Sum of three terms in a GP = 7
Product of the numbers = 8
Find:G.P
Solution:Let the three numbers be a/r , a , ar where a is the first term and r is the common ratio.
So,
⟹ a/r + a + ar = 7 -- equation (1)
And,
⟹ (a/r) * a * ar = 8
⟹ a³ = 8
⟹ a = ³√8
⟹ a = 2
Substitute the value a in equation (1).
⟹ 2/r + 2 + 2r = 7
⟹ (2 + 2r + 2r²)/r = 7
⟹ 2 + 2r + 2r² = 7r
⟹ 2r² + 2r - 7r + 2 = 0
⟹ 2r² - 5r + 2 = 0
⟹ 2r² - 4r - r + 2 = 0
⟹ 2r(r - 2) - 1 (r - 2) = 0
⟹ (2r - 1)(r - 2) = 0
★ 2r - 1 = 0
⟹ 2r = 1
⟹ r = 1/2
★ r - 2 = 0
⟹ r = 2
If r = 1/2 ;
a/r = 2/(1/2) = 2 * 2 = 4
a = 2
ar = 2 * 1/2 = 1
If r = 2 ;
a/r = 2/2 = 1
a = 2
ar = 2 * 2 = 4
∴ Required GP is 4 , 2 , 1 or 1 , 2 , 4.
I hope it will help you.
Regards.
Step-by-step explanation:
Assume that the 4 terms are a/r, a , ar, ar2.
Product of first 3 terms = a3 =8
=> a=2
Sum of last 3 terms :
a(1 + r + r2) = 14
=> r2 + r - 6 = 0
Solving the above equation r= -3 or 2
So the terms are
-2/3, 2, -6, 18
Or
1, 2, 4, 8
Evaluate the following expression. $$(10 + 2) \div 6 + 5^3$$
Answer:5
Step-by-step explanation:
Lexi runs the snack stand at Belleview Community Pool. This morning, she withdrew $150 from the stand's bank account to buy supplies. When the stand closed this evening, she deposited $437 from the day's sales. What was the total change in the stand's bank account relative to where it started?
Answer:
Step-by-step explanation:
Let the initial money in the account be y.
Lexi withdrew $150 from the stand's bank account to buy supplies. This will be:
= y - $150
Later, she deposited $437 from the day's sales. The money in the account will now be:
= y - $150 + $437
= y + $287
The total change in the stand's bank account relative to where it started will be the initial amount + $287.
Answer:
287
Step-by-step explanation:
Are the lines parallel? y = x + 4 and y = x-2
A. yes, they have the same slope and a different y-intercept
B. no, they are not parallel
Answer:
A
Step-by-step explanation:
Remember that parallel lines have the same slope.
The y-intercept does not matter.
We have the two equations:
[tex]y=x+4[/tex]
And:
[tex]y=x-2[/tex]
The slope is the coefficient in front of the x.
In the first equation, we can rewrite it as:
[tex]y=(1)x+4[/tex]
Therefore, the slope of the first equation is 1.
Similarly, for the second equation, we can rewrite it as:
[tex]y=(1)x-2[/tex]
The slope of the second equation is also 1.
Therefore, since their slopes are equivalent, they are parallel.
Thus, our correct answer is A.
Which ordered pair is in the solution y>=1/3x+4
A. (-6,1)
B. (1,-6)
C. (6,-1)
D. (-1,6)
Plz help me I’ll give brainliest
Answer:
it is A i could be wrong
Step-by-step explanation:
Help me solve this problem please
Answer:
Step-by-step explanation:
d
WILL GIVE BRAINLIEST IF CORRECT
Answer:
la respuesta correcta es laC
han ku po ammo paumahin
I chose the wrong screensMaggie is converting 10,560 feet to miles by using StartFraction 10,560 feet Over 1 EndFraction times StartFraction 1 mile Over 5,280 feet EndFraction. What should be Maggie’s answer?hots for the last one, sorry about that!
A fruit bowl contains 2 bananas, 5 oranges, and 4 apples in the simplest form, what is the ratio of apples to bananas in the fruit bowl?
