I was confused at first until I realized that you'd shared not one, not two, but three questions in one post. would you please post just one question at a time to avoid this.
I'll focus on your second question only: Solve <span>3 + |2x - 4| = 15.
Subtr. 3 from both sides. Result: |2x - 4| = 12
Divide all terms by 2, to reduce: |x - 2| = 6
Case 1: x-2 is already +, so we don't need | |:
x - 2 = 6 => x = 8 (first answer)
Case 2: x-2 is negative, so |2x-4| = -(2x-4) = 6
Then -2x + 8 = 6. Subtr. 8 from both sides: -2x = -2
Div both sides by -2: x = 1 (second answer)
Be sure to check these results by subst. them into the original equation.
Please post your other questions separately. Thanks and good luck!
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Do the second one hope this helps
The smallest one is -2/7
The largest one is 8/9 The difference between them is
8/9 - - 2/7 =
8/9 + 2/7 =
7*8/9*7 + 2*9/9*7 =
56 / 63 + 18 / 63 =
74 / 63 =
1 11/63
Answer:
C
Step-by-step explanation:
This problem is analogous to the extraction of 6 elements from a total of 10 elements. It's the same if they are marbles, chips, or in this case, people, as here we don't care about the order of the selection as we only are drawing a sample.
Thus, the problem implies solving the amount of possible combinations of 10 people if we take by 6. There is a formula for this and is:
10 C 6 = 10!(6!4!)
If we operate, knowing that for any number x, x!=x*(x-1)*(x-2)*...*1
10 C 6 = 10!(6!4!) = 10*9*8*7*6*...*1 / [(6*5*...*1) * (4*3*2*1)]
10 C 6 = 10*9*8*7*6! / [(6*5*...*1) * (4*3*2*1)]
We have a 6! multiplying and another dividing, so they get eliminated, and as 4*2=8 and 9=3*3
10 C 6 = 10*9*8*7*/ [(4*3*2*1)] = 10*3*3*8*7*/ [(8*3*1)]
We can eliminate the 8s and one of the 3s on the numerator with the one on the denominator:
10 C 6 = 10*3*7*/1 = 210/1= 210
So, option C
Answer:
C
Step-by-step explanation:
Direct variation is a special case of first order equations; in both cases, the input is multiplied by a constant which we call the "slope" or "constant of variation." However, no direct variation equation includes a constant ("y-intercept"). So, if a given equation does have a y-intersect, that equation does not represent direct variation; if it does NOT have a y-intercept, that equation represents direct variation.
A) involves a constant term, -2; NOT direct variation
B) involves a constant term, 10; NOT direct variation
C) Here 3y = x, or y = x/3, involves no constant term, so Does represent direct variation
D) involves a constant term -3; NOT direct variation
