It took 3.5 hours for a train to travel the distance between two cities at a velocity 120 km/hr. How many miles lie between the two cities?

Answer: No real number solutions

The complex number solutions are [tex]x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]

where [tex]i = \sqrt{-1}[/tex]

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Explanation:

The given equation 3x^2+2x+4 = 0 is in the form ax^2 + bx + c = 0

We have

Let's compute the discriminant.

d = b^2 - 4ac

d = (2)^2-4(3)(4)

d = -44

The result is negative, so there are no real number solutions.

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If you wanted to find the complex valued solutions, then we apply the quadratic formula.

Plug in a = 3, b = 2, c = 4

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(3)(4)}}{2(3)}\\\\x = \frac{-2\pm\sqrt{-44}}{6}\\\\x = \frac{-2\pm\sqrt{-1*4*11}}{6}\\\\x = \frac{-2\pm\sqrt{-1}*\sqrt{4}*\sqrt{11}}{6}\\\\[/tex]

[tex]x = \frac{-2\pm i*2*\sqrt{11}}{6}\\\\x = \frac{-2\pm2i\sqrt{11}}{6}\\\\x = \frac{2(-1\pm i\sqrt{11})}{6}\\\\x = \frac{-1\pm i\sqrt{11}}{3}\\\\x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]

Notice in step 3 we have -44 under the square root. The negative value in the square root leads directly to the imaginary number [tex]i = \sqrt{-1}[/tex]

Though the term "imaginary" is a bit unfair and misleading because numbers like -22 are just as imaginary and made up by humans. It just depends on context in which imaginary numbers are useful (eg: with physics or engineering).

The distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The distance between the two straight parallel lines can be found by finding the difference between the y-intercept of the two lines. Therefore, for the two of the given equation, the value of the y-intercept can be written as,

Y-intercept of -4x + 7y + 9 = 0

-4x + 7y + 9 = 0

7y = 4x - 9

y = (4x - 9)/7

y = 4x/7 - 9/7

y-intercept = -9/7

Y-intercept of y = 4/7x - 9

y = 4/7x - 9

y-intercept = -9

Now, the difference distance between the two lines will be,

Distance = Difference between the y-intercept

               = -9 - (-9/7)

               = -9 + 1.2857

               = 7.71

Hence, the distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.

Learn more about Equation of Line:

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Answer:Diya

Step-by-step explanation: she’s right because she is black and all black peoples is always right

Answer:

If AB crosses at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types. For obvious reasons, the point F is called the midpoint of the line PQ. See also Angle bisector.

(4x+5) miles..........1 hour

    x    miles .........(x-1) hour

(4x+5) * (x-1) = 1 * x

in (x - 1)h = x / (4x+5)  miles

Answer:

see below

Step-by-step explanation:

eq.1      2a   - b + 2c = -8

eq.2            5b  - 3c =  21

eq.3     -7a        -10c = -2

3 equations, 3 unknown.

first step is to eliminate b using eq1 and eq2

2a   - b + 2c = -8 (5)

      5b  - 3c =  21

10a - 5b + 10c = -40

        5b -  3c =  21

10a        + 7c = -21 ------------eq. A

lets solve a using eq. A

10a + 7c = -21

a = (-7c - 21) / 10

now substitute a into eq.3

-7a        -10c = -2

-7(-7c - 21) -10c = -2 distribute

        10

4.9c + 14.7 - 10c = -2  add similar terms

-5.1c = -2 - 14.7  simplify

c = -16.7 / -5.1

c  ≈ 3

solve b using eq. 2 and substitute c.

5b  - 3c =  21

5b = 21 + 3c

5b = 21 + 3(3.2)

b = 30.825 / 5

b ≈ 6

solve a using eq. A

10a + 7c = -21

10a + 7(3.2) = -21

10a = -21 - 22.4

a = -43.4 / 10

a ≈ -4

Answer:

a

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Answer:

1/6

Multiply 5/12 x 2/5 then cross cancel 12 and 2 and get 6 then cross cancel 5 and 5 to get 1.

