Answer:
The answer is below
Step-by-step explanation:
Second term of a geometric series is 2, the limiting sum is 9.
Get the values of first term a and common ratio r.
Solution:
A geometric series is in the form:
a + ar + ar² + ar³ + . . . + arⁿ ⁻ ¹
Where a is the first term, n is the nth term and r is the second ratio.
Since the second term of the series is 2, hence:
ar⁽² ⁻ ¹⁾ = 2
ar = 2 (1)
Also, the limiting sum is 9, hence:
a/ (1 - r) = 9
a = 9 - 9r (2)
Substitute a = 9 - 9r in eqn 1:
(9 - 9r)r = 2
9r - 9r² = 2
9r² - 9r + 2 = 0
9r² - 6r - 3r + 2 = 0
3r(3r - 2) -1(3r - 2) = 0
(3r - 1)(3r - 2) = 0
r = 1/3 or r = 2/3
When r = 1/3; a = 9 - 9r = 9 - 9(1/3) = 6
When r = 2/3; a = 9 - 9r = 9 - 9(2/3) = 3
Question:
Simplify. √(36)²
Answer:
36
Step-by-step explanation:
sqrt(36)^2
36
I hope this helps
16.
There are two adjacent supplementary angles. The larger angle is 2
more than 3 times the smaller angle. What are the degrees of both
angles? What is the difference in their measurements?
Find the slope of the line passing through the points (-6,-9) and (9,-9)
please help me .......
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Answer:
65°
Step-by-step explanation:
Any sort of bisector divides a geometry into two congruent parts. Here, we have an angle bisector that divides the larger (130°) angle into two equal parts. The measure of each of the resulting smaller angles will be 130°/2 = 65°.
∠JAE = 65°
8 3/4 divided by 3 1/2
Answer:
[tex]2\frac{1}{2}[/tex]
Step-by-step explanation:
help me please! i’m giving brainliest! :)
A desk measures 3 feet in height. How many inches does the desk measure in height?
Answer:
36 Inches
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
it would just be 12×3=36
find the next term in the sequence. please type the number only as you answer. hint first figure out if the sequence is arithmetic or geometric
-3,9,-27,81,
Helpp meeeeeeeeeeeeeeeeeee
Answer:
perimeter = 48 Area = 144
Step-by-step explanation:
was that all?
0. Folded boxes a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 5 ft by 8 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Squares with sides of length x are cut out of each corner of a square piece of cardboard with sides of length /. Find the volume of the largest open box that can be formed in this way.
Answer:
Box dimensions:
L = 3 ft
D = 6 ft
H = 1 ft
Volume V = 18 ft³
Step-by-step explanation:
a) Each side of the future box is
L = 5 - 2*x D = 8 - 2*x
height of the box is x
Then the volume of the box as function of x is:
V(x) = ( 5 - 2*x ) * ( 8 - 2*x ) * x
V(x) = ( 40 - 10*x - 16*x + 4*x² ) * x
V(x) = 40*x - 26*x² + 4*x³
Tacking derivatives on both sides of the equation:
V´(x) = 40 - 52*x + 12x² or V´(x) = 20 - 26*x + 6*x²
If V´(x) = 0
6*x² - 26*x + 20 = 0
Solving for x
x₁,₂ = (-b ± √ b² - 4*a*c ] /2*a
x₁,₂ = ( 26 ± √ 676 - 480 ) / 12
x₁,₂ = (26 ± 14 )/ 12
x₁ = 1
x₂ = 3,33 ( we dismiss this solution since is not feasible according to cardboard dimensions )
Then the sides of the box are:
L = 5 -2*x L = 5 - 2*1 L = 3 ft
D = 8 - 2*x D = 8 - 2*1 D = 6 ft
H = x = 1 ft
And the volume is V = 6*3*1 = 18 ft³
Please help. Thank you.
Answer:
-10m-9
Step-by-step explanation:
-3(4m+3)+2m
combine like terms
-12m-9+2m
-10m-9
A rectangular garden has dimensions of 100 feet by 10 feet. Next season, the garden is decreased to 2/5 of its size what is the scale of the new drawing
Answer:
4 and 40
Step-by-step explanation:
2/5 of 10 is 4
2/5 of 100 is 40
A flower bed is in the shape of a triangle, with a base of 11 feet and a height of 7 feet. What is the area of the flower bed
Answer:
38.5ft²
Step-by-step explanation:
Triangle area formula = [tex]\frac{1}{2} * b * h[/tex]
Triangle area = [tex]\frac{1}{2} * 11 * 7[/tex]
Triangle area = 0.5 * 11 * 7
Triangle area = 38.5ft²
Answer: GIVE THE GUY BRAILIEST PLEASE
The sim of any matrix and a zero matrix is
A. Undefined
B. Zero
C. The zero matrix
D. The original matrix
It’s D the answer is D
Gaelle Bosquet Nth Term of an Arithmetic Sequence Apr 10, 12:29:36 AM Find the 60th term of the arithmetic sequence 4,-1,-6, ... Answer: Submit Answer
Answer:
The nth term is [tex]a_n = 4 - 5(n-1)[/tex]
The 60th term of the sequence is -291.
