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3 years ago

Is (x-1) a factor of 2x3 - 15x2 + 22x + 15

Mathematics

1 answer:

Advocard [28]3 years ago

6 0

Answer:

Step-by-step explanation:

If x - 1 is a factor of the cubic, then 1 should result in 0 when you put it in the cubic for x. Does it?

f(1) = 2(1)^3 - 15(1)^2 + 22(1) + 15

f(1) = 2 - 15 + 22 + 15

f(1)= 24.

No the result is not zero. So x - 1 is not a factor.

However there must be something that makes this cubic go to zero. The easiest way to find it is to graph it.

The numbers that do make this zero are -0.5, 3, 5

Which mean that the factors are (2x+1)(x-3)(x - 5)

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An equilateral triangle has perimeter P. The length of one side is P/3. Which expression is equivalent to the length on one side

irina1246 [14]

Answer: $3\times \dfrac{P}{3}=P$

Step-by-step explanation:

Given

The perimeter of one equilateral triangle is P

The lengths of the equilateral triangle are equal

Suppose x is the length of each side

$\therefore 3\times x=P\\\\\Rightarrow x=\dfrac{P}{3}$

i.e.

$\Rightarrow 3\times \dfrac{P}{3}=P$

3 0

3 years ago

Find the distance between the two points in simplest radical form.<br> (-9,8) and (-3, -1)

dmitriy555 [2]

Answer:

The distance between (-9, 8) and (-3, -1) will be:

$\:d=3\sqrt{13}$ units

Step-by-step explanation:

Given the points

(-9, 8)

(-3, -1)

Finding the distance between (-9, 8) and (-3, -1)

$d\:=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$=\sqrt{\left(-3-\left(-9\right)\right)^2+\left(-1-8\right)^2}$

$=\sqrt{\left(-3+9\right)^2+\left(-1-8\right)^2}$

$=\sqrt{36+81}$

$=\sqrt{117}$

$=3\sqrt{13}$ units

Therefore, the distance between (-9, 8) and (-3, -1) will be:

$\:d=3\sqrt{13}$ units

7 0

2 years ago

Sloan [31]

Triangle ABC is similar to triangle DEC, ∠B ≅ ∠E and 3DE = 2BC

<h3>What is transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. Types of transformation are <em>rotation, reflection, translation and dilation.</em>

Dilation is the increase or decrease in the size of a figure by a scale factor.

Right triangle ABC is reflected over AC, then dilated by a scale factor of 2/3 to form triangle DEC, hence:

Triangle ABC is similar to triangle DEC, corresponding angles are congruent (∠B ≅ ∠E) and DE = (2/3)BC i.e. 3DE = 2BC

Find out more on transformation at: brainly.com/question/4289712

#SPJ1

7 0

1 year ago

Let $f(x)$ be a function defined for all positive real numbers satisfying the conditions $f(x) > 0$ for all $x > 0$ and $f

algol [13]

Suppose we choose $x=1$ and $y=\dfrac12$ . Then

$f(x-y)=\sqrt{f(xy)+1}\implies f\left(\dfrac12\right)=\sqrt{f\left(\dfrac12\right)+1}\implies f\left(\dfrac12\right)=\dfrac{1+\sqrt5}2$

Now suppose we choose $x,y$ such that

$\begin{cases}x-y=\dfrac12\\\\xy=2009\end{cases}$

where we pick the solution for this system such that $x>y>0$ . Then we find

$\dfrac{1+\sqrt5}2=\sqrt{f(2009)+1}\implies f(2009)=\dfrac{1+\sqrt5}2$

Note that you can always find a solution to the system above that satisfies $x>y>0$ as long as $x>\dfrac12$ . What this means is that you can always find the value of $f(x)$ as a (constant) function of $f\left(\dfrac12\right)$ .

3 0

3 years ago

Read 2 more answers

Is RATIONAL , IRRATIONAL,NON REAL NUMBERS <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B27" id="TexFormula1" title=" \sqrt{

Tanya [424]

Answer:

It's irrational

Step-by-step explanation:

the square root of 27 is equal to:

$\sqrt{27} = \sqrt{3\cdot3\cdot3} = 3\sqrt{3}$