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love history [14]
2 years ago
7

what is the distance between the points (4, 5) and (10, 13) on a coordinte plane a. 12 units b. 8 units c. 10 units d. 14 units

Mathematics
1 answer:
qaws [65]2 years ago
7 0

Answer:

<h2>10 units</h2>

Option C is the correct option

Step-by-step explanation:

Let the points be A and B

A ( 4 , 5 ) ------> ( x1 , y1 )

B ( 10 , 13 ) ------> ( x2 , y2 )

Now, let's find the distance between these points:

\sqrt{ {(x2 - x1)}^{2}  +  {(y2 - y1)}^{2} }

plug the values

= \:  \sqrt{(10 - 4) ^{2} +  {(13 - 5)}^{2}  }

Calculate the difference

=  \sqrt{ {(6)}^{2} +  {(8)}^{2}  }

Evaluate the power

=  \sqrt{36 + 64}

Add the numbers

=  \sqrt{100}

Write the number in exponential form with. base of 10

=  \sqrt{ {(10)}^{2} }

Reduce the index of the radical and exponent with 2

= 10 \: units

Hope this helps..

Best regards!!

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a charitable organization in Lanberry is hosting a black tie benefit. Yesterday, the organization sold 55 regular tickets and 49
jenyasd209 [6]

Answer:

  • regular: $67
  • VIP: $122

Step-by-step explanation:

Let r and v represent the costs of a regular and VIP ticket, respectively. The two sales can be represented by ...

  55r +49v = 9663

  79r +84v = 15541

We can subtract 7 times the second equation from 12 times the first to eliminate the v terms.

  12(55r +49v) -7(79r +84v) = 12(9663) -7(15541)

  660r +588v -553r -588v = 115,956 -108,787 . . . . . eliminate parentheses

  107r = 7169 . . . . . . . simplify

  r = 67 . . . . . . . . . . . divide by 107

Using this value in the first equation, we have ...

  55(67) +49v = 9663

  v = 5978/49 . . . . . . . . . subtract 3685, divide by 49

  v = 122

A regular ticket costs $67; a VIP ticket costs $122.

_____

<em>Additional comment</em>

When using "elimination" to solve a system of equations, you're looking for coefficients of the same variable that are related by small factors. Preferably, one coefficient is the same as, or a small multiple of, the other. Here, 55 and 79 (the coefficients of x) are not related by an integer, or a couple of small integers. On the other hand, the y-coefficients 49 and 84 have a common factor of 7, and are in the ratio 7:12, a pair of small numbers. This is why we chose to eliminate the y-variable.

The x-variable could be eliminated using 55 and -79 as multipliers of the equations. This results in larger numbers, and more chance for error. (Errors tend to creep in when computing or copying large numbers.)

Of course, any of several machine methods could be used to solve these equations, including graphing and matrix-solving functions. Here, we tried to honor the requirement to solve by elimination.

7 0
2 years ago
A helicopter descends at a rate of 450 feet per minute write the equation and sole the change in altitude of the helicopter afte
sweet [91]
Just divide the 450 by 5
8 0
3 years ago
The coordinates of quadrilateral PQRS are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). How can you use coordinate geometry t
Flauer [41]
We will use the formula for the slope:
m = ( y2- y1 ) / ( x2 - x1 )
For PQ : m = ( 0 - 0 ) / ( a + c - 0 ) = 0
For RS : m = ( b - b ) / ( a - ( 2a + c )) = 0
Both slopes are m = 0, so PQ and RS are parallel to x - axis and at the same time parallel to each other ( PQ | | RS ). One pair of opposite sides is parallel.
8 0
3 years ago
Read 2 more answers
which of the following is the equation of a line parallel to the line y = -x + 1, passing through the point (4,1)
fomenos

Answer:

A. x + y = 5

Step-by-step explanation:

The slope of the equation is equal for parallel lines,

; Slope = (-1)

;Use the formula

(y - y(coordinate of the given point)) = slope × [(x - x(coordinate of the given point)]

; y - 1 = (-1)(x - 4)

; y - 1 = -x + 4...then move the variable (x) to the left hand side and then move (-1) to the right hand side

; x + y = 4 + 1

; Hence,

; x + y = 5

4 0
3 years ago
What is the sign of -567.45 + 567.45−567.45
Cloud [144]

Answer:

The answer is (- 567.45)

8 0
3 years ago
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