Answers
Answer:
[tex]1.\ \ p^2q = (\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}[/tex]
[tex]2.\ \ pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}[/tex]
[tex]3.\ \ pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]
[tex]4.\ \ p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}[/tex]
Step-by-step explanation:
Required
Match each expression to their simplified form
1.
[tex](\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}[/tex]
Simplify the expression in bracket by using the following law of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
The expression becomes
[tex](\frac{p^{5-(-3)}}{q^{-4}})^{\frac{1}{4}}[/tex]
[tex](\frac{p^{5+3}}{q^{-4}})^{\frac{1}{4}}[/tex]
[tex](\frac{p^8}{q^{-4}})^{\frac{1}{4}}[/tex]
Split the fraction in the bracket
[tex](p^8*\frac{1}{q^{-4}})^{\frac{1}{4}}[/tex]
Simplify the fraction by using the following law of indices;
[tex]\frac{1}{a^{-m}} = a^m[/tex]
The expression becomes
[tex](p^8*q^4)^{\frac{1}{4}}[/tex]
Further simplify the expression in bracket by using the following law of indices;
[tex](ab)^m = a^m * b^m[/tex]
The expression becomes
[tex](p^{8*\frac{1}{4}}\ *\ q^4*^{\frac{1}{4}})[/tex]
[tex](p^{\frac{8}{4}}\ *\ q^{\frac{4}{4}})[/tex]
[tex]p^2q[/tex]
Hence,
[tex](\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}} = p^2q[/tex]
2.
[tex](\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}[/tex]
Simplify the expression in bracket by using the following law of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
The expression becomes
[tex]({p^2q^{7-4}}})^{\frac{1}{2}}[/tex]
[tex]({p^2q^3}})^{\frac{1}{2}}[/tex]
Further simplify the expression in bracket by using the following law of indices;
[tex](ab)^m = a^m * b^m[/tex]
The expression becomes
[tex]{p^{2*\frac{1}{2}}q^{3*\frac{1}{2}}}}[/tex]
[tex]pq^{\frac{3}{2}}}[/tex]
Hence,
[tex]pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}[/tex]
3.
[tex]\frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]
Simplify the numerator as thus:
[tex]\frac{p^{\frac{1}{2}} * q^3*^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]
[tex]\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]
Simplify the denominator as thus:
[tex]\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{p^{\frac{-1}{2}}q^{\frac{-1}{2}}}[/tex]
Simplify the expression in bracket by using the following law of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
The expression becomes
[tex]p^{\frac{1}{2} - (\frac{-1}{2} )} * q^{\frac{3}{2} - (\frac{-1}{2}) }[/tex]
[tex]p^{\frac{1}{2} +\frac{1}{2} } * q^{\frac{3}{2} + \frac{1}{2} }[/tex]
[tex]p^{\frac{1+1}{2}} * q^{\frac{3+1}{2}}[/tex]
[tex]p^{\frac{2}{2}} * q^{\frac{4}{2}}[/tex]
[tex]pq^2[/tex]
Hence,
[tex]pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]
4.
[tex](p^6q^{\frac{3}{2}})^{\frac{1}{3}}[/tex]
Simplify the expression in bracket by using the following law of indices;
[tex](ab)^m = a^m * b^m[/tex]
The expression becomes
[tex]p^6*^{\frac{1}{3}}\ *\ q^{\frac{3}{2}}*^{\frac{1}{3}}[/tex]
[tex]p^{\frac{6}{3}}\ *\ q^{\frac{3*1}{2*3}}[/tex]
[tex]p^2 *\ q^{\frac{3}{6}}[/tex]
[tex]p^2 *\ q^{\frac{1}{2}[/tex]
[tex]p^2q^{\frac{1}{2}[/tex]
Hence
[tex]p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}[/tex]
Related Questions
*ANSWER ASAP PLS* How can someone live smarter to reduce his/her carbon footprint? a.) remove insulation b.) live in a smart community c.) buy inefficient appliances d.) use incandescent bulbs
Answers
Answer:
remove insulation ,,,eat low on the food chain
Step-by-step explanation:
u can reduce it by 8 pounds
Answer:
remove insulation
Which expression is equivalent to (3a)-27
3a2
0
o
o
Answers
Answer:
Step-by-step explanation:
(3a) - 27 = 3a - 3^3 = 3(a - 3^2)
Next time, please share all of the answer choices. Thanks.
