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Alexxandr [17]
3 years ago
15

Two drivers are 420 miles away from each other when they started moving towards each other. They meet after 4 hours. What is the

speed of the first car, if the second car's speed is 45 mph?

Mathematics
1 answer:
77julia77 [94]3 years ago
4 0
The first car is going 60 miles per hour because if the second car is going at 45 mph, after 4 hours it has already travelled 180 miles. In order for both cars to meet from a total distance of 420 miles, the first car has to travel 420 miles - 180 miles meaning that the first car travelled 240 miles. When you look back at how it took 4 hours for both cars to meet each other, this also means that the first car traveled 4 hours. So the car traveled 240 miles in 4 hours meaning that it went 240miles/4hours or 60mph.

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The angle θ lies in Quadrant II. sinθ=3/4 What is cosθ ?
Elden [556K]

Hello from MrBillDoesMath

Answer:

[email protected] = - sqrt(7)/ 4    

which is choice B

Discussion:

This problem can be solved by drawing triangles and looking at ratios of sides or by using the trig identity:

([email protected])^2 + (sin2)^2 = 1

If [email protected] = 3/4 , the

([email protected])^2 + (3/4)^2 = 1 =>              (subtract (3/4)^2 from both sides)

([email protected])^2 = 1 - (3/4)^2  = 1 - 9/16   = 7/16

So...... taking the square root of both sides gives

[email protected] =  +\- sqrt(7)/ sqrt(16) = +\- sqrt(7)/4

But is [email protected] positive or negative?  We are told that @ is in the second quadrant and cos(@) is negative in this quadrant, so our answer must be negative

[email protected] = - sqrt(7)/ 4    

which is choice B


Thank you,

Mr. B


4 0
3 years ago
A rectangle with length n and height m. A right triangle with hypotenuse n + 1, length n, and height m.
Oksana_A [137]

9514 1404 393

Answer:

  C. 12cm

Step-by-step explanation:

The equation for the perimeter of the rectangle is ...

  P = 2(L+W)

  34 = 2(n +m)

Solving for m, we get

  m = 17 -n . . . . . . . divide by 2, subtract n

__

The Pythagorean theorem gives the relationship between the sides and the hypotenuse

  m^2 +n^2 = (n+1)^2

  (17 -n)^2 +n^2 = (n +1)^2 . . . . . . substitute for m

  289 -34n +n^2 +n^2 = n^2 +2n +1 . . . . eliminate parentheses

  n^2 -36n +288 = 0 . . . . . . . put in standard form

  (n -12)(n -24) = 0 . . . . . . . . . factor

  n = 12 . . . . . . . . . . n=24 is an extraneous solution here

The value of n is 12 cm.

8 0
3 years ago
The value of k is: <br><br> please help im struggling
iVinArrow [24]

Answer:

  • E) 48

Step-by-step explanation:

<em>Parallel lines divide the transversals proportionally.</em>

Set proportions and solve for k:

  • k/24 = 64/32
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Correct choice is E.

4 0
2 years ago
Can anyone explain how to do this? I looked at the book and now I'm even more confused. 50 points
katrin [286]

The piecewise function is basically the result of two different functions combined together. If x is 0 or larger, then h(x) = x+4. Otherwise, if x < 0, then h(x) = -x-4

No matter what number you pick for x, the h(x) function will be used in some way. So the domain is the set of all real numbers. To write this in interval notation, we write (-\infty, \infty) which means we start off at negative infinity and go to positive infinity. This is basically saying "the entire real number line". Since we can't actually reach either infinity, we always use parenthesis with them. <u>Never</u> use square brackets with either infinity

From the graph (see attached image below), we see that (0,-4) is the lowest point. This means y = -4 is the smallest y output possible, though we can't actually reach it because of the open circle at (0,-4). We can get any other larger y value. So the range is therefore: (-4, \infty) meaning we start at -4 and head off to positive infinity. The curve parenthesis next to -4 the reader "exclude -4 as part of the range". There is an open hole or gap here. Another way to state the range is to write y > -4

8 0
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Tom [10]

Answer:

gas = $0.23, electricity = $0.10

Step-by-step explanation:

4 0
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