Step-by-step explanation:
2(x -y) + 2x - 2y
2x - 2y + 2x - 2y
2x + 2x -2y - 2y
4x - 4y
Determine if each infinite geometric series is convergent or divergent.
The solution to the geometric progression are
a) The geometric progression converges , r = 0.1
b) The geometric progression converges , r = 0.2
c) The geometric progression diverges , r = 5
d) The geometric progression converges , r = 0.2
e) The geometric progression diverges , r = 5
f) The geometric progression converges , r = 0.2
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
A geometric progression is said to converge if the common ratio r lies between -1 < r < 1
So , If -1 < r < 1, the geometric sequence converges
a)
The geometric progression is A = 0.3 + 0.03 + 0.003 + ...
The common ratio r = second term / first term
The common ratio r = 0.03 / 0.3
The common ratio r = 0.1
So , -1 < r < 1 and the GP converges
b)
The geometric progression is A = 0.25 + 0.05 + 0.01 + ...
The common ratio r = second term / first term
The common ratio r = 0.05 / 0.25
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
c)
The geometric progression is A = 0.23 + 1.15 + 5.75 + ...
The common ratio r = second term / first term
The common ratio r = 1.15 / 0.23
The common ratio r = 5
So , r > 1 and the GP diverges
d)
The geometric progression is A = 0.75 + 0.15 + 0.03 + ...
The common ratio r = second term / first term
The common ratio r = 0.15 / 0.75
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
e)
The geometric progression is A = 0.00025 + 0.00125 + 0.00625 + ...
The common ratio r = second term / first term
The common ratio r = 0.00125 / 0.00025
The common ratio r = 5
So , r > 1 and the GP diverges
f)
The geometric progression is A = 128,750 + 25,750 + 5,150 + ...
The common ratio r = second term / first term
The common ratio r = 25,750 / 128,750
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
Hence , the geometric progression is solved
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At 1 P. M. the family resumes their trip, and they reach Helena at 5 P. M. The total distance from the family’s home to Helena is 485 miles. Including the 30-minute lunch stop, what is the average speed over the entire trip?
Answer: 60.6 miles per hour
Step-by-step explanation: 5 hours + 3 hours + 30 mins = 8 hours 30 mins 485 divided by 8
The total distance from the family’s home to Helena is 485 miles.
including the 30-minute lunch stop. The average speed over the entire trip is 60.6 miles per hour.
How is average speed calculated?The average speed is the ratio of total length traveled to the total time taken to travel that length.
Thus, if
[tex]d_2 = \text{final position}\\d_1 = \text{initial position}\\t_2 = \text{end time}\\t_1 = \text{start time (of travelling)}[/tex]
then,
[tex]S_a = \dfrac{d_2 - d_1}{t_2 - t_1}[/tex]
where S is the average speed of the traveler.
At 1 P. M. the family resumes their trip, and they reach Helena at 5 P. M.
The total distance from the family’s home to Helena is 485 miles.
Including the 30-minute lunch stop.
The total time taken
5 hours + 3 hours + 30 mins = 8 hours 30 mins
The average speed over the entire trip
[tex]S_a = \dfrac{d_2 - d_1}{t_2 - t_1}[/tex]
= 485/ 8
= 60.6 miles per hour
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Write 63 521. 769 correct to the nearest hundred
Consider each of the following word problems.
Write a word sentence to represent what you are going to do with the numerical values.
Include the proper brackets, exponents and operation signs.
Substitute the words with an appropriate variable.
Solve each problem in good form.
1. The school library had a used book sale. Paperbacks were 25 cents each and hardcover books
were $1.25 each. There were 54 paperbacks and 163 hardcover books sold. How much money did
the library raise?
2. Tamara has to go on a business trip. Including taxes, her round trip airfare is $398.60 and her
room costs $115.70 per night. The cab fare from the airport to the hotel is $40.00. If Tamara
stays for two nights, how much does the trip cost, excluding the cost of food?
3. Paula repairs swimming pools and earns $14.50/h for the first 35 h she works in a week. For
hours over 35 h, she earns 1.5 times as much. If she works 48 hours in a week, how much does she
earn?
4. Will and Liam collect baseball cards. Will has 26 cards and Liam has 19. They decided to combine
their cards. Because they shared, their father decided that he would triple the number of cards
that they had. After that, their friend Nestor thought that he would add his cards to their bunch.
