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aksik [14]
2 years ago
15

Solve the quadratic equations by completing the square. x^2-4x=-1

Mathematics
1 answer:
kkurt [141]2 years ago
8 0

Answer:

2 ± √3

Step-by-step explanation:

<h3>Solving quadratic equation by completing squares:  </h3>

           x² - 4x = -1

  • Divide the coefficient of x by 2.

                 4 ÷ 2 = 2

  •  Now, square the result and add that to both sides of the equation.

          2² = 2* 2 = 4

          x² - 4x + 4 = -1 + 4

          x² - 4x + 4 = 3

         x² - 2 * x * 2 + 2² = 3

  •     Compare it with a² - 2ab + b² . Now , a = x and b = 2

            (x - 2)² = 3

  •     Take square root both sides

             x - 2 = ±√3

                    x = 2 ± √3

<h3>Solutions: x = 2 +√3   ;  2 - √3</h3>
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A bicycle store costs $3600 per month to operate. The store pays an average of $80 per bike. The average selling price of each b
sweet [91]

Answer:

90 bikes.

Step-by-step explanation:

The bike store earns:

(120-80) = 40 dollars per bike sold.

Hence, to break even, the store must sell:

3600/40 = 90 bikes per month.

Hope this helped!

4 0
3 years ago
7. The cost of renting the party room for 10 people is $117.50. The cost of renting the room is $151.25 for 15 people. Write an
Viktor [21]

Answer:

C = 6.75n + 50

Step-by-step explanation:

The equation for the cost of renting the party room can be written in the form;

C= mn+k ......i

Where C = cost

n = number of people

Substituting the 2 cases into the equation we have,

Case 1

117.5 = 10m + k ......1

Case 2

151.25 = 15m + k .....2

Subtracting eqn 1 from 2 we have

151.25 - 117.50 = 15m - 10m

5m = 33.75

m = 33.75/5 = 6.75

Substituting m = 6.75 into eqn 1, we have

117.50 = 10(6.75) + k

k = 117.5 - 67.50

k = 50

Therefore, rewriting the eqn i, we have

C = 6.75n + 50

5 0
3 years ago
Keenan has 21 CDs and 33 DVDs. What is the ratio of DVDs to CDs?
mamaluj [8]
33: 21 ...........................................
7 0
3 years ago
Read 2 more answers
The bakers healthy baker can make 280 bagels in 10 hours. how many bagels can they bake in 15 hours? what was that rate per hour
Paraphin [41]
Hello there.

The bakers healthy baker can make 280 bagels in 10 hours. how many bagels can they bake in 15 hours? what was that rate per hour
Answer: First you should calculate the rate per hour.
280 / 10 = 28.
In one hour the baker can make 28 bagels.
Multiply the one hour amount by 15.
28 x 15 = 420.

In short, Your answer is the baker can make 420 bagels in 15 hours and it is 28 bagels per hour.

Hope This Helps You!
Good Luck Studying ^-^

7 0
3 years ago
Read 2 more answers
2x3 + x2 + 7x - 6)-(- 2x + 10x + 10x+9)​
AVprozaik [17]

Answer:

2x³ + x² - 11x - 15

Step-by-step explanation:

Step 1: Write out expression

2x³ + x² + 7x - 6 - (-2x + 10x + 10x + 9)

Step 2: Distribute negative

2x³ + x² + 7x - 6 + 2x - 10x - 10x - 9

Step 3: Combine like terms (x)

2x³ + x² + 9x - 10x - 10x - 9 - 6

2x³ + x² - x - 10x - 9 - 6

2x³ + x² - 11x - 9 - 6

Step 4: Combine like terms (constants)

2x³ + x² - 11x - 15

5 0
3 years ago
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