Step-by-step explanation:
with the introduction of fractions it is clear we are multiplying things to get the sequence.
that makes this a geometric sequence, meaning that every new term is created by multiplying the previous term by a certain constant number, the ratio r.
what do we have to multiply with the first term (6) to get -4 ?
6×r = -4
r = -4/6 = -2/3
to check we use the same factor with the second term and see, if we get the predefined third term :
-4 × -2/3 = 8/3
correct, perfect.
so,
a0 = 6
an = an-1 × -2/3 = a0 × (-2/3)^(n-1) = 6 × (-2/3)^(n-1)
for the sum of a finite number of terms of a geometric sequence the formula is :
Sn = a0×(r^n - 1) / (r - 1) if |r| > 1
Sn = a0×(1 - r^n) / (1 - r) if |r| < 1
Sn = a0×n if r = 1
in our case : |-2/3| = 2/3 < 1
S8 = 6×(1 - (-2/3)⁸) / (1 - (-2/3)) =
= 6×(1 - 256/6561) / (3/3 - -2/3) =
= 6×(6561/6561 - 256/6561) / (5/3) =
= 6×(6305/6561) × (3/5) = 2×(6305/2187) × (3/5) =
= 2×(1261/2187) × 3 = 2×(1261/729) =
= 2522/729 = 3.459533608...
≈ 3.46
What is the equation of a line that passes through (-1,2) and (1,8)?
Answer:
y=3x+5
Step-by-step explanation:
first you find the slope by doing rise over run. then you would put the slope into point-slope formula which is y-y1=m(x-x1), then you simplify into y=mx+b (slope intercept form). which gets you your final answer.
what is y=-2(x+1)(x-2) in standard form
[tex] \leadsto \tt y=-2(x+1)(x-2)[/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \tt y=-2(x {}^{2} - 2x + x - 2)[/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \tt y=-2(x {}^{2} - x - 2)[/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \tt y=-2x {}^{2} + x + 2[/tex]
How much would it cost to buy x pounds of oranges? If oranges were 1.25$
Answer:
$20
Step-by-step explanation:
if one ound = 16 ounces then you would do 1.25x16 witch equals $20
If oranges were 1.25$ per pound. then the cost to buy x pounds of oranges would be 1.25x $.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If oranges were 1.25$ per pound. We need to find the cost to buy x pounds of oranges.
The cost of oranges per pound = 1.25$
The cost of oranges x pound = 1.25$ × x
= 1.25x $
Thus, The cost to buy x pounds of oranges would be 1.25x $.
Learn more about the unitary method;
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What is the radius of this circle?
A) 3.14 inches
B) 5 inches
C) 10 inches
D) 20 inches
Answer:
C
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Mrs. Juarez graded ten English papers and recorded the scores.
92, 95, 100, 62, 88, 90, 100, 96, 89, 98
Which statements are true? Check all that apply.
The range of scores is 38.
Without the outlier, the range of scores would be 12.
The outlier impacts the range more than it impacts the interquartile range.
The interquartile range is 9.
The interquartile range is 4.
Without the outlier, the interquartile range would be 9.5.
Answer:
THE ONLY STATEMENT THAT IS FALSE IS THE NUMBER 5.
Step-by-step explanation:
Table of ordered data
number of value
data
1 62
2 88
3 89
4 90
5 92
6 95
7 96
8 98
9 100
10 100
Range of scores: 100 - 62 = 38
Oulier: 62 => Range without the outlier = 100 - 88 = 12
Interquartile range, IQR, = difference between third quartile and first quartile: IQR = Q3 - Q1
Quartlies of all the data:
1 62
2 88
3 89 --------------- first quartile, Q1 = 89
4 90
5 92
------------------------------------------ median, Q2 = (95 + 92) / 2 = 93.5
6 95
7 96
8 98 ---------------- third quartile, Q3 = 98
9 100
10 100
=> IQR = 98 - 89 = 9 : the interquartle range is 9
Quartlies without the outlier:
2 88
3 89
------------------------------------- first quartile, Q1 = (89 + 90) / 2 = 89.5
4 90
5 92
6 95 --------------- median, Q2 = 95
7 96
8 98
------------------------------------ third quartile, Q3 = (98 + 100) / 2 = 99
9 100
10 100
=> IQR = Q3 - Q1 = 99 - 89.5 = : the interquartle range without the outlier is 9.5
Therefore, the outlier impacts more the range than it impacts the IQR.
THE ONLY STATEMENT THAT IS FALSE IS THE NUMBER 5.
Plz help wit this
What is the value of x?
Answer:
x = 15
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )
x² = 9 × (9 + 16) = 9 × 25 = 225 ( take square root of both sides )
x = [tex]\sqrt{225}[/tex] = 15
Answer:
I did this quickly, so please check the logic.
I find x = 15
Step-by-step explanation:
See attached image. Note that I've defined 3 triangles and their Pythagorean equations. I also define a third line, RQ, as z. Rearrange the equations and substitute in a way that allows elimination of all variables except x.
Solve for x by completing the square: x2 - 12x + 11 = 0
A.
