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
Gill wears a device that counts the number of steps she takes every day. One day she did onefifteenth of her steps before breakfast, a further half walking into town and another one-tenth walking round the supermarket. a What fraction of her steps were not taken yet? b That day the device recorded 12 000 steps. How many steps were not taken yet?
Answer:
6000 steps
Step-by-step explanation:
1/15 +1/10+1/2=2/30+3/30+15/30=20/30=2/3
2/3=12000 steps
1/3=6000 steps
3/3=18000 steps
Her total steps should be 18000 and she has done 12000 steps.
18000-12000=6000 steps
6000 steps were not taken yet.
[tex]1/15 +1/10+1/2=2/30+3/30+15/30=20/30=2/3[/tex]
[tex]2/3=12000 steps[/tex]
[tex]1/3=6000 steps[/tex]
[tex]3/3=18000 steps[/tex]
Her total steps should be 18000 and she has done 12000 steps.
[tex]18000-12000=6000 steps[/tex]
What is the most important thing when walking?Walking prevents heart disease, raises the heart rate, lowers blood pressure, and strengthens the heart. Postmenopausal women who walk 1-2 miles a day can lower their blood pressure by about 11 points in 24 weeks.
For example, regular and active walking helps maintain a healthy weight and reduce body fat. Prevents or treats a variety of conditions, including heart disease, stroke, high blood pressure, cancer, and type 2 diabetes. Improves cardiovascular health.
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Four years ago the average age of A,B and C was 25 years. Five years ago the average age of B and C was 20 years. A's present age is
Four years ago average age of A , B & C was 25 years.
Find:A's present age
Solution:Let the ages of A , B , C be A , B , C years.
Age of A before 4 years = (A - 4) years. Age of B before 4 years = (B - 4) years. Age of C before 4 years = (C - 4) years.We know that,
Average = Sum of observations/Number of observations.
Here,
Sum of observations = A - 4 + B - 4 + C - 4 = (A + B + C - 12) years.
Number of observations = 3.
So, (A + B + C - 12)/3 = 25
⟹ A + B + C - 12 = 3 * 25
⟹ A + B + C = 75 + 12
⟹ A + B + C = 87 -- equation (1)
Also given that,
Average age of B & C before 5 years was 20 years.
⟹ (B - 5 + C - 5)/2 = 20
⟹ B + C - 10 = 2 * 20
⟹ B + C = 40 + 10
⟹ B + C = 50 -- equation (2)
Subtract equation (2) from equation (1).
⟹ A + B + C - (B + C) = 87 - 50
⟹ A + B + C - B - C = 37
⟹ A = 37 years
∴ A's present age is 37 years.
I hope it will help you.
Regards.
Answer:
→ md - 2nd + 3md = 2 * [ a + (n - 1)d ]
→ 4md - 2nd = 2 * [ a + (n - 1)d ]
→ 2(2md - nd) = 2 * (a + nd - d)
→ 2md - nd - a + d = nd
→ 2md - nd - (md - 2nd) + d = nd
[ From equation (1) ]
→ 2md - nd - md + 2nd + d = nd
→ md + nd + d = nd
→ (m + n + 1)d = n * d
→ (m + n + 1) = n
Step-by-step explanation:
2 1/7+3/7(3x−5)=−4
A) x= -5 1/7
B) x= -3 1/9
C) x= -1 23/49
D) x= - 8/9
The answer fam is...........B) x= -3 1/9
5/8x + 1/3x = 69 x=_
Answer:
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Step-by-step explanation:
Can you help me to solve this
Answer:
[tex]\frac{4a-2}{2a+1}[/tex]
Step-by-step explanation:
Factorise the numerator and denominator
8a² - 2 ← factor out 2 from each term
= 2(4a² - 1) ← 4a² - 1 is a difference of squares
= 2(2a - 1)(2a + 1)
4a² + 4a + 1 ← is a perfect square
= (2a + 1)²
Thus
[tex]\frac{8a^2-2}{4a^2+4a+1}[/tex]
= [tex]\frac{2(2a-1)(2a+1)}{(2a+1)(2a+1)}[/tex] ← cancel (2a + 1) on numerator/ denominator
= [tex]\frac{2(2a-1)}{2a+1}[/tex]
= [tex]\frac{4a-2}{2a+1}[/tex]
what is the area of a semicircle with a diameter of 12.5 ft
radius = 12.5/2 = 6.25 feet
area = [tex]\frac{1}{2} \pi r^{2} = \frac{1}{2}\pi (39.0625) = 19.5312\pi[/tex] square feet
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining.
