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2 years ago

Study the table.

Mathematics

1 answer:

raketka [301]2 years ago

4 0

Answer:

quadratic with a common second difference of 4

Step-by-step explanation:

quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a $x^2\\$ + b $x$ + c = 0.

from the table it is clear that,

function is y = 2 $x^2\\$

so the function is not linear as the equation specifies.

formula to find second difference of a quadratic equation:

f(x + 2) - 2f(x + 1) + f(x)

therefore;

$2(x+2)^2$ - $4(x+1)^2$ + $2x^2$

$2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2$

$2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2$

$4x^2 - 4x^2 + 8x - 8x +8 - 4$

therefore, the answer is quadratic with a common second difference of 4

learn more about quadratic equations

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Shara has a garden that has a perimeter of 14 feet and a length of 4 feet. What is the width?

defon

Answer:

C) 3 feet

Step-by-step explanation:

P = 2l + 2w

14 = 2(4) + 2w

14 = 8 + 2w

6 = 2w

3 = w

6 0

2 years ago

Find the interior angle of a regular polygon which has 6 sides

AveGali [126]

Answer:

120°.

Step-by-step explanation:

The sum of all interior angles in a polygon with $n$ sides ( $n\in \mathbb{Z}$ , $n \ge 3$ ) is equal to $(n - 2) \cdot 180^{\circ}$ . (Credit: Mathsisfun.)

The polygon here has 6 sides. $n = 6$ . Its interior angles shall add up to $(6 - 2) \times 180^{\circ} = 720^{\circ}$ .

Consider the properties of a regular polygon. (Credit: Mathsisfun.)

All sides in a regular polygon are equal in length.
All angles in a regular polygon are also equal.

There are six interior angles in a polygon with 6 sides. All six of them are equal. Thus, each of the six interior angle will be

$\displaystyle \frac{1}{6}\times 720^{\circ} = 120^{\circ}$ .

5 0

3 years ago

The addends on an algebraic expression are called the___ of the expression

sveta [45]

Answer:Terms
Hope this helps

3 0

2 years ago

Read 2 more answers

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

4 0

3 years ago

A certain radioactive isotope has leaked into a small stream. Three hundred days after the leak, 3% of the original amount of t

sesenic [268]

If the half-life is t, then every t days, the amount of the radioactive isotope will be cut in half.
(1/2)^(number of half-lives) = 3%
number of half-lives = ln(0.03) / ln(0.5)
This gives the number of half-lives as 5.06.
Then 300 days = (5.06)(length of 1 half-life)
length of 1 half-life = 300 / 5.06 = 59.29 days

6 0

4 years ago