(-11,0) and (1,0)
B.
(1,0) and (11,0)
C.
(0,1) and (0,-11)
Answer:
B
Step-by-step explanation:
x² - 12x + 11 = 0 ( subtract 11 from both sides )
x² - 12x = - 11
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 6)x + 36 = - 11 + 36
(x - 6)² = 25 ( take square root of both sides )
x - 6 = ± [tex]\sqrt{25}[/tex] = ± 5 ( add 6 to both sides )
x = 6 ± 5
Then
x = 6 - 5 = 1 ⇒ (1, 0 )
x = 6 + 5 = 11 ⇒ (11, 0 )
During his career, Michael Jordan scored an average of 31 points per
game. ESTIMATE the number of points you would expect Michael Jordan
to score in 5 games.
what should be added to (-5 a2b - 9 ab) to get
a2b + 3 ab?
Based on given conditions,
[tex]a²b + 3 ab - (-5 a²b - 9 ab) [/tex]
[tex]→a²b + 3 ab + 5 a²b + 9 ab[/tex]
[tex]→(a²b + 5 a²b) + (3ab + 9 ab[/tex]
Now collecting the coefficients and adding them,
[tex](1 + 5)a²b + (3 + 9)ab[/tex]
[tex]→6 {a}^{2}b + 12ab[/tex]
Hence, the 6a²b + 12ab should be added.
(2,-2) and m=3 Find the slope intercept.
y= mx=b.y= 3x-8
Step-by-step explanation:
lmk if its wrong
Daniel is playing on the swings at the playground. At the top of his swing, he will have _____.
neither potential nor kinetic energy
some potential energy and some kinetic energy
no potential energy and all kinetic energy
all potential energy and no kinetic energy
big points
Answer: all potential energy and no kinetic energy
Step-by-step explanation:
please help with these 2 questions!! (9 and 10) please show with solution needed!!
Can someone please help me with the square root question?
Answer:
a ≈ 9.8 yd³
Step-by-step explanation:
Given: V ≈ 941 yd³
Using the formula: V = a³
Solving for a: A = [tex]V^{\frac{1}{3} }[/tex] = [tex]941^{\frac{1}{3} }[/tex] ≈ 9.79933
Round to the nearest tenth: a ≈ 9.8
In Newport, the library is 66 miles due south of the courthouse and 88 miles due west of the community swimming pool.
What is the distance between the courthouse and the community swimming pool?
Answer:
110
Step-by-step explanation:
Use the pythagorean theorem (a^2 + b^2 = c^2) to solve it. 66 is a and 88 is b. The distance between them is c.
Sally has 24 cookies. She has to share the cookies with 3 friends. How can they split them evenly?
Answer:
They each get 8 cookies
Step-by-step explanation:
24 divided by 3 is 8. There are other ways if the question allows there to. be some cookies left over.
What is the equation of the line that passes through the point (-6, -7) and has a
slape of 0?
Answer:
y=0x-7 or y=-7
Step-by-step explanation:
Hi there!
We want to write the equation of the line that passes through the point (-6, -7), but that also has a slope of 0
There are many ways to write the equation of the line; one of the most common ways is to use slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
As we are already given the slope of this line, we can immediately plug it into the equation as m
So substitute 0 as m in the equation:
y=0*x+b
Multiply
y=0x+b
We can also rewrite it as y=b, but for right now, y=0x+b will be helpful for our calculations
We need to find b now.
As the equation passes through the point (-6, -7), we can use it to help solve for b
Substitute -6 as x and -7 as y:
-7=0(-6)+b
Multiply
-7=0+b
Simplify
-7=b
Substitute -7 as b into the equation.
y=0x-7, or y=-7
Hope this helps!
Take a look here for a similar problem for practice if you wish: https://brainly.com/question/25424204
im very c0nfused help
Answer:
x = 13°
Step-by-step explanation:
The left base angle of the triangle with x as the vertex is vertically opposite 85° and are congruent.
left base angle = 85°
the angle below the right base in the triangle is corresponding to 98° and are congruent.
right base angle = 180° - 98° = 82° ( adjacent angles on a straight line ) , then
x = 180° - (85 + 82)° = 180° - 167° = 13° ( sum of angles in a triangle )
How to find which trinomials are perfect square trinomials
Answer:
An expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form
[tex]ax 2 + bx + c[/tex]
is said to be a perfect square, if and only if it satisfies the condition b 2 = 4ac.
Step-by-step explanation:
hope it will help you have a great day bye and Mark brainlist if the answer is correct
[tex]kai6417[/tex]
Finding the measure of the angle indicated
Answer:
30
Step-by-step explanation:
the sum of the three angles in a triangle is 180
so we have,
70+70+x=180
140+x=180
x=180-140=40
now, find the sum of 40 and 63
it is 103
subtract,
180-103=77
add,
77+73=150
180-150=30
30
can you mark me brainliest
Answer:
34
Step-by-step explanation:
73 + 73 = 146
180 - 146 = 34
Have a good day!
3. Mr. James told Jill he would charge her $15 per hour, plus parts, to fix her bicycle.
The parts ended up costing $32, and
it took Mr. James 3 hours to fix the bike. Write
and evaluate an expression to determine how much Jill owes Mr. James.
