1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inysia [295]
3 years ago
6

3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the

second pike is twice the number of books in the third pile. How many books are there in the third pile.
Mathematics
1 answer:
pochemuha3 years ago
7 0

Answer:

598 books

Step-by-step explanation:

Let x be the number of books in the 3rd pile. We will have then:

1st pile: 2x + 10

2nd pile: 2x

3rd pile: x

3000 = (2x + 10) + (2x) + (x)

3000 = 5x + 10

3000 - 10 = 5x

2990 = 5x

2990/5 = x

x = 598 books in the third pile!

We can check that:

3000 = 2*598 + 10 + 2*598 + 598

3000 = 1196 + 10 + 1196 + 598

3000 = 3000 CHECK!

You might be interested in
Is square root of 4 rational<br> or irrational
lidiya [134]

Answer:

Rational

Step-by-step explanation:

√4 asks "what times itself is 4?"

The answer is 2.

2x2=4

√4 = 2

2 is rational.

6 0
2 years ago
Read 2 more answers
What is 6x+7y=7 in slope intercept form?
leva [86]

Answer: The answer is y= -6/7x+1

4 0
3 years ago
Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p
kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>
  • In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
  • In second quadrant(π/2 < θ < π), only sin and cosec are positive.
  • In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
  • In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

y= 3\cos(2(x + \pi/2)) - 2

The options are:

  1. y= 3\sin(2(x + \pi/4)) - 2
  2. y= -3\sin(2(x + \pi/4)) - 2
  3. y= 3\cos(2(x + \pi/4)) - 2
  4. y= -3\cos(2(x + \pi/2)) - 2

Checking all the options one by one:

  • Option 1: y= 3\sin(2(x + \pi/4)) - 2

y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

  • Option 2: y= -3\sin(2(x + \pi/4)) - 2

This option if would be true, then from option 1 and this option, we'd get:
-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0

which isn't true for all values of x.

Thus, this option is not same as the given function.

  • Option 3: y= 3\cos(2(x + \pi/4)) - 2

The given function is y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

This option's function simplifies as:

y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2

Thus, this option isn't true since \sin(2x) \neq \cos(2x) always (they are equal for some values of x but not for all).

  • Option 4: y= -3\cos(2(x + \pi/2)) - 2

The given function simplifies to:y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

The given option simplifies to:

y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2

Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

Learn more about sine to cosine conversion here:

brainly.com/question/1421592

4 0
2 years ago
Read 2 more answers
Simplify 5x + 2(x - 3) = -2(x - 1)
Kruka [31]

Answer:

x=8/9

Step-by-step explanation:

5x+2(x-3)=-2(x-1)

1) Distribute 2 to x and -3:

5x+2x-6=-2(x-1)

2) Distribute -2 to x and -1:

5x+2x-6=-2x+2

3) Combine alike terms:

7x-6=-2x+2

4) Add 2x to both sides:

9x-6=2

5) Add 6 to both sides:

9x=8

6) Divide both sides by 9:

x=8/9

8 0
3 years ago
Read 2 more answers
A car travels 60km in 30 minutes. In how much time will it cover 100 km?
Daniel [21]

Answer:

About 40 Minutes, Or something close to that

Step-by-step explanation:

The car covers 60 km in 90 minutes or its speed = 60 km*60/90 min = 40 km/hr . So to cover 100 km at the same speed it will take 100/40 = 40 Min

5 0
3 years ago
Read 2 more answers
Other questions:
  • The data set shown below represents the number of times some families went out for dinner the previous week.
    5·2 answers
  • Solve for x in the equation x2+10x+12=36
    11·2 answers
  • Find the whole. 700​% of what number is 5,950​?
    15·1 answer
  • 9, 2, 1, 5, 9, 7, 1, 2, 2, 5, 6<br> Question<br> What is the median for the set of data
    10·2 answers
  • 14)<br> Solve the equation for x.<br> 6(4x - 10) = 84<br> A)<br> 2<br> B)<br> 3<br> 4.<br> 6
    14·2 answers
  • Evaluate the expression when x=5: 10 | 7-x| <br> -120<br> -20<br> 20<br> 120
    7·1 answer
  • Select the two answer choices that apply.
    7·1 answer
  • Find the two pairs of numbers whose LCM is the product of the numbers<br><br>help pls
    14·1 answer
  • 10 points<br> Multiply (3.5x10^-6)x(2x10^-4) *
    7·1 answer
  • (a) It takes 40 pounds of seed to completely plant a 6-acre field. How many pounds of seed are needed per acre? poundsperacre
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!