simplify the expression [tex]-\frac{4x+7}{2} -\frac{3x-2}{2}[/tex]
Answers
Answer:
-(4x + 7)/2 - (3x - 2)/2 = (-4x - 7 - 3x + 2)/2 = (-7x - 5)/2
Suppose a cube is given.
How many non-congruent triangles can be formed by connecting 3 of the vertices of the cube?
Answers
Answer:
The number of non-congruent triangles that can be formed from the vertices of a cube are 3 triangles
Step-by-step explanation:
The number of non congruent triangles that can be formed by connecting 3 of thee vertices of the cube is found as follows;
The available different lengths of segments joining two vertices of a cube of side length s = 2 are;
2, 2·√2, and 2·√3
Therefore, since there are only three different side lengths we have the possible triangle dimensions given as follows
Distinct triangle one = 2, 2, 2·√2
Distinct triangle two = 2·√2, 2·√2, 2·√2
Distinct triangle three = 2, 2·√3, 2·√2
Therefore, there are ₃C₃ = 3 ways of forming three non-congruent triangles from the vertices of a cube.
PLEASE HURRY Solve for X assume that lines that which appear tangent are tangent
Answers
Answer:
x = 8
Step-by-step explanation:
In a circle if two chord intersects as shown in figure
and length of a chord at point of intersection is a and b
and length of another chord at point of intersection is c and b
a*b = c*d
using this relation here, we have
8*(x+7) = 10 * (4 +x)
=> 8x + 56 = 40 + 10x
subtracting 40 and 8x from both sides
=>8x + 56 - 8x -40= 40 + 10x -8x -40
=> 16 = 2x
=> x = 16/2 = 8
Thus, x = 8
Abigail was skateboarding home when the wheel axle of her skateboard broke. She had already traveled two-thirds of the way home and had to walk the rest of the way. Walking the rest of the way home took her twice as long as it took her to ride her skateboard. How many times faster is Abigail on her skateboard than she is walking?
Answers
Answer:
4 times faster
Step-by-step explanation:
From the above question, we have the following information
Let us represent the Distance traveled by Abigail as Y
On her skateboard she travelled two thirds of the way = 2/3Y
She walks the rest of the way home = Y - 2/3Y = 1/3Y
The time she used to walk home is twice the time she used to ride her skate board
Hence, let us represent the time she used to ride her skateboard as S
So, Time she used to walk home = 2 × S = 2S
The question is asking us, how fast ,this is = Speed
The formula for Speed = Distance/ Time
Speed for her skate board = 2/3Y/S = 2Y/3S
Speed as she walks = 1/3Y / 2S = Y/ 6S
How many times faster is Abigail on her skateboard than she is walking is calculated as :
Speed of Abigail while skating ÷ Speed of Abigail while walking
= 2Y/3S ÷ Y/6S
= 2Y/3S × 6S/Y
= 4
Therefore, Abigail was 4 times faster on her skateboard than she is walking.
PLSSSS HELP! Find all real zeros and complex of each solution x^3-5x^2+7x-35=0. SHOW WORK!!!
Answers
Hey there! :)
Answer:
x = 5, x = -i√7, x = i√7
Step-by-step explanation:
We can factor the equation x³ - 5x² + 7x - 35 = 0 by grouping:
x²(x - 5) + 7(x -5) = 0
We get:
(x² + 7)(x - 5) = 0
or
(x + i√7)(x - i√7)(x - 5) = 0
Use the Zero Product Property to solve for the solutions:
x - 5 = 0
x = 5.
