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iogann1982 [59]
2 years ago
9

Find the opposite of: - 4x2 - 4x + 2

Mathematics
1 answer:
vladimir2022 [97]2 years ago
8 0

Answer:

4x² + 4x - 2

Step-by-step explanation:

The opposite is the negative value

The opposite of - 4x² - 4x + 2 is

- (- 4x² - 4x + 2) ← distribute parenthesis by - 1

= 4x² + 4x - 2

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Let u= <4,3>. Find the unit vector in the direction of u, and write your answer in component form.
aksik [14]
Take the vector u = <ux, uy> = <4, 3>.

Find the magnitude of u:

||u|| = sqrt[ (ux)^2 + (uy)^2]

||u|| = sqrt[ 4^2 + 3^2 ]

||u|| = sqrt[ 16 + 9 ]

||u|| = sqrt[ 25 ]

||u|| = 5

To find the unit vector in the direction of u, and also with the same sign, just divide each coordinate of u by ||u||. So the vector you are looking for is

u/||u||

u * (1/||u||)

= <4, 3> * (1/5)

= <4/5, 3/5>

and there it is.

Writing it in component form:

= (4/5) * i + (3/5) * j

I hope this helps. =)
3 0
3 years ago
A car rental agency advertised renting a car for $26.95 per day and $0.24 per mile. If Kevin rents this car for 3 days, how many
Viefleur [7K]

Answer: 26.95 * 3 = 80.85

              250/0.24 = 60

             

6 0
2 years ago
Complete the square: -3x^2 + 30x -52 express in vertex form
nadezda [96]

the answer to this is

the two is for the top of the five  2

                                            -3(x - 5) +23

4 0
3 years ago
Ray is reading a book of 150 pages at a constant rate of 25 pages per hour. Let’s consider the following function: the pages lef
alukav5142 [94]

The formula of the given problem in function form is

L(t) = 150 - 25t where, t represents the hour

Step-by-step explanation:

Given,

Ray reads the at a constant rate of 25 pages per hour.

To find, the function L: the pages left to read

Let, t be the hours

So, in t hours he read 25T pages

After T hours he was left with (150 - 25t) pages to read.

Formula

Hence, the required function will be

L(t) = 150 - 25t where, t represents the hour

5 0
3 years ago
A motorboat is capable of traveling at a speed of 14 miles per hour in still water. On a particular day, it took 15 minutes long
Anon25 [30]

By solving a system of equations we will find that the rate of current in the stream is S = 2 mi/h.

When the motorboat travels downstream, the total velocity will be the velocity of the motorboat in still water plus the velocity of the stream, while if the motorboat travels upstream, we have the velocity of the stream subtracted.

So upstream the speed is:

(14 mi/h - S)

Downstream the speed is:

(14 mi/h + S)

Where S is the rate of current in the stream.

We know that downstream it takes 15 minutes more to travel 12 miles, then we can write the system of equations:

(14 mi/h + S)*T = 12 mi

(14 mi/h - S)*(T - 15 min) = 12 mi

To solve this, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:

T = (12 mi)/(14 mi/h + S)

Replacing that in the other equation we will get:

(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi

Now we can solve this for S. Now we can multiply both sides by (14 mi/h + S).

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)

Also notice that the speeds are in hours, so we can rewrite:

- 15 min = -0.25 h

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)

168 mi^2/h - 12mi*S  + 49mi^2/h + 0.25h*S^2 = 168mi^2/h + 12mi*S

- 12mi*S  + 49mi^2/h - 0.25h*S^2 = 12mi*S

-24mi*S -  0.25h*S^2  + 49mi^2/h = 0

This is a quadratic equation, the solutions are:

S = \frac{24mi \pm \sqrt{(-24mi)^2 - 4*(49mi^2/h)*(-0.25h)}  }{2*-0.25h} \\\\S =  \frac{24mi \pm 25 mi  }{-0.5h}

We only take the positive solution, so we get:

S = (24 mi - 25 mi)/(-0.5 mi) = 2 mi/h

The rate of current in the stream is 2 mi/h.

If you want to learn more, you can read:

4 0
2 years ago
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