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If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?
Answer
12
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Patrick Ivers, former mathematics & English instructor
Answered June 26, 2018
If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?
The puzzle is solved by defining each variable in terms of another variable & a number & then making substitutions. Begin by taking each sum to define one of the variables in terms of the other. (Different combinations are available, but I’ll follow the a,b,c order.)
a+b=8 becomes a=8-b
b+c=10 becomes b=10-c
c+a=12 becomes c=12-a
Now subtract two of the equations that contain the same variable. I’ll pick two that contain an a: c+a =12 & a+b=8. Subtracting the latter from the former eliminates the “a”s, leaving c-b=4. Adding b to both sides to isolate c gives c=b+4. From above we can take b=10-c to substitute for b in c=b+4, giving us c=(10-c) + 4). Simplify the right side to c=14-c, add c to both sides, giving 2c=14, & then divide both sides by 2 to obtain c=7.
Replace the c in b=10-c with 7 to
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Paul K. Young, Former PhD candidate in Mathematics
Answered September 28, 2016
If A = B and B = C, does A = C?
In mathematics = is assumed to be a transitive relationship. Transitivity means precisely what you stated: A = B and B = C implies A = C.
While it’s possible to use = to represent a non-transitive relationship this would be considered an abuse of notation. A ~ B or R(A, B) would be a better way to express the relation in this case.
Similar assumptions are made about operators like + and *. + is generally assumed to be commutative, whereas * can be used for noncommutative operations like matrix multiplication. E.g. A * B != B * A.
Equality in programming is another story entirely.
In many languages = is the assignment operator and == is the equality operator. Assignment is not transitive - it’s not even a relation.There are cases where the equality operator doesn’t define a transitive relation.
random khan question and I haven't done this in a year, I'm struggling.
Answer:
Add maybe
Step-by-step explanation:
add the 500+400+200 try that hope it helps have a great day
Plz help me! I’m not sure how to do these!
Step-by-step explanation:
2. x =101
3. x= 120
4. x= 30
I am very confused in question no 1 and 5 th .
hope this will be helpful to you.
plz mark my answer as brainlist if you find it useful .
I don't understand how to do this
Answer:
x = 86
Step-by-step explanation:
The top right and bottom left angles are part of the reflective property, in turn, the bottom left angle is also 94 degrees; to find the opposite relfective angle set, it would be, in this problem, the top left and bottom right angles; the two top angles make up 180 degrees, so it would be (180-94 = 86) 86 degrees for both the top left and the bottom right angles.
Hope this helps :)
Find the slope of the line passing through the points (-7, 5) and (2,5).
Answer:
slope = 0
Step-by-step explanation:
Use formula to find the slope: m = (y2 - y1) / (x2 - x1)
Set (x1, y1) = (-7, 5)
Set (x2, y2) = (2, 5)
m = (5 - 5) / (2 - (-7))
m = (5 - 5) / (2 + 7) FYI, negative * negative = positive
m = 0 / 9
If you plot the coordinates, they'll lie on a horizontal line. Therefore, the slope of the line is 0.
The equation S = 50 + 45w represents the savings, S, after w weeks working and
depositing (putting in) money into a savings account at the bank.
Determine whether there is a proportional relationship between S and w.
Explain your reasoning.
Answer:
yes
Step-by-step explanation:
50 can be the initial money in the account and she can be depositing 45 dollars every (w) weeks and it will show her (S) savings
!! PLEASE HELP, TIMED!!Multiple choice, BRAINLIEST for correct answer!
Answer:
I'm not going to lie I'm not 100% sure but I think it's c
Answer:
D
Step-by-step explanation:
4x=4+2y
3y=5+2x
how do you solve 0.7n-1.5+7.3n=14.5
Answer:
n = 2
Step-by-step explanation:
Answer:
n = 2
Step-by-step explanation:
0.7n-1.5+7.3n=14.5
Add like terms
(0.7n + 7.3n) + (-1.5) = 14.5
8n -1 .5 = 14.5
Add 1.5 to both sides.
