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maw [93]
3 years ago
10

A carnival charges $5 to enter, and $2 per ride. If you paid a total of $23, which of

Mathematics
1 answer:
emmasim [6.3K]3 years ago
7 0

Answer:

5+2x=23

Step-by-step explanation:

The number of rides you went on is 9.

You might be interested in
Solving for matrices
muminat

Answer:

D

Step-by-step explanation:

The augmented matrix for the system of three equaitons is

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\5&2&-2&|&11\\5&-4&4&|&-7\end{array}\right)

Multiply the first row by 5, the second row by -3 and add these two rows:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\5&-4&4&|&-7\end{array}\right)

Subtract the third row from the second:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&6&-6&|&18\end{array}\right)

Divide the third row by 6:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&1&-1&|&3\end{array}\right)

Now multiply  the third equation by 26 and add it to the second row:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&0&-45&|&-90\end{array}\right)

You get the system of three equations:

\left\{\begin{array}{r}3x-4y-5z=-27\\-26y-19z=-168\\-45z=-90\end{array}\right.

From the third equation

z=\dfrac{90}{45}=2.

Substitute z=2 into the second equation:

-26y-19\cdot 2=-168\\ \\-26y-38=-168\\ \\-26y=-168+38=-130\\ \\y=\dfrac{130}{26}=5.

Now substitute z=2 and y=5 into the first equation:

3x-4\cdot 5-5\cdot 2=-27\\ \\3x-20-10=-27\\ \\3x-30=-27\\ \\3x=-27+30=3\\ \\x=1.

The solution is (1,5,2)

4 0
3 years ago
Use the quadratic formula to find the complex solutions to the equation 10x2 – x + 9 = 0.
melomori [17]

Quadratic formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

a = 10

b = -1

c = 9

1 +/- sqrt((-1)^2 - 4(10)(9)) / 2(10)

1 +/- sqrt(1 - 360) / 20

x = 1 +/- sqrt(359i) / 20

Hope this helps!

7 0
3 years ago
Find the complex factors of the quadratic trinomial x^2 + 8x +17
Naily [24]

Answer: Factoring  x2+8x+17

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +17

Step-1 : Multiply the coefficient of the first term by the constant   1 • 17 = 17

Step-2 : Find two factors of  17  whose sum equals the coefficient of the middle term, which is   8 .

     -17    +    -1    =    -18

     -1    +    -17    =    -18

     1    +    17    =    18

     17    +    1    =    18

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

1

:

 x2 + 8x + 17  = 0

STEP

2

:

Parabola, Finding the Vertex:

2.1      Find the Vertex of   y = x2+8x+17

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -4.0000  

Plugging into the parabola formula  -4.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * -4.00 * -4.00 + 8.0 * -4.00 + 17.0

or   y = 1.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2+8x+17

Axis of Symmetry (dashed)  {x}={-4.00}

Vertex at  {x,y} = {-4.00, 1.00}  

Function has no real rootsvSolving   x2+8x+17 = 0 by Completing The Square .

Subtract  17  from both side of the equation :

  x2+8x = -17

Now the clever bit: Take the coefficient of  x , which is  8 , divide by two, giving  4 , and finally square it giving  16

Add  16  to both sides of the equation :

 On the right hand side we have :

  -17  +  16    or,  (-17/1)+(16/1)

 The common denominator of the two fractions is  1   Adding  (-17/1)+(16/1)  gives  -1/1

 So adding to both sides we finally get :

  x2+8x+16 = -1

Adding  16  has completed the left hand side into a perfect square :

  x2+8x+16  =

  (x+4) • (x+4)  =

 (x+4)2

Things which are equal to the same thing are also equal to one another. Since

  x2+8x+16 = -1 and

  x2+8x+16 = (x+4)2

then, according to the law of transitivity,

  (x+4)2 = -1

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+4)2   is

  (x+4)2/2 =

 (x+4)1 =

  x+4

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x+4 = √ -1

Subtract  4  from both sides to obtain:

  x = -4 + √ -1

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1

Since a square root has two values, one positive and the other negative

  x2 + 8x + 17 = 0

  has two solutions:

 x = -4 + √ 1 •  i

  or

 x = -4 - √ 1 •  i

6 0
2 years ago
Read 2 more answers
What is the best measure of center for the following data set?
Rom4ik [11]

Answer:

b) median: there are 7 numbers listed; 20 is the middle number among them

range: subtract lowest from highest number 25-2=23

mean: add all the numbers together =129

mode: place numbers in order (smallest to greatest), then see which number appears the most 2, 18, 18, 20, 22, 24, 25=18

Step-by-step explanation:

5 0
3 years ago
OUCH MY BRAIN IS HURTING AFTER TRYING TO SOLVE THIS QUESTION
maria [59]
300° CCW is the same as 60° CW. N will show up where H is now.

The 3rd selection is appropriate.
4 0
3 years ago
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