Answer:
18 and 19
Step-by-step explanation:
Answer:
![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Step-by-step explanation:
Your original number to convert is 0.333333. Let's slide the decimal point in this number to the right 1 place(s) (the same number of digits in the number 3).
If we do this, we'll get a 3.333333 (slide the decimal in the 0.333333 right 1 places, you'll get 3.333333).
So what? Well now, we have two numbers with the same repeating decimal parts, 3.333333 and 0.333333.
Now let's just work a little algebra into all of this. Let's call your original number x. And in this case, x = 0.333333. The number with the decimal point slid over can be called 10x, because 10x = 3.333333
10x = 3.33333
-x = 0.333333![\frac{10x = 3.33333 -x = 0.333333}{9x = 3}](https://tex.z-dn.net/?f=%5Cfrac%7B10x%20%3D%203.33333%20%20-x%20%3D%200.333333%7D%7B9x%20%3D%203%7D)
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Now, solving 9x=3 for x by dividing both sides of it by 9, we'll get that x=3/9. And this is your answer.
How is this your answer? Well remember that above, x was originally set equal to 0.333333 via x = 0.333333, and now we have that x is also equal to 3/9, so that means 0.333333 = 3/9..and there's 0.333333 written as a fraction.
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<u>Simplify 3/9 into the lowest terms:</u>
![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
2p² - p - 10 = 0
2 = a
- 1 = b
- 10 = c
To factor, find two numbers that multiply to equal a·c and also that have a sum of b
2p² + 4p - 5p - 10 = 0
2p (p + 2) - 5 (p + 2) = 0
<h3>Answer: ( 2p - 5 ) ( p + 2 ) = 0</h3>
Answer:
The table a not represent a proportional relationship between the two quantities
The table b represent a proportional relationship between the two quantities
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
<u><em>Verify each table</em></u>
<em>Table a</em>
Let
A ----> the independent variable or input value
B ----> the dependent variable or output value
the value of k will be
![k=\frac{B}{A}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BB%7D%7BA%7D)
For A=35, B=92 ---> ![k=\frac{92}{35}=2.63](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B92%7D%7B35%7D%3D2.63)
For A=23, B=80 ---> ![k=\frac{80}{23}=3.48](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B80%7D%7B23%7D%3D3.48)
the values of k are different
therefore
There is no proportional relationship between the two quantities
<em>Table b</em>
Let
C ----> the independent variable or input value
D ----> the dependent variable or output value
the value of k will be
![k=\frac{D}{C}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BD%7D%7BC%7D)
For C=20, D=8 ---> ![k=\frac{8}{20}=0.40](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B8%7D%7B20%7D%3D0.40)
For C=12.5, D=5 ---> ![k=\frac{5}{12.5}=0.40](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B5%7D%7B12.5%7D%3D0.40)
the values of k are equal
therefore
There is a proportional relationship between the two quantities
The linear equation is equal to
![D=0.40C](https://tex.z-dn.net/?f=D%3D0.40C)
There are 9 cans of soup and 5 cans of frozen dinner.
The variables used for soup and frozen dinner are x and y respectively.
Step-by-step explanation:
Let,
Soup = x
Frozen Dinner = y
According to given statement of sodium;
300x + 500y = 5200 eqn 1
And,
x + y = 14 eqn 2
![Multiplying\ equation\ 2\ with\ 300\\300(x+y=14)\\300x+300y=4200\ Eqn 3\\](https://tex.z-dn.net/?f=Multiplying%5C%20equation%5C%202%5C%20with%5C%20300%5C%5C300%28x%2By%3D14%29%5C%5C300x%2B300y%3D4200%5C%20Eqn%203%5C%5C)
Subtracting Eqn 3 from Eqn 1;
![(300x+500y)-(300x+300y)=5200-4200\\300x+500y-300x-300y=1000\\200y=1000\\y=\frac{1000}{200} \\y=5](https://tex.z-dn.net/?f=%28300x%2B500y%29-%28300x%2B300y%29%3D5200-4200%5C%5C300x%2B500y-300x-300y%3D1000%5C%5C200y%3D1000%5C%5Cy%3D%5Cfrac%7B1000%7D%7B200%7D%20%5C%5Cy%3D5)
Putting value of y in Eqn 1;
![300x+500(5)=5200\\300x+2500=5200\\\\Subtracting\ 2500\ from\ both\ sides\ \\300x+2500-2500=5200-2500\\300x=2700\\x=\frac{2700}{300} \\x=9](https://tex.z-dn.net/?f=300x%2B500%285%29%3D5200%5C%5C300x%2B2500%3D5200%5C%5C%5C%5CSubtracting%5C%202500%5C%20from%5C%20both%5C%20sides%5C%20%5C%5C300x%2B2500-2500%3D5200-2500%5C%5C300x%3D2700%5C%5Cx%3D%5Cfrac%7B2700%7D%7B300%7D%20%5C%5Cx%3D9)
There are 9 cans of soup and 5 cans of frozen dinner.
The variables used for soup and frozen dinner are x and y respectively.
Keywords: Variables, linear equations, subtraction.
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