8n =1 6
Divide both sides by 8.
n = 2
A ratio of two numbers a/b, where b is no zero
[tex]{ \large{ \red{{\green{✮}} \: \: \sf{A \: \: number \: \: in \: \: the \: \: form \: \: of \: \:{\pink{ \frac{a}{b} \: \: where \: \: b≠0 }}\: \:{\orange{ is \: \: called \: \: a }}\: \: { \blue{ \underline{ \underline{ \tt{Rational \: \: Number}.}}}}}}}}[/tex]
0.5 g of salt is equal to how many milligrams show your work
Answer:
Amount of salt = 500 milligrams
Step-by-step explanation:
Given:
Amount of salt = 0.5 g
Find:
Amount of salt in milligrams
Computation:
1 gram = 1,000 milligrams
So,
Amount of salt = 0.5 x 1,000
Amount of salt = 500 milligrams
A submarine was situated 832 feet below sea level. If it descends 289 feet, what is its new position?
It's new position is 1121 feet below sea level.
(In this problem u are descending into a negative value so it made sense for me to add for some reason).
Hope this helps and have a good day.
Also, as proof I included my calculator showing the logic behind it. Sorry for bad Camera quality.
-R3TR0 Z3R0
Jason planted 11 packs of seed in his 4 gardens. he Planted the same amount of seed in each garden. how many packs of Seed Were planted in each were planted in each garden?
2.75 packs
Step-by-step explanation:
11 packs ÷4 gardens =2.75 packs per garden
The price of an item has risen to $216 today. Yesterday it was $135. Find the percentage Increase.
Need help on only 27 please need ASAP thanks
Answer:
8 is not in the solution set
Step-by-step explanation:
Given, -y + 7 < -4
To find out if 8 is in the solution set, substitute y = 8 in the inequality and solve to see if the statement would be true.
Thus:
-8 + 7 < -4
-1 < -4
This -1 is less than -4. This is actually not TRUE. -1 is rather greater than -4.
Therefore, 8 is not in the solution set.
A store manager combines trail mix that is 30% raisins with a trail mix that is 55% raisins. He makes 800 lbs of trail mix that is 40% raisins. How many pounds of each trail mix does the manager use?
Answer:
320 pounds of 55% raisins trail mix
480 pounds of 30% raisins trail mix
Step-by-step explanation:
i did it on RSM and got it right
What is 13x + 21y - 14x - y simplified?
Answer:
-x + 20y
Step-by-step explanation:
trust me.. its right
Write an equation of the parabola with focus (0, 10) and vertex at the origin
Answer:
f(x) = (1/10)x²
Step-by-step explanation:
This is the answer that I think it is but I am not sure if it is right...
Hope this helps!
solve each equation for given variable
- 12 = 6i- 6
Suppose a loaded die has the following probability model: If this die is thrown and the top face shows an odd number, what is the probability that the die shows a 1
Answer:
the probability is 0.6
Step-by-step explanation:
The computation is shown below:
Let us assume the X would be the number appear on the top face
Now
= P(X = 1) ÷ P(X = 0)
= 0.3 ÷ 0.3 + 0.1 + 0.1
= 0.3 ÷ 0.5
= 0.6
hence, the probability is 0.6
The bigger
the number the more
factor pairs it has.
Use examples to show that Dexter is wrong.
Answer:
See Explanation
Step-by-step explanation:
Required
Prove that Dexter is wrong
To prove that Dexter is wrong, we use the following numbers.
[tex]Number = 4[/tex]
The factors are:
[tex]Factor = 1,2\ and\ 4[/tex]
3 factors
Using a greater number:
[tex]Number = 5[/tex]
The factors are:
[tex]Factor = 1\ and\ 5[/tex]
2 factors
From the above analysis:
4 has 3 factors and 5 has 2 factors; which shows that 5 has fewer factors
This shows that Dexter is wrong
Please help me?! I don’t have a lot of time? Please I will give brainiest for the correct answer !
Answer:
It should be -3
Hope it helped i tried to help you ASAP
Step-by-step explanation:
The width of a rectangle is (5x + 2) inches and the length is (6x − 7) inches. Find the area of the rectangle.
Answer:
30x² − 23x − 14Explanation:
Area = Length · WidthLength: (6x - 7)
Width: (5x + 2)
Create An Equation(6x - 7) (5x + 2)
= (6x + −7)(5x + 2)
(6x)(5x) + (6x)(2) + (−7)(5x) + (−7)(2)
= 30x² + 12x − 35x − 14
30x² − 23x − 14- PNW
Elena mixes 5 cups of apple juice with with 2 cups of ginger ale to make punch for a party she wants to make 35 cups of punch how much apple juice does she need to buy?
Answer:
25 cups of apple juice and 10 cups of sparking water.
