
D.ms-
Answer:
The correct choice is Option A. m ≥ -28/5
Step-by-step explanation:
What quantity of parsley would you need to make 5 times as much as the original recipe?
1. Three products from renewable resources are
Answer:
biomass energy (such as ethanol), hydropower, geothermal power, wind energy, and solar energy.
100÷50000 it's has to be step by step aka show work
100÷50000 can be written as 100/50000, then cancel out 2 of the zeroes, and you will get 1/500 or 0.002 as your final answer.
Write 128 as a product of its prime factors
Answer:
The prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2.
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
John earns $6 per hour for mowing the lawn. If t represents John's total earnings for h hours of mowing, which equations can be used to model the situation
Answer:
h=6
Step-by-step explanation:
how many metres of wire is needed to fence a circular pond of radius 7.7m if the fence is to have three strands of wire all the way around .Give your answer correct to one decimal place. (Take pi is 3.14)
Find the circumference of the pond:
Circumference = 2 x pi x radius
Circumference = 2 x 3.14 x 7.7 = 48.356 m
You want to go around 3 times so multiply the circumference by 3:
48.356 x 3 = 145.068m
Rounded to 1 decimal = 145.1m
so i need help with this pls i suck at algebra
Answer:
The 5x^2 vs -5x^2 will reflect over "X" axis
the +1 vs -2 will shift the graph down three units
the first answer is the correct answer
Step-by-step explanation:
If ram have 30 apple& each apple rs is 26 . 14 are rotten .he had eat 9 apple. 6 apple he sold each price 35 . Now say me ram have got profit or loss.
Answer:
Profit
Step-by-step explanation:
30*26
14*26
9*14
6*26*30
3. If bº = 110°, what is the value of gº?
Answer:
hello mate <3
u see here its a quadrialteral
with 4 angles b , d , 70 , g
so b + d + 70 + g = 360
now u see 60 + d = 180 (straight line)
d = 120 and b = 110 ( given)
so
110 + 120 + 70 + g = 360
g + 300 = 360
g = 360 - 300 = 60 degrees option c
brainliest?
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.
PLSSS SHOW WORK <3
Answer:
x = 18
Step-by-step explanation:
First, let's find the ratios between the two triangles
We'll use AV and AC
372 ÷ 589 = 12/19
All of the sides of the smaller triangle are 12/19 of the bigger triangle
Now let's find x
We know that AU + UB = AB
So it's 20x + 108 + 273 = AB
12/19 of a bigger triangle side equals a small triangle side
(12/19)AB = AU
For this equation multiply both sides by 19/12 to isolate AB
(12/19)AB x 19/12 = AU x 19/12
AB = (19/12)AU
Now we have this
20x + 108 + 273 = (19/12)(20x + 108)
20x + 381 = (19/12)(20x + 108)
Distribute the 19/12
20x + 381 = 95/3x + 171
Move all like terms to one side
20x + 381 = 95/3x + 171
- 171 - 171
20x + 210 = 95/3x
- 20x - 20x
Don't forget about common denominators
210 = 95/3x - 60/3x
210 = 35/3x
Multiply both sides by 3
210 x 3 = 35/3x x 3
630 = 35x
Divide both sides by 35
630/35 = 35x/35
x = 18
Answer:
Step-by-step explanation:
[tex]\frac{20x+108}{20x+381}[/tex] = [tex]\frac{372}{589}[/tex]
589( 20x + 108 ) = 372( 20x + 381 )
11780x + 63612 = 7440x + 141732
4340x = 78120
x = 18
Please help me this on the picture
Answer:
Step-by-step explanation:
125 + (a-b)³ help me
Answer:
(5 + a - b)(a² + b² - 2ab - 5a + 5b + 25)
Step-by-step explanation:
125 + (a - b)³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
Then
125 + (a- b)³
= 5³ + (a - b)³
with a = 5 and b = (a - b)
= (5 a a - b)(5² - 5(a - b) + (a - b)² )
= (5 + a - b)(25 - 5a + 5b + a² - 2ab + b²)
= (5 + a - b)(a² + b² - 2ab - 5a + 5b + 25)
The sum of 30 terms of series in A.P, whose last term is 98, is 1635. Find the first term and the common difference.
Let a(n) denote the n-th term in the sequence. Because the terms are in arithmetic progression, there is a fixed number d that separates consecutive terms, so that starting with a(1) = a, the next few terms are
a(2) = a(1) + d = a + d
a(3) = a(2) + d = a + 2d
a(4) = a(3) + d = a + 3d
and so on, up to
a(n) = a + (n - 1) d
We're given that the 30th term is 98, so
a(30) = a + 29d = 98
The sum of the first 30 terms is 1635, so that
[tex]\displaystyle \sum_{n=1}^{30}a(n) = \sum_{n=1}^{30}(a+(n-1)d) \\\\ 1635 = a\sum_{n=1}^{30}1 + d\sum_{n=1}^{30}(n-1) \\\\ 1635 = 30a + d\sum_{n=0}^{29}n \\\\ 1635 = 30a + d\sum_{n=1}^{29}n \\\\ 1635 = 30a + \frac{d\times29\times30}2[/tex]
so that
30a + 435d = 1635
Solve the equations in boldface for a and d. I'll eliminate a and solve for d first.