-----------
x² + 7 = 0
x² = -7 (We will have imaginary solutions in this instance)
x = ±i√7
Therefore, the zeros of this equation are:
x = 5, x = -i√7, x = i√7
Plot on the number line?
Answers
Answer:
See below
Step-by-step explanation:
[tex]\sqrt{6}[/tex] = 2.449
So, While plotting to the number line it will be like:
Answer:
Step-by-step explanation:
Hello!
You have to plot √6 on the number line.
The √6 is equal to 2.4494
In the given number line is depicted the scale between 2.4 and 2.5, the lines between corresponds to the second decimal digit between these two numbers, so the given scale is:
| * | | | * | * | | | * | | |
2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50
The dot corresponding to √6 is the third counting from left to right.
(See attachment)
I hope this helps!
I need help with number 5
Answers
Answer:
A
Step-by-step explanation:
62 +65=127
C+127=180
C=180-127=53°
so x=53°
53-y=11
y=53-11=42
Answer: A
Step-by-step explanation:
Since ΔCDE and ΔGHI are congruent triangles, they are equal to each other. This means x-y=11. We want to find y, but we first need to find x. We can do that by finding x° on ΔGHI.
We know that the sum of the angles is 180° in a triangle. We are given 2 angles from ΔCDE. We can use those to find x°.
62+65+x=180 [combine like terms]
127+x=180 [subtract 127 on both sides]
x=53
Now that we have x, we can find y by plugging in.
53-y=11 [subtract both sides by 53]
-y=-42 [divide both sides by -1]
y=42
Classify the following triangle. Check all that apply.
7
9
11.4
A. Equilateral
O B. Isosceles
O C. Acute
O D. Scalene
O E. Right
O F. Obtuse
Answers
Answer:
Scalene and right
The given triangle is the right-angle triangle.
What is a right-angled triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular.
The given triangle has one angle equal to 90 degrees and the line is perpendicular to the base.
Hence, the given triangle is the right-angle triangle.
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A function describes a proportional relationship for a set of discrete data. What is true about the graph of that function?
It is a series of points that fall in a straight line but are unconnected.
It is a series of points that cannot be connected by a straight line.
It is a line connecting a series of points.
It is a line drawn only in the first quadrant.
Answers
Answer:
A. It is a series of points that fall in a straight line but are unconnected.
Step-by-step explanation:
Given variables y and x, and a proportional factor k, the proportional relationship is :
y/x = k or y = k*x
This means that points fall in a straight line.
Discrete data means that the function is also discrete, that is, points are not connected between them like in a continuous function.
Answer:
its a
Step-by-step explanation:
got it right
In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.
Answers
Answer:
20
Step-by-step explanation:
A t-shirt increased in price by 1/7. After the increase it was priced at £56. What was the original price of the t-shirt?
Answers
Answer:
£48
Step-by-step explanation:
56 ÷ 7 = £8
56 - 8 = £48
Please let me know if my answer is correct.
Answer:
48
Step-by-step explanation:
solve the equation 5-8x=-1
Answers
Answer:
[tex]x = \frac{3}{4} [/tex]Step-by-step explanation:
[tex]5 - 8x = - 1[/tex]
Move constant to R.H.S and change its sign:
[tex] - 8x = - 1 - 5[/tex]
Calculate
[tex] - 8x = - 6[/tex]
The difference sign (-) will be cancelled in both sides
[tex]8x = 6[/tex]
Divide both sides of the equation by 8
[tex] \frac{8x}{8} = \frac{6}{8} [/tex]
Calculate
[tex]x = \frac{3}{4} [/tex]
Hope this helps...
Good luck on your assignment...
Answer:
Hey there!
5-8x=-1
-8x=-6
x=3/4
Hope this helps!
