Answer:
2 solutions
Step-by-step explanation:
I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...
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To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:
3x(x -4) +5 -x -(2x -7) = 0
3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses
3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms
3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor
The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.
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<em>Alternate method</em>
Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...
d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c
d = (-15)^2 -4(3)(12) = 225 -144 = 81
This positive value means the equation has 2 real solutions.
2. if the cost of 10 gallons of gasoline is 30 dollars then divide 10 by 10 and divide 30 by 10 to get 1 and 3 so the cost of 1 gallon is $3
3. if 2 packets of bread is 3 dollars then divide 2 and 3 by 2 so in conclusion 1 loaf f bread is $1.50.
4. if a cleaning service charges $1000 for 20 offices then divide 1000 by 20 and 20 by 20 to have an answer of $50 for every one office.
5. to find the answer to this problem you need to divide 320 by 4 to find out organes per bag so 80 oranges per bag.
6. if the baker ca bake 12 cakes every 45 minutes then he can bake 4 cakes every 15 minutes because divide both 12 and 45 by three so in conclusion the baker can bake 16 cakes every hour.
7. so if you can print 100 pages for $2 then multiply 100 and 2 by two to get 200 pages for $4
8. so to find the answer to this all you need to do is divide 12 by six to fin out that it is 2 apples for $1 and for the other store you divide 21 by seven to find out that it is 3 apples for $1.
9. to find out the answer for this divide 24,000 by 12 to find that his monthly income is $2,000.
10. if a 0.2 pund package is $4 then a 0.001 pound package is 20 cents.
I hope i got the answers right and that i could help! :)
Answer:
Part A
12 pieces
Part B
Tara can cut Twelve 2/5 foot pieces can be cut from 4 4/5 feet of rope.
Step-by-step explanation:
Part A: How many 2/5 foot pieces can Tara cut from the 4 4/5 feet of rope?
This is calculated as:
4 4/5 feet of rope ÷ 2/5 foot pieces
= 24/5 ÷ 2/5
= 24/5 × 5/2
= 12
Part B: Using the information in Part A, interpret the meaning of the quotient in terms of the two fractions given
The quotient in Part A is 12
Therefore, this can be interpreted as:
Tara can cut Twelve 2/5 foot pieces can be cut from 4 4/5 feet of rope.
Answer:
30 = total muffins
Step-by-step explanation:
To determine how many muffins were eaten, we take the total muffins times the fraction that were eaten
eaten muffins = total muffins * fraction
25 = total muffins* 5/6
Multiply each side by 6/5
6/5*25 = total muffins *5/6*6/5
30 = total muffins
