Question 6<br> 6. Find the length of line segment AB.

Determine if (x+1) is a factor 4x^2 + 2x - 5Use synthetic division

ikadub [295]

Given

$4x^2+2x-5$

Divide it by (x+1) using synthetic division, as shown below

The green line is a minus sign.

Thus,

$\Rightarrow4x^2+2x-5=(x+1)(4x-2)-3$

Therefore, since the remainder is different than zero, (x+1) is not a factor of 4x^2+2x-5

6 0

1 year ago

Pleaseeeee helppppp

IRINA_888 [86]

Answer:

(a) (6, 2)

Step-by-step explanation:

The system of equations has one of them in y= form, so it lends itself to solution by substitution.

__

Using the equation for y to substitute into the first equation, we have ...

2x -y = 10

2x -(-1/2x +5) = 10 . . . . . substitute for y

2x +1/2x -5 = 10 . . . . . eliminate parentheses

5/2x = 15 . . . . . . . . . add 5, collect terms

x = 6 . . . . . . . . . . . multiply by 2/5

Using the equation for y, we have ...

y = -1/2(6) +5 = -3 +5

y = 2

The solution is (x, y) = (6, 2).

3 0

2 years ago

Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds a

kirill115 [55]

Answer:

12 feet per second.

Step-by-step explanation:

Please consider the complete question.

Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds after she jumps for the bone can be represented $h(t)=-16t^2+20t$ .

What is Spot's average rate of ascent, in feet per second, from the time she jumps into the air to the time she catches the bone at t=1/2?

We will use average rate of change formula to solve our given problem.

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

$\text{Average rate of change}=\frac{h(\frac{1}{2})-h(0)}{\frac{1}{2}-0}$

$\text{Average rate of change}=\frac{-16\cdot(\frac{1}{2})^2+20\cdot \frac{1}{2}-(-16\cdot(0)^2+20\cdot (0))}{\frac{1}{2}-0}$

$\text{Average rate of change}=\frac{-16\cdot\frac{1}{4}+10-(0)}{\frac{1}{2}}$

$\text{Average rate of change}=\frac{-4+10}{\frac{1}{2}}$

$\text{Average rate of change}=\frac{6}{\frac{1}{2}}$

$\text{Average rate of change}=\frac{2\cdot 6}{1}$

$\text{Average rate of change}=12$

Therefore, Spot's average rate of ascent is 12 feet per second.

3 0

3 years ago

About waves speed i want information about waves speed

Goryan [66]

Answer:

Wave speed is the distance that a wave travels in a given amount of time. Wave speed is related to wave length and wave frequency. Wave frequency can be found by using the formula Speed=wavelength × frequency

Step-by-step explanation:

6 0

3 years ago

If f(x) = 2x^3 - 14x^2 + 38x -26 and x-1 is a factor of f(x) find all of the zeros of f(x) algebraically.

Anestetic [448]

Answer:

Step-by-step explanation:

First confirm that x = 1 is one of the zeros.

f(1) = 2(1)^3 - 14(1)^2 + 38(1) - 26

f(1) = 2 - 14 + 38 - 26

f(1) = -12 + 38 = + 26

f(1) = 26 - 26

f(1) = 0

=========================

next perform a long division

x -1 || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26

2x^3 - 2x^2

===========

-12x^2 + 28x

-12x^2 +12x

==========

26x -26

26x - 26

========

0

Now you can factor 2x^2 - 12x + 26

2(x^2 - 6x + 13)

The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16

So you are going to get a complex result.

x = -(-6) +/- sqrt(-16)

=============

2

x = 3 +/- 2i

f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)

The zeros are

1

3 +/- 2i

8 0

3 years ago

Question 6 6. Find the length of line segment AB.