If you're good at trigonometry please help me with question nine a and b and show full working out tyyyyyyyy ;)
Answers
Problem 9, part a)
Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.
With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...
tan(angle) = opposite/adjacent
tan(52) = 18.5/d
d*tan(52) = 18.5
d = 18.5/tan(52)
d = 14.4537840903742
The approximate value of d is 14.4537840903742 km
This rounds to 14.5 when rounding to one decimal place.
Answer: 14.5 km=======================================================
Problem 9, part b)
Recall that
distance = rate*time
where "rate" is another term for "speed" or "velocity"
We can solve this for the time to get
time = distance/rate
------
We found the distance back in part a) above. We are given the rate of 48 km/h
So,
time = distance/rate
time = 14.4537840903742/48
time = 0.3011205018828
This is the time it takes in hours. Multiply by 60 to convert to minutes
0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes
This rounds to the whole number 18
Answer: 18 minutesYou are making a welding fixture and must cut down a length of copper tubbing from 15 1/8 inches to 8 3/4 inches. If the leftover piece is long enough, you will use it in another fixture . How long will the leftover piece be ? 23 and 7/8 1 and 51/70 7 and 1/8 6 3/8
Answers
Answer: [tex]6\dfrac{3}{8}\text{ inches}[/tex]
Step-by-step explanation:
Given: Original length = [tex]15\dfrac{1}{8}[/tex] inches
[tex]=\dfrac{8\times15+1}{8}=\dfrac{121}{8}[/tex] inches ( In improper fraction )
Length of piece cut from original = [tex]8\dfrac{3}{4}[/tex] inches
[tex]=\dfrac{4\times8+3}{4}[/tex][tex]= \dfrac{35}{4}[/tex] inches ( In improper fraction )
Length of piece leftover piece = (Original length ) - (Length of piece cut )
[tex]=\dfrac{121}{8}-\dfrac{35}{4}\\\\=\dfrac{121-2\times35}{8}\\\\=\dfrac{121-70}{8}\\\\=\dfrac{51}{8}\\\\=6\dfrac{3}{8}\text{ inches}[/tex]
Hence, the leftover piece will be [tex]6\dfrac{3}{8}\text{ inches}[/tex] long.
(80 pts) How many different ways can a captain and a co-captain be selected for a rugby team if there are 10 players?
Answers
Answer:
There are 90 different ways
Step-by-step explanation:
We can apply factorials to help solve this equation.
Just to review, 4!= 4x3x2x1
To solve this problem, we need to use factorials but only a portion of it.
Since there are only 2 roles, we only have to go down two numbers
For captain, there are 10 players available,
But for co captain, there are 9, because the captain can't also be the co captain
So the result is 10x9
We don't have to go further since there are no more further roles to occupy
10x9=90
There are 90 different ways
Answer:
45 if two co-captains or 90 if captain and co-captain are two DISTINCT roles.
Step-by-step explanation:
METHOD ONE
Label each player (either a through j OR 1 - 10).
List combinations:
a ba c a da ea f a ga ha ia jb c (not "b a" because that would be the same as #1)b db eb fb gb hb ib jc d (not "c a" or "c b" because those would be duplicates)c ec fc gc hc i c jd ed fd gd hd id je fe ge he ie jf gf hf if jg hg ig jh ih jj iMETHOD 2
use formula
Find the value of x that will make L||M. 7x+9 & 8x+2 x=? please help!
Answers
Answer:
x = 7
Step-by-step explanation:
=> 7x+9 = 8x+2 (Corresponding angles are equal)
=> 8x-7x+2 = 9 (Subtracting 7x to both sides)
=> x = 9-2 (Subtracting 2 to both sides)
=> x = 7
A triangles angle measures are in the ratio 3: 4: 7. Find the measures of the angles
Answers
Step-by-step explanation:
total ratio = 3+4+7 = 14
3/14×180= 38.57°
4/14×180= 51.43°
7/14×180 = 90°
Answer:
total ratio = 3+4+7 = 14
3/14×180= 38.57°
4/14×180= 51.43°
7/14×180 = 90°
Step-by-step explanation:
Sarah's car travels 28 miles on on gallon of gas. Greta's car travel 18 kilometers on one liter of gas. Which car gets better gas mileage?