Final answer:

1/6

Answer:

x=-3

Step-by-step explanation:

there are three x's and five one's so the equation is 3x+5

on the other side there are 2 negative x's and 10 negative one's so the equation is -2x-10

set them equal to each other

3x+5=-2x-10

5x=-15

x=-3

Answer:

hey how old are you

Step-by-step explanation:

jnedjed

Answer:

Domain: (-∞, -5) (-1, ∞)

Step-by-step explanation:

Note:

For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.

For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.

We need to find the domain of f(x) for which f(x) < 0

From the graph, we can tell:

f(x) < 0 on (-∞, -5) ∪ (-1, ∞)

Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)

Answer:  -1/3 x -1

Step-by-step explanation:

By doing some stuff, you get the slope of the first line as -1/3. Set up -1/3 x +b and you plug in the coordinates. That makes b= -1. Hope it helps :)

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

Isosceles means that the two sides equal each other

As such, to find the value of x we must equal the two expressions together and isolate the variable

20 = 3x - 7

add 7 to both sides

27 = 3x

divide both sides by 3

9 = x

Answer:

The variable x equals 9.

Step-by-step explanation:

3x - 7 = 20

3x = 27

X = 9

Answer:

An = a1 + (n-1) d

Step-by-step explanation:

solving steps:

2( 9 - 7r ) + 8r

2(9) - 2(7r) + 8r

18 - 14r + 8r

18 - 6r

Answer:

18 - 6r

Step-by-step explanation:

2(9 - 7r) + 8r

Expand the brackets:

⇒ 2 · 9 - 2 · 7r + 8r

⇒ 18 - 14r + 8r

Combine like terms:

⇒ 18 - 6r

Answer:

Step-by-step explanation:

Given line:

We need to find a line that is perpendicular to the given line and passes through the pint (6, 9)

We know perpendicular lines have opposite-reciprocal slopes.

The slope of the line is:

Use point-slope form to find the line:

Convert the equation into slope-intercept form:

Answer:

2(3x+5) OR (6x+10)

Step-by-step explanation:

8 (2x+3)

8

Answer:

C

Step-by-step explanation:

The reason it is C is mainly because it is the only line with a negative slope. A negative slope this direct \. It is not A because that is a positive slope (/). It is not B because that line is undefined which means it would look like this x = 2. And D is wrong because that is a zero slope line which looks like this y = 5. So it is C.

Here is a helpful website for problems like this Desmos. com

What is below the question is what I mean.

Answer:

25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

4x-11=89

4x=89+11

4x=100

x= 25

I hope this will help

Answer:

Step-by-step explanation:

Here is how to solve it using factoring:

x^2 - 2x - 1 = 2

x^2 - 2x - 3 = 0

(x + 1)(x - 3) = 0

x = -1, 3.

Answer:

your process is not correct

(x^2-2x+1 = 3+1)

you were wrong here

Step-by-step explanation:

I am not good in english so it is hard for me to explain...

Answer:

b.177.14

Step-by-step explanation:

because 52.1x 3.4 = 177.14

Answer:

24

Step-by-step explanation:

12/2=6

6*4=24

Answer:

Beth will use 24 grapes.

Step-by-step explanation:

Not going to lie I forgot how i got my answer but ik its good.

Answer:

a) 4x

b) 2 + 4y

Step-by-step explanation:

a) 7x - 6x + 3x

To do this, we just need to collect the terms together. They are all coefficients of x, so all we need to do is add the number together.

7 - 6 + 3 = 4

7x - 6x + 3x = 4x

b) 2(1 + 2y)

Here we need to expand the brackets. 2 is shown to be multiplied by 1 +2y:

2(1 + 2y)

= 2*1 + 2*2y

= 2 + 4y

I hope this helps :)

Answer:

A unit is a measure of ratio between two quantities. In this instance, the unit is a pound. The ratio you need to take is the price of each fruit and divide it by the number of pounds each fruit has to get a price per pound. See below for solution.

Step-by-step explanation:

A. 4.19 dollars / 2.5 pounds = 1.676 dollars / pound

B. 5.49 dollars / 4 pounds = 1.3725 dollars / pound

C. 6.99 dollars / 5 pounds = 1.398 dollars / pound

D. 9.59 dollars / 6.5 pounds = 1.475 dollars / pound

The lowest is B, the apples.

Answer: Your answer  40°

Step-by-step explanation:

Hope this helped!

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