Express as a trinomial. (x + 4)(x

How many roots does the following equation have? f(x) = 4x5 - 16x4 + 17x3 - 19x2 + 13x - 3 = 0

Anarel [89]

It has 5 roots. You can determine this by the degree of the polynomial

4 0

3 years ago

1.

Eddi Din [679]

Answer:

a) $y=\dfrac{5}{2}x$

b) yes the two lines are perpendicular

c) $y=\dfrac{5}{4}x+6$

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form $y = mx + c$

$5y = 7 - 2x$

$y = \dfrac{7 - 2x}{5}$

$y = \dfrac{7}{5} - \dfrac{2}{5}x$

$y = -\dfrac{2}{5}x+\dfrac{7}{5}$

this is changed into the $y = mx + c$ , and we easily see that -2/5 is in the place of m, hence $m = \frac{-2}{5}$ is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

$m_1m_2=-1$ .

here both slopes $m_1$ and $m_2$ are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

$\dfrac{-2}{5}m_2=-1$ .

$m_2=\dfrac{5}{2}$ .

Finally, we can find the equation of the line of the perpendicular using:

$(y-y_1)=m(x-x_1)$

we know that the line passes through origin(0,0) and its slope is 5/2

$(y-0)=\dfrac{5}{2}(x-0)$

$y=\dfrac{5}{2}x$ is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether $m_1m_2=-1$ ?

the slopes can be easily found through rearranging both equations to $y=mx+c$

Line:1

$2x + 3y =6$

$y =\dfrac{-2x+6}{3}$

$y =\dfrac{-2}{3}x+2$

Line:2

$y = \dfrac{3}{2}x + 4$

this equation is already in the form we need.

the slopes of both equations are

$m_1 = \dfrac{-2}{3}$ and $m_2 = \dfrac{3}{2}$

using

$m_1m_2=-1$

$\dfrac{-2}{3} \times \dfrac{3}{2}=-1$

$-1=-1$

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be $m=\dfrac{-4}{5}$ and the y-intercept is $c=6$ the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

$m_1m_2=-1$

$\dfrac{-4}{5}m_2=-1$

$m_2=\dfrac{5}{4}$

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

$(y-y_1)=m(x-x_1)$

$(y-6)=\dfrac{5}{4}(x-0)$

$y=\dfrac{5}{4}x+6$

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

8 0

3 years ago

Suppose you receive a $50 gift certificate to the citywide music and books store. All CDs at the store cost $9.99 and all books

Zanzabum

Whats the question I don't get it

7 0

3 years ago

Iron Man Training While training for an iron man competition, Tony bikes for 60 miles and runs for 15 miles. If his bikes speed

ivolga24 [154]

Answer:

Tony biked 1 hour 40 minutes and run 3 hours 20 minutes.

Step-by-step explanation:

How long did Tony speed on his bike?

Let s to be Tony's running speed, then 8s is Tony's biking speed

Let's recall that Time = Distance/Speed

Bike time + Running time = 5 hrs

Replacing with the real values, we have:

60/8s + 15/s = 5

8s as Lowest Common Denominator

60 + 8 * 15 = 5 * 8s

60 + 120 = 40s

-40s = -180

s = -180-40

s = 4.5 ⇒ 8s = 36

Tony run at 4.5 mph and biked at 36 mph

Now, we can calculate the time, this way:

Bike time = Bike distance/Bike speed

Replacing with the real values, we have:

Bike time = 60/36

Bike time = 5/3 (Dividing by 12)

5/3 hours * 60 = 100 minutes or 1 hour 40 minutes

Running time = 5 hours - 1 hour 40 minutes = 3 hours 20 minutes

Tony biked 1 hour 40 minutes and run 3 hours 20 minutes.

4 0

2 years ago

Write an inequality that represents eight less than three times a number is more than 22

inysia [295]

Let x represent the number.
"three times a number" is 3x
eight less than "three times a number" is 3x-8
"is more than 22" is "> 22"

Your inequality is
3x-8 > 22

5 0

3 years ago

Read 2 more answers

Express as a trinomial. (x + 4)(x - 1)