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Zielflug [23.3K]

4 years ago

13

Please answer the following questions !!!

2 answers:

dybincka [34]4 years ago

7 0

The first one is 5 the next one is 30.6 the third one is 6.4 the fourth one is 0.8 and the last one is 10.125

REY [17]4 years ago

5 0

1. 9 1/2
2. 30 3/5
3. 6 2/5
4. 1 1/5
5. 10 1/8

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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

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Which equation has the steepest parabola?

ICE Princess25 [194]

Given:

The equations of parabolas in the options.

To find:

The steepest parabola.

Solution:

We know that, if a parabola is defined as

$(y-k)=n(x-h)^2$

Then, the greater absolute value of n, the steeper the parabola.

It can be written as

$\dfrac{1}{n}(y-k)=(x-h)^2$

$p(y-k)=(x-h)^2$

where $p=\dfrac{1}{n}$ , the smaller absolute value of p, the steeper the parabola.

Now, find the value of |p| for eac equation

For option A, $|-0.5|=0.5$

For option B, $|5|=5$

For option C, $|8|=8$

For option D, $|-10|=10$

Since, the equation is option A has smallest value of |p|, therefore, the equation $(x+2)^2=-0.5(y+3)$ represents the steepest parabola.

Hence, the correct option is A.

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3 years ago

Fred wants to split his savings of $1012.74 evenly into 3 different bank accounts. How much will be in each account

Umnica [9.8K]

Answer:

$337.58

Step-by-step explanation:

$1,012.74 ÷ 3 = $337.58

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The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner

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2 years ago

I’m so confused please explain and help! The most explanation with the reasonable answer gets BRAINLIEST

8_murik_8 [283]

Answer: I say Mike because when you multiply it you end up getting 4 for Mike

Step-by-step explanation:

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4 years ago

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