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3 years ago

Factor to solve X^2-2x-15=0

Mathematics

1 answer:

zzz [600]3 years ago

4 0

Answer:

(x+3)(x-5)

Step-by-step explanation:

find two multiples of -15 that when added together create -2

those two numbers would be -5 and +3

-5x3=-15

-5+3=-2

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If y= x+3/6-x, what is the value of y when x =7i?

djverab [1.8K]

Answer:

Option (2)

Step-by-step explanation:

Given : y = $\frac{x+3}{6-x}$

If x = 7i

y = $\frac{7i+3}{6-7i}$

By simplifying denominator of the given rational expression,

y = $\frac{7i+3}{6-7i}\times \frac{6+7i}{6+7i}$

y = $\frac{(7i+3)(6+7i)}{6^2-(7i)^2}$

y = $\frac{7i(6+7i)+3(6+7i)}{36-49i^2}$

y = $\frac{42i+49i^2+18+21i}{36+49}$ [Since, i² = (-1)]

y = $\frac{63i-49+18}{85}$

y = $\frac{63i-31}{85}$

y = $-\frac{31}{85}+\frac{63}{85}i$

Therefore, Option (2) is the correct option.

3 0

3 years ago

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify

irina [24]

Answer:

x-coordinates of relative extrema = $\frac{-1}{2}$

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

$f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}$

Differentiate with respect to x

$f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}$

$f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}$

Differentiate f'(x) with respect to x

$f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1$

At x = $\frac{-1}{2}$ ,

$f''\left ( \frac{-1}{2} \right )=\frac{4\left ( -1+4\left ( \frac{-1}{2} \right ) \right )}{3\left ( \frac{-1}{2} \right )^{\frac{5}{3}}}>0$

We know that if $f''(a)>0$ then x = a is a point of minima.

So, $x=\frac{-1}{2}$ is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

7 0

3 years ago

PLEASE HELP!!!! attached photo

alisha [4.7K]

Answer:

(-1, -2.5)

Step-by-step explanation:

The midpoint formula is just basicallyadding both of the x values and then dividing the sum of them by 2, after that you will be adding both y values and then dividing them by 2, then you will get the midpoint x and y coordinate values. You can look up midpoint formula on google to see how it's actually written. You have to make sure to add correctly when you are using the negative numbers, because they can actually turn the equations into subtraction. Keep in mind, it can beconfusing sometimes when you are working with positive and negative numbers together. So make sure to just double check your work and also to make sure you added correctly.

<u><em>Brainliest please, I need a few more :D</em></u>

8 0

3 years ago

Which expression shows how 8•54 can be rewritten using the distributive property ?

konstantin123 [22]

The distributive property is a(b+c) = ab + ac or a(b-c) = ab - ac

So here are some potential answers:

8(50 + 4) = 8·50 + 8·4

8(60 - 6) = 8·60 - 8·6

I prefer the first answer

8 0

3 years ago

Right angle trigonometry

Nady [450]

Answer:

Step-by-step explanation:

Given

sinΘ = $\frac{1}{\sqrt{2} }$ , then

Θ = $sin^{-1}$ ( $\frac{1}{\sqrt{2} }$ ) = 45° → B

7 0

3 years ago