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Hatshy [7]
2 years ago
11

PLEASE CHOSE THE RIGHT ANSWER AND EXPLAIN WHY YOU CHOSE IT PLEASE

Mathematics
1 answer:
Nikitich [7]2 years ago
7 0

Answer:

D

Step-by-step explanation:

See attached image.

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Help please!!!! Complete the following
sveta [45]
First, "graph" means graph of the given function f(x).  It is not necessary to include the graph with the question because at this level, either the user can "see" the graph mentally, or use technology (calculator or software) to graph the function.

(a) The Leading coefficient test for polynomial functions
The test is as follows.  The sign of the leading coefficient (LC, coefficient of the highest power of the variable) together with the degree (odd or even)  of the polynomial function tells us the end behaviour of the function according to the following table:

LC/degree     Even       Odd
Positive        +inf/+inf    -inf/+inf   
Negative       -inf/-inf     +inf/-inf

It can be easily memorized by comparing with a line or a parabola
y=x (positive leading coefficient, odd degree)  goes from -inf to +inf
y=x^2 (positive leading coefficient, even degree)  goes from +inf to +inf.
Any negative leading coefficient will just invert the signs.

For the given polynomial function
f(x) = x^2(x+2) = x^3+x^2
The leading coefficient is +1 (positive), and degree is three (odd)
So it behaves the same way as a straight line y=x, so the end behviours are
{-inf, +inf}  as x-> {-inf, +inf} respectively.

(b) x-intercepts
Since f(x)=x^2(x+2), the x-intercepts are x=0 (multiplicity 2) and x=-2.
=>
From the left, graph is increasing and crosses x=-2 once from negative to positive, after which graph is decreasing.  At x=0, because of the root with multiplicity 2, graph touches the origin (0,0) and turns back towards +inf.

(c) the y-intercept
from the polynomial f(x)=x^2(x+2)=x^3+x^2 = x^3+x^2+0,
we see that the y-intercept =0 because the "initial value" or the constant term is zero.

5 0
3 years ago
What is the clockwise and counterclockwise rule for 180 degrees of rotation?
Tema [17]
Either way you go 180 degrees clockwise or counter clockwise it will land in the same spot
7 0
3 years ago
On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negat
klasskru [66]

Answer:

Option A) They are parallel because their slopes are equal.

Step-by-step explanation:

We are given the following in the question:

Line AB:

(-4, -2), (4,4)

Line CD:

(0,-3), (4,0)

Formula to calculate slope =

(x_1, y_1), (x_2, y_2)\\\\\\text{Slope} = m = \dfrac{y_2 - y_1}{x_2 - x_1}

Slope of AB =

(-4, -2), (4,4)\\\\m_{AB} = \dfrac{4-(-2)}{4-(-4)} = \dfrac{6}{8} = \dfrac{3}{4}

Slope of CD =

(0,-3), (4,0)\\\\m_{CD} = \dfrac{0-(-3)}{4-0} = \dfrac{3}{4}

Thus,

m_{AB} = m_{CD}

Thus, the two lines are parallel.

Option A) They are parallel because their slopes are equal.

3 0
3 years ago
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Enter the missing value into the box to complete the ratio comparing 75 centimeters to 3 meters. 1 to
Alex_Xolod [135]
The ratio for the problem above is one to four. A ratio is a relationship between number which describes how many times the second number contains the first number. The problem above gave two metric unit of length which are the centimeter and meter and the ratio between those two is one to a hundred. Therefore, we have a comparison between two amounts which are 75 and 300 and we can conclude a ratio of one to four.
5 0
2 years ago
Read 2 more answers
The perimeter of a square is 120 inches what is its area
nata0808 [166]

Answer:

A = 900in²

Perimeter   120in

Using the formulas

A = a²

P = 4a

Step-by-step explanation:

Solving for A:

A = 1/16 P² = 1/16 · 120² = 900in²

5 0
2 years ago
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