Let’s ignore the absolute value symbols for now and focus on the expression.
-3x+7 turns into -3(6)+7.
-3 times 6 is -18.
-18+7
-18+7 = -11
The absolute value of -11 is 11.
The original number was: " 14 " .
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a + 5 = b ;
b * 7 = 133 .
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What is: "a" ?
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133 / 7 = 19 = b ;
a + 5 = b = 19 ;
a + 5 = 19 ;
Subtract "5" from each side of the equation;
to isolate "a" on one side of the equation; and to solve for "a" ;
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a + 5 − 5 = 19 − 5 ;
to get:
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a = 14 .
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Let us check our answer:
Start with "14" ;
Add "5" : "14 + 5 = 19 " .
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then multiply by "7" : "19 * 7"
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and the result is: 133 ?
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19 * 7 = ? 133 ? Yes!
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9514 1404 393
Answer:
- 100 pounds Earl Grey
- 300 pounds Orange Pekoe
Step-by-step explanation:
Let x represent the number of pounds of Earl Gray tea in the mix. Then the total cost of the mix is ...
6x +4(400-x)=4.50(400)
2x +1600 = 1800 . . . . . . . simplify
2x = 200 . . . . . . . . . . . subtract 1600
x = 100 . . . . . . . . . . . divide by 2. Pounds of Earl Grey
(400 -x) = 300 . . . . . Pounds of Orange Pekoe
The blend should have 100 pounds of Earl Grey and 300 pounds of Orange Pekoe.
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<em>Additional comment</em>
It is easy to show that the relationship between the quantities of high-cost (H) and low-cost (L) items in the mix (M) is ...
fraction of mix that is H is (M -L)/(H -L)
Here, we have H=6, L=4, M=4.5, so the fraction of the mix that is Earl Grey is ...
(4.5 -4)/(6 -4) = 0.5/2 = 0.25
There are 400 pounds of mix, so 0.25(400) = 100 pounds is Earl Grey.
The solution above is essentially 2-step, so using this relation doesn't necessarily save any steps. It just makes it possible to solve the problem in your head.
The value of c would have to be an odd integer because an odd integer minus an even integer (8) is always an odd integer. If you are looking at answer choices, the answer will probably the odd integer. (I don't know what your answer choices are. You said which of the following, so there are probably answer choices.)
It would be 156 since both angles add up to the angle