Which equations could you use to find the price of one tire patch? Select all that apply.
Answer:The answers are
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Answer:
C. 4x + 1.9 = 22.2 and E. 22.2 – 4x = 1.9
Step-by-step explanation:
What is 2+2? I think the answer is 6 :)
Answer: wut yea i think it's six too.
The answer is 4 because look at this: ♥ ♥
That's 2 hearts
If you add 2 more:
♥ ♥ ♥ ♥
1 2 3 4 --> 4 hearts!
♥ ♥ + ♥ ♥ = ♥ ♥ ♥ ♥
So, 2 + 2 = 4.
Ok :
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!
Answer:
19.04
Step-by-step explanation:
convert 170% into decimal form number:
1.7
Then multiply by 11.2:
1.7 × 11.2 = 19.04
Pls consider marking my answer as Brainliest! It would mean a lot!
1 pound of a certain candy cost $8, how many pounds can be purchased for $12?
Answer:
1.5 pounds
Step-by-step explanation:
1 pound costs $8, $1 buys 1/8 pound
$12 buys 12/8=3/2=1.5 pounds
Answer:
12-8= 4
Step-by-step explanation:
one pound of it cost 8 dollars and he only has 12 so subtract 8 from 12 he only has enough to buy 1 pack.
Scott makes $52 for 4 hours of work? How much does Scott make per hour?
Answer:
13
Step-by-step explanation:
52/4=13
$13.40
All I did was divide 52 by 4 to get the answer
A system of equations and its solution are given below system
System A
Solution: (-2,1)
To get system B below, the second equation in a system A was replaced by sum of that equation and the first equation in system A mutiplied by -2.
System B
5x - y = -11
A) The second equation in system B is 7x = 30. The solution to system B will be the same as the solution to system A.
B) The second equation in system B is 7x = 30. the solution to system B will not be the same as the solution to system A.
C) The second equation in system B is -7x = 14. The solution to system B will be the same as the solution to system A.
D) The second equation in the system B is -7x = 14. The solution to system B will not be the same as the solution to system A.
Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). ∆ABC and ∆FDE are congruent by the criterion. (Use the three-letter abbreviation without spaces.) The value of x is , and the value of y is .
*See attachment for the given diagram.
Answer:
∆ABC and ∆FDE are congruent by the SSS criterion.
The value of x is 11 and the value of y is 8
Step-by-step explanation:
Based on the Side-Side-Side (SSS) Congruence Theorem, ∆ABC and ∆FDE are congruent to each other. The 3 sides of ∆ABC are congruent to the 3 given sides of ∆FDE.
Thus:
AB ≅ DF
BC ≅ DE
CA ≅ FE
Find x:
Since BC ≅ DE, therefore measure of BC = measure of DE.
BC = x + 3
DE = 14
Thus,
x + 3 = 14
Subtract 3 from each side
x = 14 - 3
x = 11
Find y:
Since AB ≅ DF, therefore the measure of both sides are equal.
AB = 3
DF = x - y
Thus,
x - y = 3
Substitute x = 11 into the equation
11 - y = 3
Subtract 11 from both sides
-y = 3 - 11
-y = -8
Divide both sides by -1
y = -8/-1
y = 8
Answer:
Below
Step-by-step explanation:
got it right
∠A and \angle B∠B are supplementary angles. If m\angle A=(2x-14)^{\circ}∠A=(2x−14)
∘
and m\angle B=(3x-6)^{\circ}∠B=(3x−6)
∘
, then find the measure of \angle A∠A.
