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Tema [17]
3 years ago
8

Ravi is on the swim team. Each week he swims a total of 9,000 meters. How many kilometers does he swim each week? Be sure to inc

lude the correct unit in your answer.
Mathematics
2 answers:
Fed [463]3 years ago
7 0
Ravi swims 9 kilometers a week

1 kilometers (km) = 1,000 meters (m)

9000 m / 1000 = km

to simplify : 9/1 = 9

9,000 meters = 9 kilometers
Art [367]3 years ago
5 0
Ravi swims an average of 9 kilometers a week
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For an integer n ≥ 0, show that (n/2) - (-n/2) = n.<br><br> Use greatest integer function
mars1129 [50]

The greatest integer function returns the largest integer smaller than the number you provide it. That is, if <em>n</em> ≤ <em>x</em> < <em>n</em> + 1, where <em>n</em> is an integer, then the "greatest integer of <em>x</em>" is [<em>x</em>] = <em>n</em>.

• Let <em>n</em> be even. Then we can write <em>n</em> = 2<em>k</em> for some integer <em>k</em> ≥ 0. Now,

[<em>n</em>/2] = [<em>k</em>] = <em>k</em>

while

[-<em>n</em>/2] = [-<em>k</em>] = -<em>k</em>

so that

[<em>n</em>/2] - [-<em>n</em>/2] = 2<em>k</em> = <em>n</em>

<em />

• Let <em>n</em> be odd. Then <em>n</em> = 2<em>k</em> + 1 for some integer <em>k</em> ≥ 0. Every odd integer occurs between two even integers, so that

<em>n</em> - 1 < <em>n</em> < <em>n</em> + 1

or equivalently,

2<em>k</em> < <em>n</em> < 2<em>k</em> + 2

so that

<em>k</em> < <em>n</em>/2 < <em>k</em> + 1

It follows that [<em>n</em>/2] = <em>k</em>.

Similarly, if we negative the previous inequality, we have

-<em>k</em> > -<em>n</em>/2 > -(<em>k</em> + 1), or -<em>k</em> - 1 < -<em>n</em>/2 < -<em>k</em>

which means [-<em>n</em>/2] = -<em>k</em> - 1.

So we make the same conclusion,

[<em>n</em>/2] - [-<em>n</em>/2] = <em>k</em> - (-<em>k</em> - 1) = 2<em>k</em> + 1 = <em>n</em>

3 0
2 years ago
Solve the inequality for x<br> 3^(6x+18)&lt;27^(3x)
Lera25 [3.4K]

Answer:

\displaystyle x > 6

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Algebra I</u>

  • Terms/Coefficients
  • Factoring

<u>Algebra II</u>

  • Exponential Rule [Powering]: \displaystyle (b^m)^n = b^{m \cdot n}
  • Solving exponential equations

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle 3^{6x + 18} < 27^{3x}<em />

<em />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Rewrite:                                                                                                             \displaystyle 3^{6x + 18} < 3^{3(3x)}
  2. Set:                                                                                                                     \displaystyle 6x + 18 < 3(3x)
  3. Factor:                                                                                                               \displaystyle 3(2x + 6) < 3(3x)
  4. [Division Property of Equality] Divide 3 on both sides:                                  \displaystyle 2x + 6 < 3x
  5. [Subtraction Property of Equality] Subtract 3x on both sides:                       \displaystyle -x + 6 < 0
  6. [Subtraction Property of Equality] Subtract 6 on both sides:                        \displaystyle -x < -6
  7. [Division Property of Equality] Divide -1 on both sides:                                 \displaystyle x > 6
8 0
3 years ago
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If Luke pushes his sister in a wagon down the driveway that is 14 meters long and it takes 22 Newtons of force, how much work di
erica [24]

Hello!

The answer is:

Luke did a work of 308N.m or 308 Joules.

<h2>Why?</h2>

When a force is applied on a object making it to move covering a distance we call it "work". The movement caused by the force, will follow the same direction that the force.

We can calculate the work done by using the following equation:

Work=Force*distance*Cos(\alpha)

Where,

Work is the transferred energy.

Force, is the force applied to the object.

Distance, is the distance covered due to the applied force.

α, is the angle at the work is done.

We are given the following information to calculate the work done:

Force=22N\\Distance=14m

So, substituting the given information into the equation to calculate work, we have:

Work=Force*distance\\Work=22N*14m=308N.m

Hence, we have that Luke did a work of 308N.m or 308 Jouls.

Have a nice day!

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3 years ago
How do you solve this?
NNADVOKAT [17]

Answer:

C.)

Step-by-step explanation:

The graph is positive this time, so right away you can eliminate A and B.

If y=2x, the graph would be much steeper so the answer is C.) you can also check by graphing it in desmos.

4 0
2 years ago
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There are 61 centimetres of liquorice to be shared equally among 7 people. What length of liquorice will each person get?
Simora [160]

Answer:

8.71428571

do 61 divided by 7. Simple math.

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2 years ago
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