8 A geometric sequence has all
positive terms. The sum of the
first two terms is 15 and the sum
to infinity is 27.
a
Find the value of the common
ratio.
b Hence, find the first term.
Answers
Let the terms be a, ar, ar², ...
The sum to infinity being 27 means that:
\(\frac{a}{1-r}=27 \implies a=27(1-r)\)
The sum of the first two terms being 15 means:
\(a+ar=15 \\ \\ (27-27r)+r(27-27r)=15 \\ \\ 27-27r+27r-27r^2 =15 \\ \\ 27r^2 -12=0 \\ \\ 27r^2 =12 \\ \\ r^2=\frac{12}{27}\)
Since all the terms are positive, r>0.
\(\boxed{r=\frac{2}{3}} \\ \\ \implies a=27\left(1-\frac{2}{3} \right)=\boxed{9}\)
Related Questions
Find the volume of the figure below.
5 m
6 m
-8 m
10 m
a
40 meters cubed
42 meters cubed
OOOO
36 meters cubed
120 meters cubed
Answers
Answer:
Where is the figure??
..
This is indirect measurement, I need some help on this one ):
Answers
The height of the building , given the shadow that it casts would be 93 meters tall .
How to find the height of the building ?Utilizing proportions can be an effective method to tackle this issue. By defining ' h ' as the height of the building responsible for casting a 39.75 meter shadow, we may establish the ensuing proportion :
h / 39. 75 = 3. 2 / 1. 37
Solving for h gives us :
h / 39. 75 = 2. 336
h = 2. 336 x 39. 75
h = 92. 8 56
h = 93 meters tall
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What is the arc length of arc cd in the circle below. The circle has a radius of 6ft and an angle measure of 30
Answers
9514 1404 393
Answer:
π ft ≈ 3.14 ft
Step-by-step explanation:
The angle is 1/12 of the number of degrees in a circle, so the arc length will be 1/12 of the circumference of the circle.
C = 2πr
1/12C = 2/12π(6 ft) = π ft ≈ 3.14 ft
The arc length is about 3.14 feet.
Fill in table using this function rule y= -4x - 2
Answers
Answer:
Step-by-step explanation:
x y
-2 6
-1 2
0 -2
1 -6
2 -10
the correct answer.
Which inequality represents the values of that ensure triangle ABC exists?
A
2x+4
B
O D.
18
OA.
<< 1
OB. -< < ¹
O c. 1 < x < 5
6x
2 < < 6
Answers
The Inequality which ensure triangle exists is A. 7/4 < x < 11/2
What is the inequalityInequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.
Theorem used In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
Substitute the value in the inequality to ensure triangle exists we get 7/4 < x < 11/2. The correct option is A.
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Which expression is equivalent to -2 1/4 divide -2/3?
Answers
Answer:
-9/4 divide (-2/3)
Step-by-step explanation:
WILL GIVE BRAINLIEST TO WHOEVER IS RIGHT
Answers
Answer:
lies you wont give brainliest
Step-by-step explanation:
i beg u guys pleas help
Answers
Answer:
a^-7
Step-by-step explanation:
Option C. a^-7 is the answer.
PLEASE HELP ME PLEASEEEEE Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of a (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square
Answers
Answer:
4.5·π cm² + 18 cm²
Step-by-step explanation:
Answer:
what is there perimeter
Simplify:
5.5 + 7 [(6.3 + 2.1) X 4+ (10 – 4) = 21
Answers
Answer:
x=4√−0.45068027,−4√0.45068027
Step-by-step explanation:
Triangle ABC has the vertices A(2, 0), B(4, 2), and C(3, 4).
Name the ordered pair of C' after a reflection across the
x-axis.
Answers
Answer: C’(3,-4)
Step-by-step explanation: All you have to do is count how many blocks away is the point from the x axis and then count down the x axis where you stop counting and that is how you get your point.
Help ASAP please!!
Which distance measures 5 units?