Answer:
512
Solution:
so first you multiply 15 times 32 and get 480 than you add 32 and get 512.
In the diagram, the circle is inscribed in triangle PQR. Find arc EF, FG, and GE.
Check the picture below.
In essence, the two triangles made by the radii and the twin tangent lines are congruent by SSS or even for right-triangles congruence by LL.
Applying the tangents theorem, the arc measures are:
Arc EG = 140°
Arc EF = 120°
Arc FG = 100°
What is the Tangents Theorem?The tangents theorem states that a tangent to a circle forms a right angle (90 degrees) at the point of tangency, and also, if two tangents meet at point outside a circle, both tangents are equal.
Using the tangent theorem, we would find the central angles opposite arc EF, FG, and GE which are all the same measure as their central angles.
Let the center of the circle be point O.
m∠EOG = 2[180 - m∠PEG + m∠EOP)] (central angle opposite to arc EG)
Substitute
m∠EOG = 2[180 - 90 + 1/2(40)]
m∠EOG = 140°
Arc EG = m∠EOG = 140°
Arc EG = 140°
m∠EOF= 2[180 - m∠QFO + m∠FQO)] (central angle opposite to arc EF)
Substitute
m∠EOF = 2[180 - 90 + 1/2(60)]
m∠EOF = 120°
Arc EF = m∠EOF = 120°
Arc EF = 120°
m∠FOG = 2[180 - m∠RFO + m∠FRO)] (central angle opposite to arc FG)
Substitute
m∠FOG = 2[180 - 90 + 1/2(80)]
m∠FOG = 100°
Arc FG = m∠FOG = 140°
Arc FG = 100°
Therefore, applying the tangents theorem, the arc measures are:
Arc EG = 140°
Arc EF = 120°
Arc FG = 100°
Learn more about tangents theorem on:
https://brainly.com/question/9892082
help me please!! IM NEVER GONNA GET THIS DONEE
Answer:
105/120
48/120
50/120
Step-by-step explanation:
8, 5, 12
8 = 2³
5 = 5
12 = 2² × 3
LCD = 2³ × 3 × 5 = 8 × 3 × 5 = 120
120/8 = 15
7/8 = (7 × 15)/(8 × 15) = 105/120
120/5 = 24
2/5 = (2 × 24)/(5 × 24) = 48/120
120/12 = 10
5/12 = (5 × 10)/(12 × 10) = 50/120
what is the unit rate for 247 heartbeats in 612 minutes
Answer:
247/612
Step-by-step explanation:
247 heart beats / 612 minutes
beats/ minutes
HELP ANOTHER QUESTION, I REALLY NEED HELP. !!!!!!!!!!!!!!!!!!!!!
Answer:
x = 30
Step-by-step explanation:
Answer:
Step-by-step explanation:
2. Pepper went to the movies and spent $13.83. How
much did she spend, rounded to the nearest whole
dollar?
$
Darrell bought 4 books about animals, 4 books about outer space, and 1 book about trains. Each book cost $13. How much did Darrell spend on the books
A ribbon 4 m long is cut into 8 equal pieces.
What is the length of each piece?
Give your answer as a fraction in its simplest form.
Answer:
1/2 m
Step-by-step explanation:
It is because 4 = 4/1, 8 = 8/1 and 4/1 divided by 8/1 is also equal to 4/1 times by 1/8 which equals 4/8.
4/8 is simplified to make 1/2m
hope this helps mark brainliest
simplify 16/5 +30/7+3/2-13/5
Answer:
Simplifying the same denominators first:
16/5 - 13/5 = 3/5
So, we're brought down to:
3/5 + 30/7 + 3/2
35 goes into 5 and 7, so I'll simply 3/5 + 30/7 next -
7 x (3/5) to get 21/35
5 x (30/7) to get 150/35
Now add the two to get 171/35
(150+21=171)
Finally find a common denominator for 35 and 2.
(35x2=70)
2 x (171/35) --> 342/70
35 x (3/2) --> 105/70
Add up 342+105 to get 447 & put over 70.
Answer is 447/70
(It can't be simplified any further than this.)
Hope this helps!
What would the surface area be ?
Answer:
320.44Step-by-step explanation:
the equation for right cylinder surface area: 2πrh+2πr^2
Answer:
33π cm²
Step-by-step explanation:
To find surface area you add the area of every face.
Area of the 2 circle faces:
The formula for the area of circle is πr². If the diameter is 6 you divide that by 2 to get a radius of 3. The area of the circle is 9π. Sense the top and bottom are both circles you multiply the area by 2 to get 18π.
Area of side face:
To find the area of the side, it is the same as a rectangle (length [circumference] multiplied by height [2.5]). The forumla for the circumference of a circle is πd. The circumference is 6π so multiply that by the height of 2.5 to get the area of the side of 15π.
Total surface area:
Now add the 18π (area of 2 circle faces) with the 15π (area of side face) to get 33π cm² surface area.
help me with geometry please
answer
x=180-87-33
= 60