Step-by-step explanation:
Please show work so i know how you got your answer..thank you and have a nice day<3
Answer:
V=whl=2·2.5·4=20
Step-by-step explanation:
Answer:
2880 feet³
Step-by-step explanation:
since the question is asking for cubic feet we know we're finding volume.
v=l·w·b
v=4·24·30
=2880
zach read a book10 min every weekend for the first month 20min in 2nd month 40 min in third month and 80 min in 4th month
victoria read a book 35 everyweekend for first month 50 min second month 65 min third month 80 min 4 the month which method is used linear or exponential
Answer:
Zach time of reading every weekend forms a sequence with these terms: 10, 20, 40, 80. On the other hand, that of Victoria forms a sequence with terms: 35, 50, 65, 80. By keenly observing the sequences, Zach's sequence is a geometric sequence with a common ratio equal to 2 and Victoria's sequence is an arithmetic or linear sequence with a common difference of 15. Thus, the answer is letter B.
Step-by-step explanation:
What is the volume of the rectangular prism?
Answer:
15 0/0
Step-by-step explanation:
15 cubes on each side which totals to 30 cubes. To get the volume 15 cm multiply 30 x 1/2 = 15 the amount of volume
Answer:
15[tex]cm^{3}[/tex]
Step-by-step explanation:
ok...each of those boxes are 1/2 cm
What is the easiest thing to do is to count the front of the rectangular prism and there are 15 cubes. Now double it, and you get 30 cubes, now since each cube is 1/2 or 0.5, we get can do 0.5 x 30 and we get 15
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Need help with math points and brainlest
Answer: 10 because if they have the same shape then it must be 10.
I'm not sure if they want the same area or the same length. But if you want the volume then it would be 2. Because 2 x 75 = 150 and 15 x 10 = 150. Wait for more responses if needed.
a typing question please help and make brainleist
The Wall Street Journal reported that the median salary for middle-level manager jobs was approximately $85,000 (The Wall Street Journal, August 6, 2013). Suppose that an independent study of middle-level managers employed at companies located in Atlanta, Georgia, was conducted to compare the salaries of managers working at firms in Atlanta to the national average. The following data show the salary, in thousands of dollars, for a 8. sample of 15 middle-level managers.
108 83 106 73 53 85 80 63 67 75 124 55 93 118 77
a. Compute the median salary for the sample of 15 middle-level managers. How does the median for this group compare to the median reported by The Wall Street Journal?
b. Compute the mean annual salary and discuss how and why it differs from the median a. b. computed in part (a).
c. Compute the first and third quartiles.
Answer:
Median = $80,000 ; Mean = $84,000 ; Q1 = 67,000 ; Q3 = 106,000
Step-by-step explanation:
Given the data :
108 83 106 73 53 85 80 63 67 75 124 55 93 118 77
Reorderd data :
53, 55, 63, 67, 73, 75, 77, 80, 83, 85, 93, 106, 108, 118, 124
The median salary:
1/2(n+1)th term
Sample size, n = 15
1/2 (15 + 1)th term
1/2(16)th term
8th term = 80
Median is $80,000
Median reported by Wall Street Journal approximately $85000
The obtained and reported values are close
The mean annual salary :
ΣX / n = 1260 / 15 = 84
Mean annual salary = $84,000
Mean is the average of all earnings combined, median is the mid value of he data.
First and third quartile :
Q1 = 1/4(n+1)th term
Q1 = 1/4(16)th term
Q1 = 4th term = 67
Third quartile:.
Q3 = 3/4(n+1)th term
Q3 = 3/4(16)th term
Q3 = 12th term = 106
Help plz:)))I’ll mark u Brainliest
Answer:
18 foot ladder will reach at 14.4 feet up the wall.
Step-by-step explanation:
Triangles formed by the ladder against wall and the ground are similar,
ΔABC ~ ΔDEC
Therefore, their corresponding sides will be proportional.
[tex]\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}[/tex]
[tex]\frac{AB}{DE}= \frac{BC}{EC}[/tex]
[tex]\frac{18}{10}=\frac{BC}{8}[/tex]
BC = [tex]\frac{18\times 8}{10}[/tex]
= 14.4
Therefore, 18 foot ladder will reach at 14.4 feet up the wall.
1. Maya had a dozen white eggs
and a dozen brown eggs in her
refrigerator. She used 6 white
eggs and 8 brown eggs to make
breakfast. How many eggs does
she have left?
Answer:
6 white & 4 brown
Step-by-step explanation:
12-6=6
12-8=4