-30 (a + 29d) + (30a + 435d) = -30 (98) + 1635
-30a - 870d + 30a + 435d = -2940 + 1635
-435d = -1305
d = 3
Then
a + 29 (3) = 98
a + 87 = 98
a = 11
Setting y = 0 allows you to determine the what
of a graph
[tex]y=0[/tex] allows you to determine the x-intercept of a graph.
x-intercept and y-intercept:The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept. Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.When y is 0, the x-intercept is reached. The graph's intersection with the y-axis, or (0, b), is known as the y-intercept. When x is 0, the y-intercept is reached. When y is 0, the x-intercept is reached.Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.
Know more about x-intercept and y-intercept here:
https://brainly.com/question/24363347
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What number line shows Point A at -4, Point B at 2.5, Point C at -2 1/2, and Point D, which is the opposite of Point A.
Answer: Choice A
Explanation:
Since -3/5 > -0.8, this means -3/5 is to the right of -0.8
Larger stuff is to the right of smaller stuff. Another example would be 10 > 7, meaning we have 10 to the right of 7 since 10 is larger.
Any negative value is always to the left of 0, so -3/5 is to the left of 0.
That's why the answer is choice A.
 A study found that healthy eating can help to cut the risk of heart disease. Therefore, a person can conclude that if they eat healthy they definitely will not have any heart issues.
True or false?
Answer:
False
Step-by-step explanation:
It only cuts the risk as stated and other factors such as lifestyle, age, bloodpressure and past medical background also have an impact so you can still have heart issues.
2. If you move 50 meters in 10 seconds, what is your speed?
Answer:
5 meters per second
Step-by-step explanation:
Find your speed by dividing the number of meters traveled by the number of seconds it took:
50/10
= 5
Your speed is 5 meters per second.
Answer:
5 m/sec
Step-by-step explanation:
The speed would be calculated as follows, as a unit rate:
50 m
----------- = 5 m/sec
10 sec
I need help ASAP!! Please explain how to solve the problem
Answer:
B=.5*8*6=.5*48=24
h = 8
P=10+6+8=24
Surface area =2*24+24*8=48+192=240
Step-by-step explanation:
The base is a triangle, and the area of a triangle is 1/2 base (or width) times height (or length). In this case, base is 8 and height is 6, so the area can be found either by multiplying .5*8*6 or by dividing 8*6 by 2, either of which will give you the same answer of B=24.
Height is given, h=8.
Perimeter is simply the sum of the sides, which are given, so the perimeter is 8+6+10=24.
The formula for surface area is given, so all you need to do is plug in your previous answers and you've got it!
HELPPP PLZZZZ DUE SOONnnn
Answer:
x = 7, EF = 10, FG = 12
Step-by-step explanation:
EF = 4x - 18
FG = 3x - 9
EG = 22
EG = 22
EF + FG = 22
4x - 18 + 3x - 9 = 22
4x + 3x - 18 - 9 = 22
7x = 22 + 18 + 9
7x = 49
x = 7
EF = 4x - 18
EF = 4*7 - 18
EF = 28 - 18
EF = 10
FG = 3x - 9
FG = 3*7 - 9
FG = 21 - 9
FG = 12
simplify 4x^2-3xy+2xy+9x^2
Answer:
13x^2 - xy
Step-by-step explanation:
4x^2-3xy+2xy+9x^2
=13x^2-xy
"A parabola has the equation = ^ + − . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way
Answer:
1
Step-by-step explanation:
1
What is 4,327 rounded to the nearest thousand?
Answer: 4,000
Step-by-step explanation: To round 4,327 to the nearest thousand, we first find the digit in the rounding place, which in this case is the 4 in the thousands place. Next, we look at the digit to the right of the 4, which is 3.
According to the rules of rounding, since the digit to
the right of the rounding place is less than 5, we round down.
So the 4 in the rounding place stays the same
and all digits to the right of the 4 become 0.
So 4,327 rounded to the nearest thousand is 4,000.
if a = 6 b=5, then find the value (a+b)
Step-by-step explanation:
Put the numbers as the value is given
So,
(6+5)= 11 Answer
What is the slope of a trend line that passes through the points (1, 3) and (10, 25)?
Negative StartFraction 15 Over 2 EndFraction
Negative one-half
StartFraction 22 Over 9 EndFraction
StartFraction 24 Over 7 EndFraction
Answer:
[tex]\displaystyle m = \frac{22}{9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (1, 3)
Point (10, 25)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{25 - 3}{10 - 1}[/tex]Subtract: [tex]\displaystyle m = \frac{22}{9}[/tex]Answer:
c
Step-by-step explanation:
1. The position of a particle moving along a coordinate axis is given by: s(t) = t^2 - 5t + 1. a) Find the speed of the particle b) Find the acceleration of the particle c) Find the velocity of the particle
Answer: [tex]\left | 2t-5\right |,\ 2,\ 2t-5[/tex]
Step-by-step explanation:
Given
Position of the particle moving along the coordinate axis is given by
[tex]s(t)=t^2-5t+1[/tex]
Speed of the particle is given by
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=\left | 2t-5\right |[/tex]
Acceleration of the particle is
[tex]\Rightarrow a=\dfrac{dv}{dt}\\\\\Rightarrow a=2[/tex]
velocity can be negative, but speed cannot
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=2t-5[/tex]