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and it is called common difference.
The nth term is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
4,-1,-6
The common difference is:
[tex]d = -1 - 4 = -5[/tex]
First term [tex]a_1 = 4[/tex]
So
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]a_n = 4 - 5(n-1)[/tex]
60th term:
[tex]a_{60}[/tex]. Si
[tex]a_{60} = 4 - 5(60-1) = -291[/tex]
The 60th term of the sequence is -291.
5/8 in simplest form.
Answer:
5/8 in simplest form is 5/8
Step-by-step explanation:
Answer:
5/8 is in the simplest form already.
Step-by-step explanation:
It cant be lowered anymore, due to 5 not being divisible by 4, 2, or 8, which is what 8 is divisible by.
joseph left the house at 11:17 A.M and returned at 12:45 P.M how many minutes was joseph gone from the house
Help me I beg u! The pre-image coordinates of a triangle are J(-6,9), K(-6,4), and L(-3,4). The coordinates of the transformed triangle are J'(2,9), K'(2,4), and L'(5,4). What transformation has occurred? A. translation B. reflection C. dilation D. rotation Reset Next Question
Answer:
A. Translation
Step-by-step explanation:
Given
Preimage
[tex]J = (-6,9)[/tex]
[tex]K = (-6,4)[/tex]
[tex]L = (-3,4)[/tex]
Image
[tex]J' = (2,9)[/tex]
[tex]K' = (2,4)[/tex]
[tex]L' = (5,4)[/tex]
Required
Which transformation occurred
The transformation that occurs is translation because each of the preimage were translated or shifter right by 8 units.
The rule applied here is:
[tex](x,y)=>(x+8,y)[/tex]
So, we have:
[tex]J = (-6,9)[/tex] [tex]==> (-6+8,9) = (2,9)[/tex]
[tex]K = (-6,4)[/tex] [tex]==> (-6+8,4) = (2,4)[/tex]
[tex]L = (-3,4)[/tex] [tex]==> (-3+8,4) = (5,4)[/tex]
Hence, the transformation is (a) Translation
St. Patrick's Day Problem Solving
Use the weight on the scales to determine the weight of each egg.
Note: Identical eggs weigh the same amount,
3.5
6
5.5
Pls help with this asap
PLEASE HELP!! NO SCAM LINKS
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Answer:
(d) new line is less steep
Step-by-step explanation:
Changing the slope from 3 to 1/3 makes the line less steep.
__
In the attachment, the blue line is the new line.
guys help im bad at math
Answer:
A = 13
B = 50
C = 22.5
D = 3.5
E = 16.3
Step-by-step explanation:
divide each area by 4
ex: 52 ÷ 4 = 13
What 1,500 rounded to the nearest hundredth
Answer:
2,000
Step-by-step explanation:
Jimmy has 6 computers and 7 printers to choose from. How many possible computer- printer combinations are there to make?
O 42
O 13
Answer:
13
Step-by-step explanation:
Computers=6
Printers=7
Now,
=6+7
=13
Please help me I need this due
whcich expression are equivialant to the one below 3^4*3^x
Answer:
3x+4
Step-by-step explanation:
Order these numbers from least to greatest:
|-17|
|-18|
-18
|19|
20
Answer:
-18, |-17|, |-18|, |19|, 20
Step-by-step explanation:
the absolute value of -17 is 17, the absolute value of -18 is 18, and the absolute value of 19 is just 19. Absolute values are never negative.
Hope this helps!
The Thompson family is buying a car that can travel 70 miles
Answer:
The car gets 35 miles per gallons.
Step-by-step explanation:
CLICK ON PHOTO AND NOOOOO LINKS PLSSSS
A block of wood measures 5.5 inches by 3.5 inches by 9 inches. What is the volume of the block of wood
Answer:
V = 173.25 in³Steps:
V = 5.5 × 3.5 × 9
V = 173.25 in³
Can someone help me with this question?
Answer:
D
Step-by-step explanation:
2 x 2 = 4 x PI = 12.56