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solmaris [256]
3 years ago
14

Determine the number of real solutions for the equation: 6x^2+8x=7

Mathematics
1 answer:
densk [106]3 years ago
7 0

Answer:

Step-by-step explanation:

You could factor this to find out how many real roots you have, but it's easier to use the rule of the discriminate.  The discriminate comes from the quadratic formula:

b^2-4ac

Plug in the numbers from the quadratic and see what the value of it is.  If the:

discriminate < 0, you have 2 imaginary roots

discriminate = 0, you have 1 real root, multiplicity 2 and

discriminate > 0, you have 2 real roots

Our b is 8, our a is 6 and our c is -7 (remember you have to set the polynomial equal to 0 to do this).

8^2-4(6)(-7)=232

Because 232 is > 0, we have 2 real roots.

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What is the quotient of 2 3/4 and 5 1/2?
Juli2301 [7.4K]

Answer:

  1/2

Step-by-step explanation:

This can be done several ways. Perhaps the easiest is to use the decimal equivalents:

  (2 3/4)/(5 1/2) = 2.75/5.5 = 0.5

__

If you want to use the numbers given, the usual procedure is to convert them to improper fractions and do the division that way:

  2 3/4 = (4·2 +3)/4 = 11/4

  5 1/2 = (2·5 +1)/2 = 11/2

Now, the problem can be written as ...

  (2 3/4) / (5 1/2) = (11/4) / (11/2)

This sort of division problem can be solved two ways:

  <u>invert and multiply</u> (the denominator is inverted)

  = (11/4) × (2/11) = (11·2)/(11·4) = 2/4 = 1/2

  <u>use a common denominator</u> (for the two fractions)

  = (11/4) / (11/2) = (11/4) / (22/4) = 11/22 = 1/2

The quotient is 1/2.

_____

<em>Additional comments</em>

It is helpful in many cases to just use decimal equivalents for the calculation. To do that, you need to be familiar with the equivalents of commonly used fractions. I find it is usually sufficient to know the unit fractions in each case. Then you can multiply or add to find the others.

1/9 = 0.1...(1-digit repeat), 1/8 = 0.125, 1/7 = 0.142857...(6-digit repeat), 1/6 = 0.16...(1-digit repeat), 1/5 = 0.2, 1/4 = 0.25, 1/3 = 0.3...(1-digit repeat), 1/2 = 0.5

__

I learned the "invert and multiply" method for dividing fractions when I was in school. The Common Core math apparently also teaches the method of matching the denominators of a compound fraction. Then the result is the ratio of numerators. (A variation not taught is that you can match the numerators and use the inverse of the ratio of denominators. Both of these methods can be validated using the "invert and multiply" method. (11/4)/(11/2) = 2/4)

"Invert and multiply" is another way of saying that division is the same as multiplication by the reciprocal. This applies everywhere, not just in fraction problems.

8 0
3 years ago
60 points Need help Asap
Anna [14]

Answer:

45 units ^2

Step-by-step explanation:

make sure to divide the triangle and sqaure up when finding the area of this polygon..

hope this helps!!

8 0
3 years ago
Jacob is visiting Argentina, and he hears a warning that the temperature may drop as low as -12.4°C. How cold is that in °F, to
earnstyle [38]
The answer would be C

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3 years ago
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Solve each expression using the correct order of operations,<br>7- 5 + 3 x 10<br>​
Lynna [10]

Answer:

28 is your answer

Step-by-step explanation:

you start with multiplication and continue with addition and then go to subtraction

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3 years ago
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How do I find 0.000238 in scientific notation
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<span>2.38 x 10^(-4) 0.072 = 7.2 x 10^(-2) 723,600,000 = 7.236 x 10^(8)</span>
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