MATHEMATICS HIGH SCHOOL

Determine the value of k so that 2x^2+kx+5=0 has each type of solutions: 2 real solutions:
2complex,nonreal solutions:
Exactly 1 real solution:

Answers

Answer 1
Answer: 2x^2+kx+5=0 \n \na=2 \n b=k \n c=5 \n \Delta=b^2-4ac=k^2-4 * 2 * 5=k^2-40

When the discriminant Δ is greater than 0, the equation has 2 real solutions:
k^2-40 > 0 \nk^2>40 \nk>√(40) \ \lor \ k<-√(40) \nk>2√(10) \ \lor \ k<-2√(10) \n\boxed{k \in (-\infty,-2√(10)) \cup (2√(10), +\infty)}

When the discriminant Δ is less than 0, the equation has 2 complex and no real solutions:
k^2-40<0 \nk^2<40 \nk<√(40) \ \land \ k>-√(40) \nk<2√(10) \ \land \ k>-2√(10) \n\boxed{k \in (-2√(10),2√(10))}

When the discriminant Δ is equal to 0, the equation has exactly 1 real solution:
k^2-40=0 \nk^2=40 \nk=√(40) \ \lor \ k=-√(40) \nk=2√(10) \ \lor \ k=-2√(10) \n\boxed{k \in \{ -2√(10), 2√(10) \} }

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One day at St. Philip's High School, 1/2 of the pupils walked to school, 1/5 of the pupils came to school by bus, and the remaining 57 pupils came by car.What fraction came to school by car?

Answers

The first thing to do is the make the denominators of the fractions the same. 

5/10 of the pupils walked to school and 2/10 of the pupils came to school by bus. 
5/10 + 2/10 = 7/10. 
10/10 - 7/10 = 3/10. 

3/10 of the pupils came to school by car. 

What's the missing side length on the triangle if side a=√33 and side b=4

Answers

Answer:

7

Step-by-step explanation:

to find the missing side length you use the pythagorean theorem a^(2) +b^(2) = c^(2)

so (√(33) )^(2) + 4^(2) =49^(2) and then you take the square root of 49^(2) and you end up with an answer of 7.

Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimeters longer than twice the length of the first shelf. The third shelf is 12 centimeters shorter than the first The remaining shelf centimeters longer than the first shelf. If Robert must use the entire 2 5 meter board for the shelves. what is the length of the second shelf, in centimeters?

Answers

114 cm/ 1.14 m this will give you your answer.

Please help it's emergency

Answers

2050=.34x-623.67
2673.67=.34x
x=2673.67/.34
x= 7863.74
x~ 7864

If two circles have the same diameter, do they have the same circumference?

Answers

Yes they will have the same circumference

The numbers 1 through 50 are written with red marker on slips of paper while the numbers 51 through 100 are written with blue marker on slips of paper. All the papers are put into a bag and shuffled. One card is
randomly selected.
a. Find the probability of selecting a number less than 16 or a number written in red.
b. Find the probability of selecting a number written in blue or a multiple of 5.

Answers

A. we want to pull 15 or less from the bag and there are 100 possibilities
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B. we are trying to pull a 55,60,65,75,80,85,90,95,or 100 that is 9 possibilities out of 100

(9)/(100)  is the possibility of pulling a multiple of 5 that is blue 
 
a. The probability of picking a number less than 16 or a number in red is 65/100.
b. The probability of picking a number written in blue or a multiple of 5 is 70/100. 
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