Answer:
∠ A = 66°
Step-by-step explanation:
Supplementary angles sum to 180° thus
∠ A + ∠ B = 180 , substitute values
2x - 14 + 3x - 6 = 180 , that is
5x - 20 = 180 ( add 20 to both sides )
5x = 200 ( divide both sides by 5 )
x = 40
Thus
∠ A = 2x - 14 = 2(40) - 14 = 80 - 14 = 66°
how do I do slope? i know nothing about it and i need to learn it.
Answer:
slope is easy it is rise over run.
Step-by-step explanation:
rise/run
rise means up
run means move sideways.
Answer: what do you mean by slope?
Step-by-step explanation:
the game that you have to control a ball and you have power-ups and you have to stay on platforms and you have to avoid the red rectangles?
Is this a good freestyle poem
Do you have a recommendation
What would people say if I were gone?
What would they write on my tombstone?
In 10 years would they even remember me?
If I don't even like myself why would people like me?
I feel like I am carrying my problems up a mountain, people have tried and helped but after a while, they just walk away.
Someone asks me can you take some of mine, of course, why not.
I feel like I am letting myself be crushed by my own problems but I want to help everyone else.
I don't want anyone to feel like I do so I try to take their problems to.
I have taken to many I am finally falling.
I am falling off the mountain will anyone even try to stop me from falling or will they let me go.
Let me go. Let me go.
Sometimes I wish someone would save me because I have been trying to save myself for too long.
But others times I wnder do they really want to help me or do they just want me to take some of their pain?
Answer:
Yes that is actually a good free verse, it contains emotions, questions, ( rhetorical) it don't have a repletion, a word that repeats in each stanza, but yes it is very good i actually showed this to my teacher and she said it was good :)
3. John has $500 and wants to buy a used car but does not have sufficient money.
He decides to save $80 per week for a number of weeks to make up the deficit.
a. Given that he has $500 at the beginning of the first week, how much will he
have saved at the end of the 2nd, 3rd, 45, and 5 weeks?
b. Make a graph to represent the pattern from part a.
c. Create a function that represents the relationship between weeks (w) and
money (m)
d. Explain each part of your function.
Answer:820
Step-by-step explanation:
Since he got $500 the first week multiply 80x4 which is 320+500 is 820$
Name The Angle Pair And Find The Missing Value.
Answer:
Angle 1 and angle 2
x=9
Step-by-step explanation:
The angle pair is complementary since it makes a right angle, so you could technically name it anything like angle 1 and angle 2. You make the equation 4x+8+5x+1=90. Then, you combine like terms and get 9x+9=90. Then, subtract the 9 from 90, 81. 9x=81. Then, divide the 9 from 81. X=9.
Can you explain pls
Answer:
d
Step-by-step explanation:
If you're solving for a, you'll want to isolate it on one side of the equals sign. When doing this, you have to add q to the left side so it equals zero; and whatever you do to the right, you do the left so (3/4a=k+q). After this, you want to use the same logic to get rid of of the 3/4 on the left side. Since the opposite of 3/4 is 4/3, multiply (3/4)x(4/3) instead of (3/4)/(3/4) to make it easier. Since you did that to the left side, you should do it to the right (a=4/3(k+q)). Sorry for my bad handwriting.
Ayden filled up his car with gas before embarking on a road trip across the country. The car uses 2 gallons of gas for every hour driven, and after driving for 4 hours, there were 4 gallons of gas left in the tank. Write an equation for G,G, in terms of t,t, representing the number of gallons of gas remaining in Ayden's gas tank after tt hours of driving.
Answer:
G=-2t=12
Step-by-step explanation:
uh well i did delta thats was the answer they gave me...
