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3 years ago

Identify whether each phrase is an expression, equation, or inequality.

Mathematics

1 answer:

Kay [80]3 years ago

8 0

Expression

$bc + 1 - (8d - 4)$

Equation

${w}^{4} = 81$

Inequality

$63 < 9k$

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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

HELP ME PLEASE THIS IS REALLY IMPORTANT

andrezito [222]

Answer:

Step-by-step explanation:

COUNT ALL (16) DIVIDE BY 4

8 0

3 years ago

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This table shows the number of customers who have come in to Trent’s Hobby Shop each day since he opened the doors. Is this func

taurus [48]

Answer:

Discrete

Step-by-step explanation:

The points that you would plot are (1,3) (2,11), etc. You would not be able to draw a line because you can't have like 1/2 of a customer.

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4 years ago

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Tamir wants to buy a snowboard. The original price is $760. How much will Tamir pay if he buys it during the sale?

grandymaker [24]

Depends on how much it’s on sale

4 0

3 years ago

The low temperatures for 5 days was 5, -2, -11 ,0 and-3.What was the average low temperature for those days

Daniel [21]

Data:
Average (A): ?
Arithmetic mean (A.M) = 5, -2, -11, 0, -3sum of n numbers = 5

Solving:
$A = \frac{AM}{n} = \frac{5+(-2)+(-11)+0+(-3)}{5} = \frac{5-2-11-3}{5} = \frac{\diagup\!\!\!\!3-11-\diagup\!\!\!\!3}{5} = \frac{-11}{5} = - 2.2$

Answer:

<span>The average low temperature of these days is -2.2</span>

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3 years ago