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WITCHER [35]
3 years ago
5

How to find the discriminant of a quadratic equation and describe the nature of the roots?

Mathematics
1 answer:
emmasim [6.3K]3 years ago
5 0
In the quadratic ax²+bx+c the discriminant is determined by b²-4ac. If this expression is positive the roots are real; if negative, the roots are complex; if the expression is zero the quadratic is a perfect square of the form x-b/2a.
If b²-4ac is a perfect square and positive the roots are rational, otherwise they are irrational.
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The bill for five glasses of apple juice and four salads is $9.50, but the bill for four glasses of apple juice and five salads
Elena L [17]

Answer: the bill for a glass of apple juice is $0.7 and the bill for a salad is $1.5

Step-by-step explanation:

Let x represent the bill for a glass of apple juice.

Let y represent the bill for a salad.

The bill for five glasses of apple juice and four salads is $9.50. It means that

5x + 4y = 9.5 - - - - - - - - - - - 1

The bill for four glasses of apple juice and five salads is $10.30. This means that

4x + 5y = 10.30- - - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

20x + 16y = 38

20x + 25y = 51.5

Subtracting, it becomes

- 9y = - 13.5

y = - 13.5/-9

y = 1.5

Substituting y = 1.5 into equation 1, it becomes

5x + 4 × 1.5 = 9.5

5x + 6 = 9.5

5x = 9.5 - 6 = 3.5

x = 3.5/5 = 0.7

3 0
4 years ago
A card is randomly selected from a standard 52-card deck. What are the odds that the selected card is a red king?
tatuchka [14]

Answer:

Total there are 2 king of red color out of 52 cards. Therefore, the probability of getting a king of red color will be 2/52 or 1/26. Three cards are drawn from the top of a 52 card playing deck.

5 0
3 years ago
Describe features that determine a translation, rotation, and reflection.
yulyashka [42]
Hii I hope this helps! :)
Translation: It’s a transformation that moves every point in a figure the same distance in the same direction.
Rotation: It’s a a transformation that turns a figure about a fixed point.
Reflection: It’s a transformation that takes a shape/preimage and flips it across a line called the line of reflection to create a new shape/image.
7 0
3 years ago
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Angels 1 and 2 are complementary the measure of angle 2 is 2 times the measure of Angel 1 write and solve an equation to find th
creativ13 [48]

Two complementary angles sum is 90 degrees.

Angle 1 = x

Angle 2 = 2x ( two times angle 1)

Equation: x + 2x = 90

Solve:

Combine like terms:

3x = 90

Divide both sides by 3:

X = 90/3

X = 30

Angle 1= 30

Angle 2 = 60

4 0
3 years ago
Find the value of x such that sin (90-x) = cos 50
Arte-miy333 [17]
Sin (90-x) = cos x

so x = 40 
3 0
3 years ago
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