MATHEMATICS HIGH SCHOOL

Which represents a quadratic function?f(x) = −8x^3 − 16x^2 − 4x

f (x) = 3/4 x ^2 + 2x − 5

f(x) = 4/x^2 - 2/x + 1

f(x) = 0x^2 − 9x + 7

Answers

Answer 1
Answer: A quadratic equation is of the format:

ax² + bx + c = 0,  where a ≠ 0.

The first option is not quadratic, it is a cubic, it has highest power of 3.

The second option f (x) = 3/4 x ^2 + 2x − 5, is quadratic, that is the answer.

The third f(x) = 4/x^2 - 2/x + 1, doesn't qualify because of the 2/x.

The last f(x) = 0x^2 − 9x + 7 , doesn't qualify because of the a = 0, and the rule is that a ≠ 0.

Therefore  f (x) = 3/4 x ^2 + 2x − 5 represents a quadratic function.

I hope this helps.
Answer 2
Answer: Hello,

a quadratic function has y=ax²+bx+c with a!=0 for equation.
Thus the only answer is f(x)=3/4 x²+2x-5

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Which of the following is not equivalent to cos pi over 5 1. Cos negative pi over 5 2. Cos 9pi over 5 3. Cos 4 pi over 5 4. Cos 11 pi over 5

Answers

Answer:

The expression that is not equivalent to \cos ((\pi)/(5)) is:

                   3.   \cos((4\pi)/(5))

Step-by-step explanation:

We are asked to find which of the expression is not equivalent to:

                  \cos ((\pi)/(5))

1)

     \cos((-\pi)/(5))

We know that:

\cos(-\theta)=\cos(\theta)

Hence, we get:

\cos((-\pi)/(5))=\cos((\pi)/(5))

Hence, option: 1 is incorrect.

2)

            \cos((9\pi)/(5))

We know that:

\cos((9\pi)/(5))=\cos( 2\pi-(\pi)/(5))

As we know that:

\cos(2\pi-\theta)=\cos(\theta)

Hence, we have:

\cos((9\pi)/(5))=\cos((\pi)/(5))

Hence, option: 2 is incorrect.

4)

            \cos((11\pi)/(5))

We know that:

\cos((11\pi)/(5))=\cos( 2\pi+(\pi)/(5))

As we know that:

\cos(2\pi+\theta)=\cos(\theta)

Hence, we have:

\cos((11\pi)/(5))=\cos((\pi)/(5))

Hence, option: 4 is incorrect.    

3)

                 \cos((4\pi)/(5))

We know that:

\cos((4\pi)/(5))=\cos(\pi-(\pi)/(5))

As we know that:

\cos(\pi-\theta)=-\cos(\theta)

Hence, we have:

\cos((4\pi)/(5))=-\cos((\pi)/(5))\neq \cos ((\pi)/(5))

                Hence, option: 3 is the answer.
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Answers

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Answers

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The sum of two odd numbers is 198. Both of the numbers are multiples of 3. One of the numbers is 5 times the other. Which equation could you use to find the two numbers?

Answers

Answer:

The equation used to find the two numbers is:

x+5x=198

and numbers are:

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Step-by-step explanation:

The sum of two odd numbers is 198.

One of the numbers is 5 times the other.

Let one number be x

other number=5x

⇒ x+5x=198

⇒ 6x=198

Dividing both sides by 6,we get

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Other number=5x=5×33=165

The equation used to find the two numbers is:

x+5x=198

and numbers are:

33 and 165
You could use m= the lesser number and n as the greater number. Since one is 5 times the other you will start with m+5m=198. Then you will combine like terms so it will become 6m=198. Then you will solve it as a regular equation. m=33 and n=165.

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