•the distance between points W and X
•the distance between points X and Y
•the distance between points X and Z
•the distance between points Y and Z
Answers
Answer: The distance between W and X
if it helps, jump from the dash under W to the next dash until you get to X, you'll get 5 units
Hope this helps you and I hope you have a nice day :)
What is greater 1.0275 or 1.029
Answers
Answer:
1.029 is greater than 1.0275
Step-by-step explanation:
Answer:
1.029
Step-by-step explanation:
What is greater 1.0275 or 1.029
.027 < .029
So, 1.029 is greater.
26. Tyler has been saving his winning lottery tickets. He has 23 tickets that are worth a total of $175. If each ticket is worth either $5 or $10, how many of each does he have?
Answers
Marcus was showing how he solved a division problem with the area model below. His pen exploded ink on some of his work.
What is the divisor that is covered with ink on the left side of the model?
A. 100
B. 80
C. 56
D. 29
Answers
Answer:
C
Step-by-step explanation:
"select all the numbers that are solutions to the equation x^3=27"
Answers
3^3 = 27
the cubed root of 27 is 3
The x = ∛27 and x = 3 are solution to the equation x³=27 option (B) and option (C) are correct.
What is a cube root?It is defined as the sum of two or more numbers. The original number is obtained by multiplying the cube root of a number three times; for example, the cube root of x is z.
We have equation:
x³ = 27
Taking cube root both side
∛x³ = ∛27
x = ∛27
x = 3
Thus, the x = ∛27 and x = 3 are solution to the equation x³=27 option (B) and option (C) are correct.
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2. Your bank account has $15 in it. You deposit $3 per day. How much money is in your account after 5 days?
Answers
Answer:
30 dollars. I think
Step-by-step explanation:
3x5=15
15+15=30
Note: Deposit means to put in!
The correct answer is 30 dollars.
How did I get my answer? Well I did:
$3 per day times 5 days which is $15. I then added that $15 to the $15 it already contained which was $30
—————
Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
—————
What is a reasonable estimate of -3 4/5 + (-5.25) and the actual value?
Answers
Answer:
The actual value is -181/20. Estimate could be -200/20
Step-by-step explanation:
(ixl) Find the missing number so that the equation has infinitely many solutions. 3x–18=3(x–10)+
Answers
The value of x for the equation to have infinite solution is 12
Equation and expressionFor an equation to have infinite solution, the expression on both sides must be equal
Given the expression below
3x–18=3(x–10)+ x
expand
3x - 18 = 3x - 30 + x
Equate
-18 = -30 + x
x = -18 + 30
x = 12
Hence the value of x for the equation to have infinite solution is 12
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a classroom had 35 glue sticks at the ratio of glue sticks to glue bottles with 5 to 2 how many glue bottles does a classroom have
Answers
Answer:
the answer should be 12 if not sorry
A mechanic charges a very reasonable $ 40 $ 40 per hour to work on cars. For a particular repair, $ 120 $ 120 worth of parts are required. Let x x represent the number of hours that the mechanic works on the car, and let y y represent the total cost of the repair: 1 2 3 4 5 6 7 8 -1 -2 40 80 120 160 200 240 280 320 360 -40
Answers
The relationship between the number of hours and cost shows a proportional relationship.
How to illustrate the proportion?A proportion is an equation that sets two ratios at the same value. A proportion is an equation that sets two ratios at the same value. One variable in a proportional relationship is always a constant value multiplied by the other.