Nestor didn’t know how many cards he had but he knew that he could lay them out in rows and that
they would make a square with one side of his square having 8 cards. How many cards did the boys
have altogether?
The amount and numbers are 1. $217.25, 2. $710, 3. $790.25 and 4. 167.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number
1. Cost of a paperback = 25 cents = $0.25
Cost of a hardcover book = $1.25
There were 54 paperbacks and 163 hardcover books sold.
Money library raised = (0.25 × 54) + (1.25 × 163) = $217.25
2. Cost for round trip airfare = $398.60
Cost of room per night = $115.70
Cost of room for two nights = 2 × $115.70 = $231.40
Cab fare from airport to hotel = $40.00
Total fare from airport to hotel and the return = 2 × $40.00 = $80.00
Total cost = $398.60 + $231.40 + $80.00 = $710
3. Total working hour of Paula = 48 hours
Earning for first 35 hours = $14.50/h × 35
= $507.50
Remaining hours = 48 - 35 = 13 hours
Earning for next 13 hours = ($14.50/h × 1.5) × 13
= $282.75
Total earnings = $507.50 + $282.75 = $790.25
4. Number of cards Will has = 26
Number of cards Liam has = 19
When they combine, total cards = 26 + 19 = 45
When father also shared, total number of cards = 3 × 45 = 135
Number of cards Nestor has = 4 × 8 = 32
Total number of cards = 135 + 32 = 167
Hence all the questions are cleared using multiplication as one of the basic operations.
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PLEASEEE HELPPP !!
picture attached
If m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles, find m ∠ Q.
The value of m ∠ Q is 23°.
What are complementary angles?
Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary. We say two angles "Complement" one other when their sums equal 90 degrees.
Here, we have
Given: m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles.
The sum of the measures of two complementary angles is 90°.
So, m∠P + m∠Q = 90°
Substitute 12x+7 for m∠P and 6x−7 for m∠Q.
12x+7 + 6x−7 = 90°
18x = 90°
x = 5°
To find m∠Q, substitute 5 for x in 6x−7.
6×5 - 7 = 23°
m ∠ Q = 23°
Hence, the value of m ∠ Q is 23°.
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Check
A jeweler is thinking about using this solid silver bead in a necklace
he is designing. He only has 5.000 grams of silver. If pure silver's
mass is 10.5 grams per cubic centimeter, can he make this bead?
if so, how many grams of silver will the jeweler have left?
11 cm
10 cm
2 cm
Answer:
assalam o aalaikum
Step-by-step explanation:
I finished my homework this morning. __________________,
Write a statement to represent the expression h-9
expression h-9 is represented as statement 'h decreased by 9'.
What is subtraction?Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two".
Given expression
h-9
Here h is a variable, 9 is constant and - is the symbol of subtraction.
the phrase "decreased by" tells us to use subtraction.
Statement for the above expression
h decreased by 9.
Hence, the statement 'h decreased by 9' represents expression h - 9.
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Help me please please please it’s due tonight!!!!!!!!!!!
Answer:
A. (4, 18)
Step-by-step explanation:
The "y" coordinate of the midpoint will be equal to the average of the y coordinates of the endpoints, and the x coordinate of the midpoint will be equal to the average of the x coordinates of the endpoints, and so we get that...
The x coordinate of the midpoint = (5 + 3) / 2 = 8 / 2 = 4
The y coordinate of the midpoint = (21 + 15) / 2 = 36 / 2 = 18
So the right answer is A (4, 18)
Write −0.39¯¯¯¯¯ as a fraction in simplest form.
Answer:
-0.3999... = -⅖
-0.393939... = -13/33
Step-by-step explanation:
Only ones I could think of.
Answer:
-39/100
Step-by-step explanation:
f ( x ) = 0.1 ( 3 x − 2 ) aWhat is the value of f ( 5 ) ?
Answer:
3
Step-by-step explanation:
First, plot the graph of the function
and the graph of the line
This line intersects the graph of the function f(x) at 4 different points. So, there are 4 different values for b at which
Only 3 of them have positive values.
At these positive values, f(x)=2 (because the graph of the function and the graph of the line y=2 intersect at these points), then for these three b with positive values,
Jamie spends the day at an amusement park. The table shows how many
tickets Jamie has after riding some amusement park rides. It represents a
linear function.
Number of rides
Number of tickets
0
1 2 3
24 18 12
4
6 0
What is the y-intercept of the function shown in the table, and what does it
represent?
