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2 years ago

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

Mathematics

1 answer:

Advocard [28]2 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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In Exercise, find the derivative of the function.<br> y = ln(3 + x2)

erastovalidia [21]

Answer: $\dfrac{2x}{3 + x^2}$

Step-by-step explanation:

We know the property of derivative: $\dfrac{d}{dx}(\log (x))=\dfrac{1}{x}$

Given function : $y=\ln(3 + x^2)$

Differentiate both sides with respect to x , we get

$\dfrac{dy}{dx}=\dfrac{d}{dx}(\ln(3 + x^2))$

$\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot\dfrac{d}{dx}(3 + x^2)$ [By Chain rule]

$\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot(0+2x)$

[Since $\dfrac{d}{dx}(a)=0$ , where a is scalar and $\dfrac{d}{dx}(x^n)=n(x)^{n-1}$ ]

$\Rightarrow\ \dfrac{dy}{dx}=\dfrac{2x}{3 + x^2}$

Hence, the derivative of the given function is $\dfrac{2x}{3 + x^2}$ .

5 0

2 years ago

Triangle ABC is isosceles.

lana66690 [7]

Answer: 75°

Step-by-step explanation:

Using the Base Angles Theorem, we can conclude that <ABC and <ACB are congruent. The angles of a triangle add up to 180 degrees so we can write this equation to solve for x:

x + 5 + 3x + 3x = 180

simplify

7x + 5 = 180

subtract 5 from both sides

7x = 175

divide each side by 7

x = 25

plug 25 in for x to find the angle measure

3(25) = 75

3 0

2 years ago

Read 2 more answers

Deshawn paid $9.20 for coffee and left a $2.30 tip.If he the same rate later today while out at dinner,how much will his tip be

xenn [34]

Around 4.50 would be the tip

8 0

2 years ago

John’s teacher gave him the following system of equations and asked him to find the point of intersection. 3x + 2 = y 2x – 3= y

Galina-37 [17]

1) to this case you must match both equations

3x+2 = 2x-3 ⇒3x-2x = -3-2⇒x= -5

now the value of x substitute it in the any of two equations, y = 3(-5)+2 = -13

and the other equation is the same value

y = 2(-5)-3 = -13

the point is ( -5,-13)

7 0

2 years ago

Solve the equation

motikmotik

Answer:

Step-by-step explanation:

$\frac{1}{2}$ (2x + 2) - $\frac{1}{4}$ (3x - 1) = 15

multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

2(2x + 2) - (3x - 1) = 60 ← distribute parenthesis and simplify left side

4x + 4 - 3x + 1 = 60

x + 5 = 60 ( subtract 5 from both sides )

x = 55

3 0

1 year ago