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2 years ago

Classify the following polynomial function, −3x(x2−4)(2x2+5)based on degree and number of terms.

Mathematics

1 answer:

Free_Kalibri [48]2 years ago

5 0

Answer:

Quintic Trinomial (2nd option)

Step-by-step explanation:

We know that this is a quintic polynomial because the degrees add up to 5. If we expand the polynomial, we have $-3x(x^2-4)(2x^2+5)=(-3x^3-12x)(2x^2+5)=-6x^5-45x^3-24x^3-60x=-6x^5-69x^3-60x$

So, there are 3 terms, which is a trinomial.

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Need help ASAP

joja [24]

Part (1) : The solution is $729$

Part (2): The solution is $\frac{1}{16 x^{8}}$

Part (3): The solution is $\frac{2 x^{2}}{3 y z^{7}}$

Explanation:

Part (1): The expression is $3^{2} \cdot3^{4}$

Applying the exponent rule, $a^{b} \cdot a^{c}=a^{b+c}$ , we get,

$3^{2} \cdot 3^{4}=3^{2+4}$

Adding the exponent, we get,

$3^{2} \cdot3^{4}=3^6=729$

Thus, the simplified value of the expression is $729$

Part (2): The expression is $\left(2 x^{2}\right)^{-4}$

Applying the exponent rule, $a^{-b}=\frac{1}{a^{b}}$ , we have,

$\left(2 x^{2}\right)^{-4}=\frac{1}{\left(2 x^{2}\right)^{4}}$

Simplifying the expression, we have,

$\frac{1}{2^4x^8}$

Thus, we have,

$\frac{1}{16 x^{8}}$

Thus, the value of the expression is $\frac{1}{16 x^{8}}$

Part (3): The expression is $\frac{2 x^{4} y^{-4} z^{-3}}{3 x^{2} y^{-3} z^{4}}$

Applying the exponent rule, $\frac{x^{a}}{x^{b}}=x^{a-b}$ , we have,

$\frac{2x^{4-2}y^{-4+3}z^{-3-4}}{3}$

Adding the powers, we get,

$\frac{2x^{2}y^{-1}z^{-7}}{3}$

Applying the exponent rule, $a^{-b}=\frac{1}{a^{b}}$ , we have,

$\frac{2 x^{2}}{3 y z^{7}}$

Thus, the value of the expression is $\frac{2 x^{2}}{3 y z^{7}}$

8 0

4 years ago

The table below shows the cost for different numbers of tickets.

Black_prince [1.1K]

Answer:

Step-by-step explanation: It's not going up by 6 or 2, and it's not going down in numbers, so D

7 0

3 years ago

There are 84 boys in a freshman class of 146 students. Find the ratio of boys to girls.

fredd [130]

There are 146 - 84 = 62 girls

ratio is 84:62

simplifies to 42:31

5 0

3 years ago

Which inequality statement best represents the graph?

I am Lyosha [343]

Answer:

f(x) < –x2 + x – 1

Step-by-step explanation:

The graph is going down so we know that there is a maximum, therefore the A value has to be negative. This rules out f(x) < x2 + x – 1 and f(x) > x2 + x – 1 . The shaded area of the graph is below which indicates that f(x) has to be less than the function. This means the correct answer is f(x) < –x2 + x – 1 .

7 0

3 years ago

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Find the area of the regular octagon if the apothem is 4.2 and a side is 3.4 In. Round to the nearest whole number. A. 114 B. 57

Elena-2011 [213]

The area of the regular octagon is calculated as half of the product of the perimeter and the apothem (ap), using the formula of the area of the regular polygon.
We have then:
A = ((p) * (ap)) / 2
Where,
p: perimeter
ap: apotema
Substituting values:
A = ((8 * 3.4) * (4.2)) / 2
A = 57.12 in ^ 2
Answer:
the area of the regular octagon is:
B. 57

6 0

3 years ago

Read 2 more answers