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ANEK [815]
2 years ago
11

Factoring polynomial expressions(quadratic) x^2-6x+5

Mathematics
1 answer:
weeeeeb [17]2 years ago
5 0

Answer:

x = 5 and x = 1 are the factors

Step-by-step explanation:

<h2>step 1) </h2>

identify the a, b, and c values (a=1 b= -6 c=5)

<h2>step 2) </h2>

plug them into the quadratic formula

x = -(-6) ± √(-6)² - 4(1)(5) / 2(1)

<h2>step 3) </h2>

multiply -1 by -6 to get 6

x = 6 ± √(-6)² - 4(1)(5) / 2(1)

<h2>step 4)</h2>

multiply -6 by -6 to get 36

x = 6 ± √36 - 4(1)(5) / 2(1)

<h2>step 5)</h2>

multiply 4 by 1 to get 4

x = 6 ± √36 - 4(5) / 2(1)

<h2>step 6) </h2>

multiply 4 by 5 to get 20

x = 6 ± √36 - 20 / 2(1)

<h2>step 7)</h2>

subtract 36 by 20 to get 16

x = 6 ± √16 / 2(1)

<h2>step 8) </h2>

take the square root of 16 to get 4

x = 6 ± 4 / 2(1)

<h2>step 9)</h2>

multiply 2 by 1 to get 2

x = 6 ± 4 / 2

<h2>step 10) </h2>

add 6 by 4 to get 10

x = 10 / 2

<h2>step 11) </h2>

divide 10 by 2 to get 5 (now you know the first factor is x=5)

x = 5

<h2>step 12)</h2>

subtract 6 by 4 to get 2

x = 2 / 2

<h2>step 13)</h2>

divide 2 by 2 to get 1 (now you have found the final factor x=1)

<h2>step 14)</h2>

you know know that the factors of x²- 6x + 5 are<em><u> x = 5 and x = 1</u></em>

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7 0
3 years ago
Solve the problem using the six-step method: A pharmacist found at the end of the day she had 7/4 as many prescriptions for anti
svet-max [94.6K]
<h3>Given</h3>

1 (female) pharmacist counting prescriptions at the end of the day

(prescriptions for antibiotics) = (7/4)×(prescriptions for tranquilizers)

33 = (prescriptions for tranquilizers) + (prescriptions for antibiotics)

<h3>Find</h3>

The number of (prescriptions for tranquilizers)

<h3>Solution</h3>

Let <em>x</em> represent the number of <em>prescriptions for tranquilizers</em>. Then the number of prescriptions for antibiotics is (7/4)x, and the total number of prescriptions is

... 33 = x + (7/4)x . . . . . . . . . . put the given information in the given relation

... 33 = (4/4)x + (7/4)x . . . . . . rewrite 1 as 4/4 so we can add to 7/4

... 33 = ((4+7)/4)x = (11/4)x . . . simplify

... 33×(4/11) = (4/11)×(11/4)x . . . multiply by the reciprocal of the coefficient of x

... 12 = x . . . . . . . . . . . . . . . . . simplify

The pharmacist had 12 prescriptions for tranquilizers.

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7 0
3 years ago
Find the value of xxx in the triangle shown below. Choose 1 answer: Choose 1 answer: (Choice A) A x=\sqrt{21}x= 21 ​ x, equals,
Keith_Richards [23]

Answer:

x = 15.8114

Step-by-step explanation:

The complete question is:

"The problem is asking for value of x. Two right triangles side by side, the altitude is 9. The bottom of whole triangle is 25. One side is 15 and the other side is x. What is the value of x?"

Solution:-

- Develop a diagram for the information given " Two right triangles side by side" The altitude i.e height (common to both triangle ) = 9. The total base length of both triangles is = 25. One side is 15 and other side is x.

                                x

                             x x  x

                           x   x    x

                         x     x       x  

                       x       x          x       x = ?

                     x         x             x

           15     x          x                x

                 x             x   9              x

               x               x                      x

             x                 x                         x

           x                   x                            x

         x                     x                               x

       x                       x                                  x

  B  x x x x x x x x x x x x x x x x x x x x x x x  C

                  y           D                  25-y

- We will first determine the value of "y" using the left hand side triangle and apply pythagorean theorem. Where, H = 15 , P = 9 , B = y.

                                H^2 = P^2 + B^2

                                15^2 = 9^2 + y^2

                                y = √(225 - 81 )

                                y = 12

- Now we can use the value of y and apply pythagorean theorem on right hand side triangle with sides. H = x , P = 9 , B = 25-y = 25 - 12 = 13.

                               H^2 = P^2 + B^2

                               x^2 = 9^2 + 13^2

                               x = √( 81 + 169 )

                               x = 15.8114

3 0
2 years ago
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