In this case, mechanic charges a very reasonable price per hour to work on cars. This was illustrated as the relationship between the number of hours and cost was given
For 1 hour, cost is $40, for 2 hours, the cost is $80. In this case, there's a proportional relationship. The cost per hour will be:
= $20 / 1
= $20
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Complete question
mechanic charges a very reasonable $ 40 $ 40 per hour to work on cars. For a particular repair, $ 120 $ 120 worth of parts are required. Let x x represent the number of hours that the mechanic works on the car, and let y y represent the total cost of the repair: 1 2 3 4 5 6 7 8 -1 -2 40 80 120 160 200 240 280 320 360 -40. Is the relationship proportional?
for each parallel lines. you are given the measure of one angle
Answers
Answer:
The question is not complete
In exercises 17-20, approximate the logarithm using the properties of logarithms, given the values logb2 = 0.3562, logb3 = 0.5646, and logb = 0.8271. Round your result to four decimal places.
I only need 19 and 20!
19. logb 16/25
20. logb \(\sqrt{3}\)
Answers
The solution of the logarithmic expressions will be:-
19) 2logb4 - 2logb5
20) (1/2)logb (3)
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two expressions are logb 16/25 and logb √3.
The expressions will be solved as:-
E = logb 16/25
E = logb 16 - logb 25
E = logb 4² - logb 5²
E = 2logb 4 - 2logb 5
The second expression will be solved as:-
E = logb √3.
E = ( 1 / 2 ) logb 3
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Three workers worked for 5 hours, 7 hours and 12 hours. The total wage of $
13200 was divided among the three workers according to the number of hours of
work they did. How much did each get?
Answers
Answer:
Worked 5 hours: $550
Worked 7 hours: $2,750
Worked 12 hours: $6,600
Step-by-step explanation:
5+7+12=24
13200/24 = 550
(5)*(550) = 2,750
(7)*(550) = 3,850
(12)*(550) = 6,600
c−7.6=−4
c=
.............................................................
Answers
The value of c from c−7.6=−4 is 3.6.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
c−7.6=−4
Now, solve for c
Add 7.6 both side
c- 7.6 + 7.6 = -4 + 7.6
c = 3.6
Hence, the value of c is 3.6.
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2. XYZW is a parallelogram with diagonals XZ and YW that intersect at point A.
If XA = 3m, ZA = 5m - 4, and YW = 10m, find AW.
Answer:
Answers
Answer:
AW=10
Step-by-step explanation:
In a parallelogram opposite sides are congruent meaning XA and AZ are congruent. YA and AW are congruent. So...
Solving for XA and AZ
XA=AZ
3m=5m-4
-2m=-4
m=2
If YW=10m then 10 x 2 = 20
20 divided by 2 = 10
When Amella started painting, the paint can had 7/8 gallon in it. She used 3/8 gallons How much paint is left in the can?
Answers
Answer: If Amella started with 7/8 gallon of paint in the can and used 3/8 gallons, then the amount of paint left in the can can be found by subtracting the amount used from the amount started with:
Amount left = Amount started with - Amount used
Amount left = 7/8 - 3/8
Amount left = 4/8 or 1/2 gallon
Therefore, Amella has 1/2 gallon of paint left in the can.
Step-by-step explanation:
You spinner that has 12 equal sides sections number 1 through 12 find each probability probability three or four
Answers
Answer:
1 in 12 chance of landing on 3
1 in 12 chance of landing on 4
1 in 6 chance of landing on either 3 or 4
Step-by-step explanation:
12 equal sections means probability is 1 in 12 of landing on any one numbered section.
2 in 12 or 1 in 6 chance of landing on either of two numbered sections in one attempt.
A high positive correlation is represented by a line that
A. is horizontal
B. slopes downward to the right,
C. slopes upward to the right
D. is vertical
Answers
can someone help me with evaluating functions?
Answers
5^2 - (8*5) + 21.
When you simplify that, you get
25 - 40 + 21 = -15 + 21 = 6
g(x+4) is the same thing. Just put (x+4) instead of x in g(x) function to get
(x+4)^2 - (8*(x+4)) + 21.
When you simplify that by multiplying, distributing, and combining like terms, you get
(x^2+8x+16) - (8x+4) + 21 = x^2+8x+16 -8x-4 +21 = x^2 + (8x-8x) + (16-4+21) = x^2+33
Hope this helps.