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Nikitich [7]
3 years ago
8

Which number is a perfect square ? a. 33 b. 37 c. 48 d. 49

Mathematics
2 answers:
maksim [4K]3 years ago
8 0

Answer:

49

Step-by-step explanation:

Because sqrt(49)=7

others are Real numbers

choli [55]3 years ago
7 0

Answer:

49.

Step-by-step explanation:

A perfect square is a number that can be expressed as the product of two equal integers. The only way to accurately calculate if a number is a perfect square is to find the factors.

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Describe how both the Rational Root Theorem and Descartes’ Rules of Signs help you to find the zeros of a polynomial? Give me an
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Answer:

Step-by-step explanation:

Rational Root Theorem: If the polynomial

P(x) = a n x n + a n – 1 x n – 1 + ... + a 2 x 2 + a 1 x + a 0

has any rational roots, then they must be of the form of (factors of a0/factors of an).

Example: F(x) = 4x² + 5x +2

If this polynomial has any rational roots, then they must be (factors of 2)/(factors of 4), so (±1, ±2)/(±1, ±2, ±4). So if this polynomial has any rational roots, they must be either: ±1, ±1/2, ±1/4, or ±2. Notice that this polynomial doesn't have to have any rational roots, but if it does, then the roots must fit the Rational Root Theorem.

Descartes' Rules of Signs:

a). In a polynomial, how many time the sign changes is how many positive roots the polynomial will have.

Example: 5x³ + 6x² - 2x - 1

In this expression, the sign only changed once, between 6x² and 2x, so it will only have one positive root.

Example 2: 6x³ - 4x² + x - 6

In this expression, the sign changed 3 times (remember there is a invisible "+" sign before the 6x³), so it will have 3 positive roots.

b). In a polynomial, if you plug in "-x" for all "x", then how many times the new polynomial changes sign is how many negative roots the old polynomial have.

Example: 5x³ + 6x² - 2x - 1.

If we plug in "-x" for all "x", then we get 5(-x)³ + 6(-x)² - 2(-x) -1, which simplifies to -5x³ + 6x² + 2x -1. In this new expression, the sign changed twice, so we have two negative roots for the expression. Notice how we got one positive root the first time and two negative roots the second time, and 1 + 2 = 3. The Fundamental Theorem of Algebra states that for a nth degree polynomial, it will have n complex roots. The polynomial we worked with was a 3rd degree polynomial, and we got 1 + 2 = 3 roots in the end.

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kramer

Answer:

The transformation in this figure is rotation.

Step-by-step explanation:

The transformation in this figure is rotation.

There are four types of transformation.

<u>Translation:</u>

Movement of the object without rotating it or changing its size.

<u>Reflection:</u>

Flipping the object about a line of reflection. The mirror image is formed after transformation.

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Step-by-step explanation:

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