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3 years ago

14

Plot the following ordered pairs on a graph and then determine whether or not the points represent a function.

2 answers:

Alex777 [14]3 years ago

5 0

The answer is :

YES: These points represent a function because none of the vertical lines I drew passed through more than one point.

snow_lady [41]3 years ago

3 0

The answer is yes i'm pretty sure

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A level maths factor theorem <br>help in part (b) please

Rina8888 [55]

Given polynomial $f(x)=4 x^{3}-12 x^{2}+2 x-6$ .

(a) To show that (x – 3) is a factor of f(x).

Factor theorem:

<em>A polynomial f(x) has a factor of (x – a), if and only if f(a) = 0.</em>

$f(x)=4 x^{3}-12 x^{2}+2 x-6$

$f(3)=4 (3)^{3}-12 (3)^{2}+2 (3)-6$

$=4(27)-12(9)+6-6$

$=108-108$

= 0

f(3) = 0

Hence (x – 3) is a factor of f(x).

(b) $f(x)=0$

$4 x^{3}-12 x^{2}+2 x-6=0$

Here $4x^2$ is common in first 2 terms and 2 is common in next 2 terms.

$4x^2(x-3 )+2 (x-3)=0$

Now, (x – 3) is common in both terms.

$(x-3)(4x^2+2)=0$

$(x-3)=0$ and $(4x^2+2)=0$

x = 3 and $4x^2+2=0$

3 is the real root.

using quadratic formula solve $4x^2+2=0$ and find the other roots.

$$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$$x=\frac{-0 \pm \sqrt{0^{2}-4 (4) (2)}}{2 (4)}$

$$x=\pm\frac{\sqrt{-32}}{8}$

$$x=\pm\frac{4\sqrt{2}i}{8}$

$$x=\pm\frac{\sqrt{2}i}{2}$

These are complex roots.

Hence 3 is the only real root of the equation f(x) = 0.

8 0

4 years ago

Read 2 more answers

Use the properties of radicals to simplify the expression

Ludmilka [50]

Given:

The expression is

$\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}$

To find:

The simplified form of given expression.

Solution:

We have,

$\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}$

It can be written as

$\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}=\sqrt[3]{\dfrac{9}{4}}$ $\left[\because \dfrac{\sqrt[a]{x}}{\sqrt[a]{y}}=\sqrt[a]{\dfrac{x}{y}}\right]$

Therefore, the simplified form of given expression is $\sqrt[3]{\dfrac{9}{4}}$ .

Note: We can further simplify this expression but be need use exponential properties.

4 0

3 years ago

Can someone help me pls

iVinArrow [24]

Answer:

$\frac{8}{27}$

Step-by-step explanation:

$\frac{2}{3} \times \frac{2}{ 3} = \frac{4}{9}$

because its cubed, times by 2/3 again.

$\frac{4}{9} \times \frac{2}{3} = \frac{8}{27}$

hope this helps

6 0

3 years ago

Graph the relation and tell whether it is a function (1,3) (2,3) (-1,4) (|-1), (-3,2)

kramer

Answer:

no

Step-by-step explanation: does not pass the vertical line test

3 0

3 years ago

Find the slope from the graph and from the table to compare the speeds of two marathon runners.

seraphim [82]

B

una unidad de sentido, y es por medio de ellas que los hablantes logran expresar una proposición lógica

6 0

3 years ago