Answers
Answer:
Gretas car gets better gas mileage
Step-by-step explanation:
18 km= 18,000 miles
18,000>28
So, Gretas car gets better gas mileage
Hope this help!
A container of club soda has a volume of 3200 cubic meter. How many liters of soda does the container hold
Answers
Answer:
3200000
Step-by-step explanation:
multiply the volume value by 1000
Solve the inequality 3x - 5 < 4.
Answers
Answer:
I got x<3
Step-by-step explanation:
Answer:
x < 3
Step-by-step explanation:
Add 5 to both sides. Then: 3x < 9 and x < 3.
The solution is the area to the left of x = 3 (but not touching x = 3).
Find the probability of rolling an even sum or a sum greater than 7 when a pair of dice is rolled
Answers
Answer:
Step-by-step explanation:
The total sum of the answers or sums that we can get when we roll a pair(2) dice is 36. Yes, there are repeated sums.
All the even sums: 2,4,6,4,6,8,4,6,8,6,8,10..., if you notice, there are 18 even sums.
All the sums that are odd by greater than 7: 9,9,9,11,9,11, if you notice, there are 6 of them.
Total: 6 + 18 = 24
Probability(A) = number of favorable outcomes/ total number of outcomes
The probability is 24/36 = 2/3
The probability of rolling an even sum or a sum greater than 7 when a pair of dice is rolled is 2/3.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
We need to find the probability of rolling an even sum or a sum greater than 7 when a pair of dice is rolled.
The total sum of the answers or sums that we can get when we roll a pair(2) dice is 36.
All the even sums: 2,4,6,4,6,8,4,6,8,6,8,10...,
there are 18 even sums.
All the sums that are odd by greater than 7: 9,9,9,11,9,11, there are 6 of them.
Total: 6 + 18 = 24
Probability(A) = number of favorable outcomes/ total number of outcomes
Therefore, The probability is 24/36 = 2/3
Hence, the probability of rolling an even sum or a sum greater than 7 when a pair of dice is rolled is 2/3.
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Which of the following are reasons used in the proof that the angle-bisector construction can be used to bisect any angle?
Check all that apply
A. Any Line segment can be extended indefinitely
B. All of the radii of a circle are congruent
C .CPCTC
D. SSS triangle congruence postulate
Answers
Answer: B C D
Step-by-step explanation:
just answered it for AP3X
Reasons used in the proof that the angle-bisector construction can be used to bisect any angle are as follows:
B. All of the radii of a circle are congruent
C .CPCTC
D. SSS triangle congruence postulate
What is angle bisector ?" Angle bisector is defined as the ray which divides the angle into two equal parts."
According to the question,
A. Any Line segment can be extended indefinitely is not required to bisect any angle .
Therefore , it is not a correct option.
B. All of the radii of a circle are congruent : To bisect an angle draw an arc with same radii is used in constructing an angle bisector .
Therefore , Option B is a correct option.
C. CPCTC : Corresponding parts of a congruent triangle are congruent is required to proof angle bisector. As it proofs two triangles are congruent.
Therefore, Option C is the correct option.
D. SSS triangle congruence postulate : It is required an important step to prove that two triangles are congruent which imply proof of angle - bisector construction.
Therefore, Option D is the correct option.
Hence, Option B, Option C , Option D are the correct answer.
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PLEASE HELP ME ASAP!!!
I need help on b!!!
Answers
Answer:
See below hot to plot.
Step-by-step explanation:
You did part a correctly and now have 3 points of this graph. For part b you need to plot the line by first plotting the points.
Plot the points on the graph and then connect them with a line.
