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
Archy [21]
3 years ago
10

April is an avid chess player. She sets up a coordinate system on her chess board so she can record the position of the pieces d

uring a game. In a recent game, April noted that her king was at (4,2) at the same time that her opponent's king was at (7,8). How far apart were the two kings? Round to the nearest tenth of a unit if necessary.
Mathematics
1 answer:
NemiM [27]3 years ago
4 0

Answer:

6.7

Step-by-step explanation:

To solve this problem, we need to calculate the distance between two points in the XY coordinate plane.

The formula to calculate this distance is:

d = sqrt(dx^2 + dy^2)

where dx is the difference between the X coordinate of the points, dy is the difference between the Y coordinate of the points, and d is the distance.

(sqrt is the square root of what is in the parenthesis)

The first point (April's king) has X=4 and Y=2, the second point (the opponent's king) has X=7 and Y=8.

So, we have that dx = 4-7 = -3 and dy = 2-8 = -6

Now, we calculate the distance:

d = sqrt[ (-3)^2 + (-6)^2 ] = sqrt(9+36) = sqrt(45) = 6.7082 = 6.7

You might be interested in
The square below represents a unit or a whole. What fraction is represented by the
Mkey [24]
20/28 or 10/14 or 5/7
You can keep reducing until both sides of the fraction can't be divided by the same number anymore.
5 0
2 years ago
chegg evaluate the following integral using trigonometric substitution. dx/square root(x^2-81), x > 9
vesna_86 [32]

Integration will be ln | ( x /9 ) + ( \sqrt{(x/9)^{2} - 1 } ) | + c  .

Given  ∫ 1 dx / ( x^{2} - 81 )

Put ,

x = 9 secθ

dx = 9 secθ tanθ dθ

and

\sqrt{x^{2}  - 9^{2} } = 9 tanθ

Substituting values in  ∫ 1 dx / ( x^{2} - 81 ) ,

∫ (9 secθ tanθ ) dθ / ( 9 tanθ )

∫ secθ dθ = ln | secθ + tanθ | + c

                = ln | ( x /9 ) + ( \sqrt{x^{2}  - 9^{2} } / 9 ) | + c

              = ln | ( x /9 ) + ( \sqrt{(x/9)^{2} - 1 } ) | + c

Hence , the integration will be ln | ( x /9 ) + ( \sqrt{(x/9)^{2} - 1 } ) | + c .

To learn more on integration follow link :

brainly.com/question/20156869

#SPJ4

6 0
1 year ago
(x-4)/5=9-(2x-41)/9
jok3333 [9.3K]
For this question, you have to take Least Common Multiplier for which in this case will be "45" as, the denominators can get similar and get multiplied by a same value to form a similar expression. This allows us to cancel out them by common factors. Full process shown below.

\mathbf{Given \: \: Expression: \: \dfrac{x - 4}{5} = 9 - \dfrac{2x - 41}{9}}

\mathbf{\dfrac{x - 4}{5} \times 45 = 9 \times 45 - \dfrac{2x - 41}{9} \times 45}

\mathbf{9(x - 4) = 405 - 5 (2x - 41)}

\mathbf{9x - 36 = 405 - 10x + 205}

\mathbf{9x - 36 = - 10x + 610}

\mathbf{9x - 36 + 36 = - 10x + 610 + 36}

\mathbf{9x = - 10x + 646}

\mathbf{9x + 10x = - 10x + 646 + 10x}

\mathbf{19x = 646}

\mathbf{\dfrac{19x}{19} = \dfrac{646}{19}}

\mathbf{\therefore \quad x = 34}

\boxed{\mathbf{\underline{\therefore \quad Final \: \: Answer \: \: is; \: \: x = 34}}}

Hope it helps.
3 0
2 years ago
What equals -8 when multiplied but when added together is -7​
kirza4 [7]

Answer:

-8 and 1

Step-by-step explanation:

-8 × 1 = -8

-8 + 1 = -7

3 0
2 years ago
2x + 2x + 2 = 4x + 2<br> Do this equation has one solution,many solutions,or no solutions?
Slav-nsk [51]

Step-by-step explanation:

2x + 2x + 2 = 4x + 2           <em>combine like terms</em>

4x + 2 = 4x + 2          <em>subtract 4x from both sides</em>

4x - 4x + 2 = 4x - 4x + 2

2 = 2   TRUE

<h2>CONCLUSION:</h2><h3>This equation has an infinitely many solutions. The solution to this equation is any real number.</h3>
3 0
2 years ago
Other questions:
  • Suppose point P (4,−9) is translated according to the rule (x,y) → ( x+3, y−2). What are the coordinates of P′? Explain.
    12·1 answer
  • Are 18:3 and 6:1 equivalent radios?
    7·2 answers
  • Robert sliced a large loaf of bread to make 12 sandwiches. He makes 3 turkey sandwiches and 5 veggie sandwiches. What fraction o
    9·2 answers
  • Find a set of parametric equations of the line with the given characteristics. (Enter your answer as a comma-separated list of e
    9·1 answer
  • MATH WILL GIVE BRAINLIEST!
    9·1 answer
  • Due in 20 mins help pls
    14·2 answers
  • Can u please answer the question
    12·2 answers
  • A ladder leans against a wall 6 ft above the ground. The base of the ladder is 3 ft from the wall. How long is the ladder?
    7·1 answer
  • Enter the coordinates for this 90 degree counter clockwise rotation around the origin.
    15·1 answer
  • The answer to this question
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!