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jok3333 [9.3K]
3 years ago
7

Solve 5x^2 - 7x+2 -0 by completing the square. What are the solutions?

Mathematics
1 answer:
trapecia [35]3 years ago
6 0

5<em>x</em>² - 7<em>x</em> + 2 = 0

5(<em>x</em>² - 7/5 <em>x</em>) + 2 = 0

5(<em>x</em>² - 7/5 <em>x</em> + 49/100 - 49/100) + 2 = 0

5(<em>x</em>² - 2 • 7/10 <em>x</em> + (7/10)²) - 49/20 + 2 = 0

5(<em>x</em> - 7/10)² - 9/20 = 0

5(<em>x</em> - 7/10)² = 9/20

(<em>x</em> - 7/10)² = 9/100

<em>x</em> - 7/10 = ± √(9/100)

<em>x</em> - 7/10 = ± 3/10

<em>x</em> = 7/10 ± 3/10

<em>x</em> = 10/10 = 1   or   <em>x</em> = 4/10 = 2/5

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How many adult tickets were sold if each adult ticket sold was $6 and each student ticket was $4.50 and 260 tickets were sold fo
erik [133]

Answer:

   Adult tickets sold:   156

Step-by-step explanation:

   Adult ticket:   x

Student ticket:  y

x + y = 260                  ===>   -6(x + y = 260)     ===>  -6x -6y = -1560

6x + 4.5y = 1404         ===>                                           6x + 4.5y = 1404

                                                                                  ________________

add the two equations to eliminate a variable:                  -1.5y = -156

divide by -1.5:                                                                              y = 104

substitution to find x:

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5 0
3 years ago
PLEASE I NEED THE ANSWER DON'T IGNORE MY QUESTION!!!
kenny6666 [7]

Answer:

x=7.8

Step-by-step explanation:

take 49 degree as reference angle

using cos rule

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3 years ago
Read 2 more answers
PLEASE HELP!<br>Calculate $40^{13} \pmod{85}.$
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In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85

Notice

40*40*40=64,000

so we check how many time does 85 fit into 64,000:

64,000/85=752.94

85*753=64,005;       64000-64,005=-5

this means that 

40^{3} =-5\pmod{85}

thus

40^{13} =40^{3*4+1}={(40^{3})}^{4}*40=(-5)^{4}*40 \pmod{85}=\\\\625*40\pmod{85}=(7*85+30)*40\pmod{85}=30*40\pmod{85}\\\\=1200\pmod{85}=(14*85+10)\pmod{85}=10\pmod{85}


Answer: 10 (mod85)

Remark, the set of all solutions is:

{......-75, 10, 95, .....}, that is 85k +10
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