Answer:
Ratio of apple to banana is 2:1
Step-by-step explanation:
To find ratio of x type of one thing and y type of other thing we divide
x by y and ratio is written as
ratio = x:y
_________________________________
Number of banana = 2
Number of apples = 4
Ratio of apple to banana = Number of apples :Number of banana
Ratio of apple to banana = 4:2
since 4 is divisible by 2 , to get the ratio in simplest form
we divide both numerator and denominator by 2
Ratio of apple to banana = 4/2:2 /2 = 2:1
Thus,
Ratio of apple to banana is 2:1
HELP ASAPPPP Aleisha works for a company with over 1,000 employees, of whom 81% have pierced ears. Every year, each employee draws another employee's name and gives them a gift. Let T be the number of names Aleisha draws until she draws an employee's name who does not have pierced ears.
What type of variable is T?
a.Neither
b.Geometric random variable (Do until successful)
c.Binomial random variable (FIXED # of trials before experiment)
Answer: Geometric
Step-by-step explanation:
Because you do trails until it is successful
I need help please it’s a test and I don’t understand
Answer:
to get x look at that triangle that it is in I know the angles in a triangle add up to 180° so it will be 180 - 63 degrees plus 36 degrees then to get z it will be 36 + 63 because interior angles add up to one exterior angle then to get y addz + 13 degrees then subtract it from 180°
I need help
Indicate the quadrant in which the point belongs.
(-18, -12)
Answer:
3rd quadrant is where the point is
After completing the fraction division 5 divided by five-thirds, Miko used the multiplication shown to check her work. 3 times five-thirds = StartFraction 3 Over 1 EndFraction times five-thirds = StartFraction 15 Over 3 EndFraction or 5 Which is the most accurate description of Miko's work?
Step-by-step explanation:
5 divided by five-thirds can be written in the fractional form is as follows :
[tex]\dfrac{5}{\dfrac{5}{3}}[/tex]
It can be also written as :
[tex]\dfrac{5}{\dfrac{5}{3}}=5\times \dfrac{3}{5}\\\\=3[/tex]
He has done calculations as follows :
3 x 5/3=3/1 x 5/3 = 15/3 or 5
Miko was wrong in the first step where he multiplied 3 by (5/3). It should be 5 multiplied by (3/5). He has done multiplication incorrectly.
Answer: A
Step-by-step explanation: i took the test
Simplify 9 to the 2nd power\ 9 to the 7th power
Answer:
9^2/9^7 = 9^-5
Step-by-step explanation:
The cost of using a telephone in a hotel meeting
room is $0.20 per minute. Which of the following
equations represents the total cost in dollars, for
h hours of phone use?
so its 12 dollars an hour
x means the cost
12(h)= x
Answer:
c = 0.20 (60h)
Step-by-step explanation:
The hotel charges $0.20 per minute to use the meeting‑room phone. This per‑minute rate can be converted to the hourly rate using the conversion 1 hour =60 minutes, as shown in the following equation.
[tex]\frac{0.20}{minute}[/tex] × [tex]\frac{60 minutes}{1 hour}[/tex] =[tex]\frac{0.20 * 60}{hour}[/tex]
Thus, the hotel charges 0.20×60 per hour to use the meeting‑room phone.
Therefore, the cost c, in dollars, for h hours of use is c=(0.20×60)h which is equivalent to c=0.20(60h).
Describe how the value of the digit 2 changes in each place in the number 22.222.
Answer:
ones, ten, hundreds, thousands, ten thousand, ect.
on the right side of the decimal represents a part of a number Ex. .222 is equal to 222/1000 of a number.
How does the Electoral College work?
A
It guarantees that the winner of the popular vote wins the presidency.
B
The Electoral College casts its votes on the first Tuesday in November.
The Electoral College casts its votes on January 20.
D
Each state casts a number of electoral votes equal to their members of Congress.
Answer:
D
Step-by-step explanation:
Seth is trying to pay off his credit card. He plans to pay it off in 24 months. Interest on the card is compounded monthly at a fixed annual rate of 11.6%. Seth currently has a balance of $18,875 on his credit card. Use the formula for the sum of a finite geometric series to determine Seth’s approximate monthly payment.
A.
Seth’s approximate monthly payment will be $753.97.
B.
Seth’s approximate monthly payment will be $834.75.
C.
Seth’s approximate monthly payment will be $884.99.