OA. The y-intercept is (4,0). Jamie goes on 4 rides.
OB. The y-intercept is (4.0). Jamie uses 4 tickets per ride.
OC. The y-intercept is (0, 24). Jamie has 24 tickets before going on any
rides.
OD. The y-intercept is (0, 24). Jamie uses 24 tickets per ride.
Answer:
C. The y-intercept is (0,24). Jamie has 24 tickets before going on any rides.
Step-by-step explanation:
Rides Tickets Left
0 24
1 18
2 12
3 6
4 0
Let x be the number of rides taken and y be the number of tickets remaining. We can write the equation for this linear function as:
y = -6x + 24
The y-intercept, 24, tells us how many tickets Jamie has before taking any rides (x = 0). He has 24 tickets. His first ride reduces that amount by 6, so the slope of this line is -6 (Jamie uses 6 tickets per ride).
The y-intercept is written as (0,24): Jamie has 24 tickets before any ride is taken. This is option C.
3x + 8 = 3x
x=________________
Answer:
No Solutions
Step-by-step explanation:
3x + 8 = 3x
*subtract 3x from each side*
3x - 3x = 0
3x - 3x cancels out
we're left with 8 = 0
Hence there are no solutions to the problem
Answer:
0=-8
Step-by-step explanation:
3x+8=3x
-8. -8
3x=3x-8
-3x -3x
0= -8
symplify the following equation 28 - 3(2+4) divided by 9
Answer:
10 / 9
Step-by-step explanation:
[ 28 - 3 ( 2 + 4 ) ] / 9
= [ 28 - 3 ( 6 ) ] / 9
= [ 28 - 18 ] / 9
= 10 / 9
In a certain urban are, the relationship between , number of students ,x, in thousands, and the number schools, y, has an x-intercept of -4 and a y-intercept of 3. Write an equation for this relationship in standard form.
Answer:
-12 = 3x - 4y
Step-by-step explanation:
Two points on the graph are (-4, 0) and (0, 3). Moving from the first point to the second, we see x (the 'run') increase by 4 and y (the 'rise') increase by 3. Thus, the slope of this line is m = rise / run = 3/4.
Using the point slope form, we get:
y - 3 = (3/4)(x - 0), or
4y - 12 = 3x, or
-12 = 3x - 4y (which is in Standard Form).
New tablets are on sale for 40% off. They're
normally $149.50. What will I pay for my tablet
when I get 40% off?
Answer:
$89.7
Step-by-step explanation:
First, find the 40% of 149.5, which is 59.8. Then, subtract the percentage (59.8) from 149.5 which equals 89.7.
So it is $89.7 dollars when it is 40% off.
HOPE THIS HELPS!!!!
BEST OF LUCK!!!
Which problem solving strategy would be best to solve this problem? Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn? A. write an equation B. make a table, chart or list C. compute or simplify D. guess, check and revise
The best approach to solve the problem is writing an equation. Given Avelina earns half of what Gus earns, the equation becomes Avelina's earnings = Gus's earnings / 2. On substituting Gus's earnings with $125, we get Avelina's earnings to be $62.50.
Explanation:The best problem-solving strategy that would be apt to solve this problem, 'Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn?' is to write an equation. We know that Avelina earned half of what Gus earned. This can be represented by the equation: Avelina's earnings = Gus's earnings / 2.
Since we know that Gus earned $125, we can substitute this value into our equation: Avelina's earnings = $125 / 2. Solving this equation gives us the answer: Avelina earned $62.50.
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another one 2 more after this
help i cant solve it
Answer:
Step-by-step explanation:
We have,
x = 3y - 3 ---> x - 3y = -3 ------(1)
5x + 4y = 23 -----(2)
Multiplying eq. (1) by 5:
5x - 15y = -15 ------(3)
5x + 4y = 23
Subtracting (1) from (3):
-19y = - 38
y = 2
therefore, x - 6 = -3
x = 3
I never help quick! A kaleidoscope is made of stained glass in the shape of a triangular prism. The bases are equilateral triangles. Find the surface area of the kaleidoscope
Answer:
46.8 in²Step-by-step explanation:
Total surface area comprises of two bases and 3 faces:
S = 2(1/2*1.5*1.2) + 3(1.5*10) = 46.8 in²Answer:
Solution given:
length=10in
again
base=2√{1.5²-1.3²)=1.49
Total surface area =lateral surface area +2 curved surface area
=perimeter of triangle ×length +2×1/2 base×height
=(1.49+1.5+1.5)×10+1.3×1.49=46.837in²
How do you solve longest side?
