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3 years ago

Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.

2 answers:

5 0

Hey there.

When writing a polynomial in standard form, you always want to start from the highest degree (exponent), so let's simplify our expression before doing so.

-2 $x^{3}$ + 6 $x^{3}$ = 4 $x^{3}$ ;
This number will go first as it has the highest degree.
Up next will be '-3x', as it has a degree of 1.
After this, we have 6, having a degree of 0.

Let's set up our new polynomial with this information;
4 $x^{3}$ - 3x + 6.

This is known as a cubic trinomial since it has three terms and has a degree of 3.

Your correct answer is "D.)"

I hope this helps!

beks73 [17]3 years ago

3 0

4x3 – 3x + 6; cubic trinomial

its the answer

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Maths functions question!!

Marina86 [1]

Answer:

5) DE = 7 units and DF = 4 units

6) ST = 8 units

$\textsf{7)} \quad \sf OM=\dfrac{3}{2}\:units$

8) x ≤ -3 and x ≥ 3

Step-by-step explanation:

<u>Information from Parts 1-4:</u>

brainly.com/question/28193969

$f(x)=-x+3$

$g(x)=x^2-9$

A = (3, 0) and C = (-3, 0)

Points A and D are the <u>points of intersection</u> of the two functions.

To find the x-values of the points of intersection, equate the two functions and solve for x:

$\implies g(x)=f(x)$

$\implies x^2-9=-x+3$

$\implies x^2+x-12=0$

$\implies x^2+4x-3x-12=0$

$\implies x(x+4)-3(x+4)=0$

$\implies (x-3)(x+4)=0$

Apply the zero-product property:

$\implies (x-3)= \implies x=3$

$\implies (x+4)=0 \implies x=-4$

From inspection of the graph, we can see that the x-value of point D is <u>negative</u>, therefore the x-value of point D is x = -4.

To find the y-value of point D, substitute the found value of x into one of the functions:

$\implies f(-4)=-(-4)=7$

Therefore, D = (-4, 7).

The length of DE is the difference between the y-value of D and the x-axis:

⇒ DE = 7 units

The length of DF is the difference between the x-value of D and the x-axis:

⇒ DF = 4 units

To find point S, substitute the x-value of point T into function g(x):

$\implies g(4)=(4)^2-9=7$

Therefore, S = (4, 7).

The length ST is the difference between the y-values of points S and T:

$\implies ST=y_S-y_T=7-(-1)=8$

Therefore, ST = 8 units.

The given length of QR (⁴⁵/₄) is the difference between the functions at the same value of x. To find the x-value of points Q and R (and therefore the x-value of point M), subtract g(x) from f(x) and equate to QR, then solve for x:

$\implies f(x)-g(x)=QR$

$\implies -x+3-(x^2-9)=\dfrac{45}{4}$

$\implies -x+3-x^2+9=\dfrac{45}{4}$

$\implies -x^2-x+\dfrac{3}{4}=0$

$\implies -4\left(-x^2-x+\dfrac{3}{4}\right)=-4(0)$

$\implies 4x^2+4x-3=0$

$\implies 4x^2+6x-2x-3=0$

$\implies 2x(2x+3)-1(2x+3)=0$

$\implies (2x-1)(2x+3)=0$

Apply the zero-product property:

$\implies (2x-1)=0 \implies x=\dfrac{1}{2}$

$\implies (2x+3)=0 \implies x=-\dfrac{3}{2}$

As the x-value of points M, Q and P is negative, x = -³/₂.

Length OM is the difference between the x-values of points M and the origin O:

$\implies x_O-x_m=o-(-\frac{3}{2})=\dfrac{3}{2}$

Therefore, OM = ³/₂ units.

The values of x for which g(x) ≥ 0 are the values of x when the parabola is above the x-axis.

Therefore, g(x) ≥ 0 when x ≤ -3 and x ≥ 3.

8 0

1 year ago

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Janine wants a necklace 20 beads long. She needs ..... red beads and ..... blue beads.

Tcecarenko [31]

10 red beads

10 blue beads

10 + 10 = 20

4 0

3 years ago

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Find the axis of symmetry for this parabola

mariarad [96]

The axis of symmetry is 1.

To find this, do -b/2a, putting -8 in the place of b and -4 in the place of a. Proceed to solve to get 1.

The equation provided is vertex form, so to find the needed components, you need to solve for the vertex. To do so, implement 1 in as x and solve for the vertex.

The vertex is 1, -16.

(y - 16) = -4(x - 1)^2

Although it is not exactly vertex form, the only difference is that instead of it being +k at the end, it is subtracted with the y.

Hope this helps!

7 0

3 years ago

Frilly, Bom, and Tamika are getting ready to run a race. They want to know how many different ways they could finish in first, s

Komok [63]

Answer: 9 Outcomes, decently sure

Step-by-step explanation:

So we can do 3 x 3 = 9 to get all possibilities!

6 0

2 years ago

A line goes through the point (–2,3) and has a slope of –4. What is the y-intercept of the line?

NISA [10]

Answer:

-5

Step-by-step explanation:

y-3=-4(x+2)

y-3=-4x-8

y=-4x-5

8 0

3 years ago

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