D.
Seth’s approximate monthly payment will be $868.35.
Answer:
$884.99
Step-by-step explanation:
Just took the quiz and this was the right answer. :)
Answer:
884.99
Step-by-step explanation:
What is the answer?
2500/x+20
=2500/(48.59)+20
is this a function or not
Answer:
I believe it is
Step-by-step explanation:
None of the x and y values have the same number
Answer:
It is not the input 5 has 2 different output values, same as the input 3 it has more than one different output
Step-by-step explanation:
Hope this helps!
Please help!
I will mark brainliest!! ;)
Answer:ok
Step-by step explanation:
Determine which quadrant the point is in: (-3,-4)
Quadrant
the answer is quadrant 3
Answer:
Its in quadrant 3
Step-by-step explanation:
Since they are both negative they go into the third quadrant
Solve the equation using the Properties of Equality.
1/2y +1/3 = 2/3
y= ?
Jon is stuck on the side of a cliff. Jon is at the midpoint from the ground to the top of the
cliff. Jon is 40 + 2 feet away from the bottom of the cliff. The cliff is 200 feet tall.
Solve for x.
How far is Jon from the top of the cliff
Complete question is;
Jon is stuck on the side of a cliff. Jon is at the midpoint from the ground to the top of the cliff. Jon is 40 + 2x feet away from the bottom of the cliff. The cliff is 200 feet tall.
Solve for x.
How far is Jon from the top of the cliff
Answer:
x = 30 ft
Jon is 100 ft from the top of the cliff
Step-by-step explanation:
We are told that Jon is at the mid point of the Cliff.
Since The cliff is 200 feet tall, the Jon is; 200/2 ft = 100 ft from either the top or bottom.
Now, we are told that Jon is 40 + 2x from the bottom of the cliff.
Thus;
40 + 2x = 100
Subtract 40 from both sides;
40 - 40 + 2x = 100 - 40
2x = 60
x = 60/2
x = 30 ft
And Jon is 100 ft from the top of the cliff as earlier seen
Chandler wants to start saving money for vacation. She currently has $300 in her bank account and plan to save $100 more each month until she reaches her goal of $1500. How long will chandler have to save until she can afford her vacation.
(write equation in y=mx+b)
d) 48 + (6 + 2) =
Please help I am stupid at maths!
Answer:
= 48 + 8
= 56
Step-by-step explanation:
hope its helps
good luck
what is the answer to this?
The cubed root of -512 is 8.
What is the answer??
Answer:
A
Step-by-step explanation:
7(y-2)=7y-14 I’m kinda confused
Answer:
Infinitely many solutions
Step-by-step explanation:
Equation:
7(y-2)= 7y - 14
1. Simplify each side
7y - 14 = 7y - 14
Infinitely many solutions
Which steps should be followed to write an equivalent ratio to find 2% of 6700? Write 2% as the ratio StartFraction 200 Over 100 EndFraction. Write the equivalent ratio StartFraction question mark Over 6700 EndFraction. (100)(67) = 6700, so (20)(67) = 1340. Write 2% as the ratio StartFraction 20 Over 100 EndFraction. Write the equivalent ratio StartFraction 6700 Over question mark EndFraction. (20)(335) = 6700, so (100)(335) = 33,500. Write 2% as the ratio StartFraction 2 Over 100 EndFraction. Write the equivalent ratio StartFraction question mark Over 6700 EndFraction. (100)(67) = 6700, so (2)(67) = 134. Write 2% as the ratio StartFraction 2 Over 100 EndFraction. Write the equivalent ratio StartFraction question mark Over 6700 EndFraction. (100)(6.7) = 6700, so (20)(6.7) = 13.4
Answer:
Step-by-step explanation:
To evaluate the expression 2% 0f 6700, we can follow the steps;
2% = 2/100
6700 = 67(100)
2% of 6700 = 2/100 * 67(100)
The 10 at the numerator will cancel out that at the denominator
2/100 * 67(100) = 2(67)
2(67) = 134
Answer:
Write 2% as the ratio 2/100. Write the equivalent ratio_?_ . (100)(67)= 6700, so (2)(67)=134
6700
Step-by-step explanation: Just did it on edg 2020. IF THIS HELPS IT IS C.