HELP TIMED! In the figure, lines a and b are parallel lines. Which of the following statements is true? Select all that apply.
Answer:
B C and E
Step-by-step explanation:
Answer:
I believe the answer is B, C, E.
A rock is thrown from the top of a building . The height, h, of the rock t seconds after it thrown is given by h(t) = - 16t ^ 2 - 2t + 240 . How long will it take the rock to reach a height of 180 feet?
Answer:
1.875 sec
Step-by-step explanation:
Let h(t) = 180
180 = -16t^2 - 2t + 240
16t^2 + 2t - 60 = 0
2(8t^2 + t - 30) = 0
2(t + 2)(8t - 15) = 0
t = -2 or t = 15/8= 1.875 sec
Note: time cannot be negative, so -2 is disregarded
The time is taken by the rock to reach the height of 180 feet is 1.875 sec
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The solution will be:-
Let h(t) = 180
180 = -16t²- 2t + 240
16t² + 2t - 60 = 0
2(8t² + t - 30) = 0
2(t + 2)(8t - 15) = 0
t = -2 or t = 15/8= 1.875 sec
Therefore the time is taken by the rock to reach the height of 180 feet is 1.875 sec
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just need help with #7. A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
Surface Area : Volume = 6 : s
What is cube ?A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
Surface Area of a Cube = 6a² in a square units
Volume of cube = a³ cubic units
where a is the side length of the cube.
Given length of the cube = s
Surface Area of cube A = 6s²
Volume of cube V = s³
Ratio between Surface Area and volume:
Surface Area / Volume = 6s² / s³
Surface Area / Volume = 6 / s
Surface Area : Volume = 6 : s
Hence the ratio between Surface area and volume of cube is 6 : s.
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cheng drew the model below to represent an equation.What value of x makes the equation true?
Answer:
So what’s the answer?
Step-by-step explanation:
Help please s s s what is ittyt
9514 1404 393
Answer:
point (-12, -5)slope 1/2Step-by-step explanation:
Compare the given equation to ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
You find that k = -5, m = 1/2, h = -12.
The point is (h, k) = (-12, 5). The slope is m = 1/2.
Make a table as y=x^2.
Answer:
-0
Step-by-step explanation:
What is the best definition of a decimal?
A) Decimals are ratios out of one hundred
B) Decimals are whole counting numbers
C) Decimals are ratios relating one integer to another
D) Decimals are integers followed by a decimal point and a number less than one
Answer:
D
Step-by-step explanation:
I think it would be D hope this helps!
The best definition of a decimal is decimals are whole counting numbers.
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcdefg and belongs to the decimal numerical system.
Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.
Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.
Thus, we write abcd.efg as:
[tex]a \times 10^3 + b \times 10^2 + c \times 10^1 + d \times 10^{0} + e \times 10^{-1} + f \times 10^{-2} + g \times 10^{-3}[/tex]
We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.
We call e as digit at 10th place (division by 10), f as digit at hundredth place and so on.
Therefore, the definition will be Decimals are whole counting numbers,
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Jenson needs to create a graph using the data he collected from the baseball tournament over the weekend. Jenson must create a graph where exact data points are provided.
Which of the following would NOT be a good graph for Jenson to use?
A. Stem-and-Leaf Plot
B. Dot Plot
C. Histogram
Here's link[tex]^{}[/tex] to the answer:
bit.[tex]^{}[/tex]ly/3gVQKw3
HELPPPPPP PLEASEeeeeeeeeeeeeee
it is this answer x≥
3
8
I don't know the step by step solution
Solve the following system of equations: −2x + 3y = 7 y = 3x + 7 (−5, −1) (−2, 1) (−1, 4) (1, 3)
Answer:
(-2, 1)
Step-by-step explanation:
−2x + 3y = 7
y = 3x + 7
Since the second equation is already solved for y, we can use the substitution method. Substitute y of the first equation with 3x + 7 and solve for x.
-2x + 3y = 7
-2x + 3(3x + 7) = 7
-2x + 9x + 21 = 7
7x = -14
x = -2
Now substitute x in the second equation with -2 and solve for y.
y = 3x + 7
y = 3(-2) + 7
y = 1
Answer: (-2, 1)