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iris [78.8K]
3 years ago
14

Solve each equation by completing the square r² = –12r - 35​

Mathematics
1 answer:
Fittoniya [83]3 years ago
7 0

Answer:

r = - 7, r = - 5

Step-by-step explanation:

Given

r² = - 12r - 35 ( add 12r to both sides )

r² + 12r = - 35

To complete the square

add ( half the coefficient of the r- term )² to both sides

r² + 2(6)r + 36 = - 35 + 36

(r + 6)² = 1 ← take the square root of both sides )

r + 6 = ± 1 ( subtract 6 from both sides )

r = - 6 ± 1, thus

r = - 6 - 1 = - 7 or r = - 6 + 1 = - 5

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In a data ,range is 17 and coefficient of range is 0.2 find the smallest term of the data.
anygoal [31]

Answer:

Step-by-step explanation:

Let largest value of data be L

and smallest value of data be S.

We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.

Range formula is given by = Largest value - Smallest value

                   17  =   L - S

                  L = 17 + S ---------- [Equation 1]

Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)

                                       0.2   =    l-s/l+s

                                      0.2 = 17/l+s

                 L + S = 17/0.2 = 85

So,    L + S = 85

       17 + S + S = 85   {using equation 1}

           2*S = 80

             S = 80/2 = 40

Putting value of S in equation 1, we get L = 20 + 40 = 60

Therefore,  Largest value, L = 60

               smallest value, S = 40

                         

5 0
3 years ago
Please please please help!! i need this asap and i have no where else to go!
nadezda [96]
1   1   1        2
2  -3   1      -11            -2R1 + R2 → R2
-1  2  -1        8                R1 + R3 → R3

1    1    1      2
0    -5  -1   -15             R2 ⇔ R3
0    3    0     10

1    1    1      2
0    3    0     10             -R3
0   -5   -1    -15

1    1    1      2
0    3    0     10             1/3 R2
0    5    1     15

1    1    1      2                   -R2 + R1
0    1    0     10/3             -5R2 + R3
0    5    1     15

1    0    1      -4/3              
0    1    0     10/3             -R3 + R1
0    0    1      -5/3

1    0    0       1/3             
0    1    0     10/3           
0    0    1      -5/3

Therefore, x = 1/3, y = 10/3, z = -5/3
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