A portion of the Quadratic Formula proof is shown. Fill in the missing reason. Statements Reasons ax2 + bx + c = 0 Given ax2 + bx = −c Subtract c from both sides of the equation x squared plus b over a times x equals negative c over a Divide both sides of the equation by a x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation x squared plus b over a times x plus the quantity b over 2 times a end quantity squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared Find a common denominator on the right side of the equation x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared ? Rewrite the perfect square trinomial as a binomial squared on the left side of the equation Take the square root of both sides of the equation Multiply both sides of the equation by 2 Square the left side of the equation
Answers
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
I was taking the test and couldn't find the answer to this question anywhere so let me help you out...
abidemiokin provided a wonderful step-by-step explanation for solving the formula, but left out the actual answer for the question which is what I'm here for. I read through abidemiokin's explanation and reviewed my options before choosing the best answer. As you see in step 5 of my edited version of abidemiokin's explanation the missing step is there. In the provided question we see steps 1,2, 3, and 4 being identical to those in the explanation below. From this, it is clear the next step (step 5) would be the next step, and as it is one of the options we can trust that it is correct.
(If you still have doubts then trust the fact that I took the test and the answer I provided above was indeed correct.)
Given the quadratic equation ax²+bx+c = 0, to derive the quadratic formula from the equation, the following steps must be followed;
ax²+bx+c = 0
Step 1: Subtract c from both sides
ax²+bx+c-c = 0-c
ax²+bx = -c
Step 2: Divide both sides of the equation by a
ax²/a + bx/a = -c/a
x² + bx/a = -c/a
Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides
x² + bx/a + (b/2a)² = -c/a + (b/2a)²
Step 4: Square the quantity b/2a on the right side of the equation
x² + bx/a + (b/2a)² = -c/a + b²/4a²
Step 5: Find a common denominator on the right side of the equation which is 4a²
x² + bx/a + (b/2a)² = -4ac/4a² + b²/4a²
Step 6: Add the fractions together on the right side of the equation
x² + bx/a + (b/2a)² = (-4ac+ b²)/4a²
Note: The fraction at the right-hand side of the equation is to be added together not multiplied as shown in the question.
Step 7: The equation on the left is to be written as a perfect square as shown
(x+b/2a)² = (-4ac+ b²)/4a²
Step 8: Take the square root of both sides
√(x+b/2a)² = √ (-4ac+ b²)/4a²
(x+b/2a) = √(-4ac+ b²)/2a
Step 9: subtract b/2a from both sides
x+b/2a - b/2a = -b/2a + √(-4ac+ b²)/2a
x = -b/2a + √(-4ac+ b²)/2a
Step 10: Add the fractions together on the right-hand side
x = -b±√(-4ac+ b²)/2a
This gives the required equation
Answer: A Find a common denominator on the right side of the equation
Step-by-step explanation: Took the test of FLVS
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Estimate the value of 21*3.86/0.207 anyone knw the estimate for this?
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Answers
Answer:
There will be 387
Step-by-step explanation:
This question is an example of compound decrease.
To work this out you would first have to convert the percentage of 6 into a decimal. You can do this by dividing the percentage of 6 by 100, this gives you 0.06. This is because percentages are out of 100.
The next step is to minus 0.06 from 1, this gives you 0.94. This is because we are working out the percentage decrease.
Finally to work this out you would multiply the amount of 720 by 0.94 to the power of 10, this gives you 387.80. However there can not be a decimal of a person and so it becomes 387. This is because it is working out 6% and subtracting it and then working out 6% of that new amount. This repeats 10 times.
1) Divide 6 by 100.
2) Minus 0.06 from 1.
3) Multiply 720 by 0.94 to the power of 10.
4) Round down
387
We would represent this as: 0.06
We would represent 720 as: 720(1- .05)^0=720
So the equation would be: 720(1-0.06)^10=X
720(0.94)^10=X
720(0.53861511409)=X
387.8=X
388=X
So, after 10 years the company would have 388 employees left.
B. The sum of Equation 1 and Equation 2
C. An equation that replaces only the coefficient of x with the sum of the coefficients of x in Equation 1 and Equation 2.
D. An equation that replaces only the coefficient of y with the sum of the coefficients of y in Equation 1 and Equation 2.
E. The sum of a multiple of Equation 1 and Equation 2.
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Adding and multiplying the terms allow them to keep working. However, you must make sure that each variable is changed each time. Not just one as in C and D.
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Answer:
220 ft per hour
Step-by-step explanation:
5280 divided by 24
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25*0.1 is 2.5
25+2.5 =27.5
27.5 x 8 = 220
220
The answer is $220
EXPLANATION
To work this out, you would have to firstly add the 10% to $25. To do this you need to find 10% (which is $2.50) and then add it to $25, making the hourly income $27.50
We would then times this by 8 to get the final answer of $220.
Hope this helps!
Answers
3/6+2/6=5/6
The answer is 5/6.
1/2=0.5 and 1/3=0.33 repeated then you add them together and get 0.8333 repeated.
Answers
you have to,
divide 48 with 100 = 48/100 = 0.48
when you got your decimal then u can easily say that it is closer to 0.5 or 1/2
1/2 is 50/100 simplified!
1/2 and 48/100 are larger than 0 so 0 automatically cancels out!