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netineya [11]
2 years ago
5

-x + 2y = 21 5x + 6y = 23

Mathematics
2 answers:
netineya [11]2 years ago
7 0

Answer:

(-5, 8)

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination
  • Solving systems of equation by graphing

Step-by-step explanation:

<u>Step 1: Define systems</u>

-x + 2y = 21

5x + 6y = 23

<u>Step 2: Rewrite systems</u>

-x + 2y = 21

  1. Subtract 2y on both sides:                    -x = 21 - 2y
  2. Divide -1 on both sides:                         x = -21 + 2y
  3. Rearrange:                                              x = 2y - 21

<u>Step 3: Redefine systems</u>

x = 2y - 21

5x + 6y = 23

<u>Step 4: Solve for </u><em><u>y</u></em>

<em>Substitution</em>

  1. Substitute in <em>x</em>:                         5(2y - 21) + 6y = 23
  2. Distribute 5:                             10y - 105 + 6y = 23
  3. Combine like terms:                16y - 105 = 23
  4. Add 105 on both sides:           16y = 128
  5. Divide 16 on both sides:          y = 8

<u>Step 5: Solve for </u><em><u>x</u></em>

  1. Define original equation:                    5x + 6y = 23
  2. Substitute in <em>y</em>:                                     5x + 6(8) = 23
  3. Multiply:                                                5x + 48 = 23
  4. Subtract 48 on both sides:                 5x = -25
  5. Divide 5 on both sides:                       x = -5

<u>Step 6: Graph systems</u>

<em>Check the solution set.</em>

9966 [12]2 years ago
6 0
( x , y ) = ( -5 , 8 )
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We must multiply the first numerator by 5, because 3*5=15 and the second numerator by 3 because 5*3=15.

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Two number cubes are rolled for two separate events:
andrew11 [14]

Answer:  \bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}

<u>Step-by-step explanation:</u>

The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)

P(B|A)=\dfrac{P(B\cap A)}{P(A)}

P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)

          (2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)

          (3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)

                    (4, 5), (4, 4), (4, 3), (4, 2), (4, 1)

                              (5, 4), (5, 3), (5, 2), (5, 1)

                                        (6, 3), (6, 2), (6, 1)

       = 30

P(B) = (1, 2), (2, 1)                                   sum = 3

          (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)    sum = 6

          (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)  sum = 9

          (6, 6)                                           sum = 12

                       

      = 12

P(A ∩ B) =  (1, 2), (2, 1)

                  (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

                  (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)

             = 11

7 0
3 years ago
Help me plzzzzzzzzz<br> solve for x
Svet_ta [14]

Answer:

7) \frac{x+20}{x}=\frac{46}{30}

30(x+20)=46x

30x+600=46x

46x-30x=600

16x=600

x=75/2

x=37.5

---------------------

8) \frac{10}{3x+1} =\frac{22}{7x-1}

10(7x-1)=22(3x+1)

70x-10=66x+22

70x-66x=22+10

4x=32

x=\frac{32}{4}

x=8

<u>---------------------</u>

hope it helps...

have a great day!!

4 0
3 years ago
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