The three points are (-5, -3), (0, 2), and (3, 5).
To plot (-5, -3):
Start at (0, 0), the origin, where the x-axis and y-axis intersect.
Go 5 units left to the -5. Now go 3 units down. That is point (-5, -3). Put a dot on it.
To plot (0, 2):
Start at (0, 0), the origin, where the x-axis and y-axis intersect.
Since the x-coordinate is 0, don't go right or left. Now go 2 units up to where you see a 2 on the y-axis. That is point (0, 2). Put a dot on it.
To plot (3, 5):
Start at (0, 0), the origin, where the x-axis and y-axis intersect.
Go 3 units right to the 3 on the x-axis. Now go 5 units up. That is point (3, 5). Put a dot on it.
Now connect the three dots with a line. Put arrow heads at both ends of the line.
Answer:
Hope this helps
Solve for x. Then, find m∠FDG and m∠GOF. answers: 1) x = 29; m∠FDG = 66°; m∠GOF = 126° 2) x = 28; m∠FDG = 64°; m∠GOF = 116° 3) x = 27; m∠FDG = 62°; m∠GOF = 118° 4) x = 24; m∠FDG = 56°; m∠GOF = 106°
Answers
Answer:
3) x = 27; m∠FDG = 62°; m∠GOF = 118°
Step-by-step explanation:
2x + 8 + 4x + 10 = 180
6x + 18 = 180
6x = 162
x = 27
Answer:
x = 27; m∠FDG = 62°; m∠GOF = 118°
Step-by-step explanation:I took the test
PLEASE HELP Plot 2 2/3 and 1 5/9
Answers
Answer:
Answer attached
whats 35x25 because idonk know i need a good resoning.
Answers
Answer:
875
Step-by-step explanation:
35 x 25 =
30x25 + 5x25
750 + 125
875
The Answer is 875
✍️(◔◡◔) hope this helps <3
Factorise fully 72-2y^2
Answers
Answer: 2(y + 6)(-y + 6)
Step-by-step explanation: Factor 72 - 2y^2
-2y^2 + 72
= 2(y + 6)(-y + 6)
Answer:
[tex]-2\left(y+6\right)\left(y-6\right)[/tex]
Step-by-step explanation:
[tex]72-2y^2[/tex]
[tex]-2y^2+72[/tex]
Factor out GCF.
[tex]2(-y^2+36)[/tex]
Apply difference of two squares formula.
[tex]-2\left(y+6\right)\left(y-6\right)[/tex]
Three tins, A, B and C, each contain buttons.
Tin A contains x buttons.
Tin B contains 4 times the number of buttons that tin A contains.
Tin C contains 7 fewer buttons than tin A.
The total number of buttons in the three tins is 137
Work out the number of buttons in tin C.
Answers
x+4x+x-7= 137
combine like terms
6x-7=137
isolate the variable by adding 7 to both sides
6x=144
divide
x=24
but remember, tin c is x-7 so plug the 24 in, and the answer is 17.
The number of buttons in C is 17 buttons
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the three tins be A , B and C respectively
The number of buttons in tin A = x
The number of buttons in tin B = 4 times the number of buttons in tin A
= 4x
The number of buttons in tin C = 7 fewer buttons than tin A
= x - 7
The total number of buttons in tin A , tin B and tin C together = 137 buttons
So , the total number of buttons =
number of buttons in tin A + number of buttons in tin B + number of buttons in tin C
So , the equation will be
Total number of buttons = x + 4x + ( x - 7 )
x + 4x + ( x - 7 ) = 137
6x - 7 = 137
Adding 7 on both sides , we get
6x = 144
Divide by 6 on both sides , we get
x = 24 buttons
So , the number of buttons in tin A is 24 buttons
So , number of buttons in tin B = 4 x 24
= 96 buttons
Therefore , the number of buttons in tin C = 17 buttons
Hence , the number of buttons in tin C is 17 buttons
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