Total capacity: 12 gallons
Equation: G = 12 - R*t
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let R be rate of gas consumption by car = 2 gallons/hr
Let G be the gallons in the car left
let g be the gallons used by the car while driving
Driven time, t = 4 hrs
Remaining gas =4 gallons
according to the question,
consumption rate, R = g/t
After driving for 4 hours
2 = g/4
g = 2*4 = 8 gallons
remaining gas = 4 gallons
therefore, total capacity of the car = 8 + 4 = 12 gallons
equation in terms of gas left,
G = 12 - R*t
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answer number 1 or 2 or both please<3
Answer:
1. 1.96 g/L
2. 1 g/cm³
Step-by-step explanation:
Density is found by dividing mass by volume: d = m/v.
1.
We know that the mass is 0.196 grams, while the volume is 100 mL.
Converting the volume to liters, we get:
100 mL = 0.1 L
Then, applying our density formula:
d = m/v
d = 0.196 g / 0.1 L = 1.96 g/L
2.
Here, we know that the mass is 27 grams. However, we don't know the volume, which we need to find.
The block of wood is 3 cm on all sides, which means it's a cube. The volume of a cube is denoted by V = s³, where s is the side length. Here, s = 3, so V = s³ = 3³ = 27 cm³.
Applying our density formula gives:
d = m/v
d = 27 g / 27 cm³ = 1 g/cm³
~ an aesthetics lover
NEED HELP PLEASE IM BEGGING YOU PLEASE!!!!!!!!!!!
I NEED HELP ON ALL THREE PLEASE!!!!
Answer:
16. H
17. C
18. G
Graph y > 2x - 3 , Is (3 , -1) a possible solution to the inequality graphed above?
Answer:
No it cant
Step-by-step explanation:
(3,-1) is not a possible solution for the equation y > 2x-3
The points that touch the x and y intercept are (1.5,0) and (0,-3)
The total budget for a landscaping project was $349.02, and the project called for 42 plants. What is the average cost per plant? Explain the method used for solving the problem.
Answer:
$8.31
Step-by-step explanation:
you have your budget of $349.02 that's for 42 trees you are deciding tour budget by 42 giving you $8.31 per tree.
Donna deposits $700 Into an account that pays simple interest at a rate of 5% per year. How much Interest will she be paid in the first 5 years?
please help me!! :)
Answer:
1/2
Step-by-step explanation:
hope this helps :o
HELP ME ASAP BRO THIS IS DUED BY TONIGHT, LITERALLY ANYONE OUT THERE
What is the type of angle 12 and 6 form? and what is their relationship?
Answer:
Alternate angles
Step-by-step explanation:
Alternates angles are in a form of Z so the relationship between angle 12 and 6 are alternate angles.
What are the y-intercepts to graph the equation -4x – 3y = 36?
4x-3y =36
Move the constant to the left by adding its opposite to both sides
4x-3y-36=36-36
The sum of two opposites equals 0
Answer: 4x-3y-36=0
PLEASE MARK ME AS BRAINLIEST
f(x) = -2x+3
find f(-3)
Answer:
3
Step-by-step explanation:
this is because 3 would be the answer
Kevin and monica lead visitor tours at a museum. Last month, both kevin and monica led the same number of vistors. Kevin lead 150 adults, plus 6 student groups. Monica led 134 adults, plus 8 student groups. If each student group had the same number of students, which equation could be used to determine the number of students in each group?
Answer:
Number of students in each group = 8
Step-by-step explanation:
kevin and monica led the same number of vistors.
Let x = number of students in each group
Kevin lead 150 adults, plus 6 student groups.
150 + 6x
Monica led 134 adults, plus 8 student groups.
134 + 8x
Equate both equations
150 + 6x = 134 + 8x
Collect like terms
150 - 134 = 8x - 6x
16 = 2x
Divide both sides by 2
x = 16 / 2
= 8
x = 8
Number of students in each group = 8