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Scrat [10]
3 years ago
8

11 Prove that

Mathematics
1 answer:
ale4655 [162]3 years ago
5 0

9514 1404 393

Answer:

  • the discriminant is non-negative for  k ≥ 2√2
  • k ≤ -2√2 will also give real roots

Step-by-step explanation:

The discriminant of this quadratic equation is ...

  d = b² -4ac

  d = k² -4(1)(2) = k² -8

For real roots, we require ...

  k² -8 ≥ 0

  k² ≥ 8

  |k| ≥ √8 = 2√2

That is, the equation will have real roots when ...

  k ≥ 2√2 . . . . . . . what you're asked to show

  k ≤ -2√2 . . . . . alternate values of k

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Hey besties help me
forsale [732]

2x + 6 = 4x/2 + 12/2

To solve this, we need to transpose like terms to the same side.

2x - 4x/2 = 12/2 - 6

2x - 2x = 6 - 6

0 = 0

Since both sides are zero, it means that the equation has infinite number of solutions.

7 0
3 years ago
Read 2 more answers
Carlo used this number line to find the product of 2 and −3. A number line going from negative 7 to positive 3. An arrow goes fr
Vesnalui [34]

Answer:

The errors are;

a. negative 4 to negative 6

b. negative 2 to negative 4

Step-by-step explanation:

The number line is the mathematical representation of numbers in the horizontal line or the x-axis.

The result of the multiplication of a positive 2 and a negative 3 is;

           2 x -3 = -6 ,  gives a negative 6.

So the number line should scale to accommodate the operands and the result, which is from negative 7 to positive 3, in the option given.

8 0
4 years ago
At Katya’s fruit stand, a basket of strawberries costs $4 and a basket of raspberries costs $9. In one morning, Katya sells 96 b
Tcecarenko [31]

Answer:

The number of strawberry baskets sold was 44

Step-by-step explanation:

Let

x ----> the number of strawberry baskets sold

y ---> the number of raspberries baskets sold

we know that

In one morning, Katya sells 96 baskets for $644

so

x+y=96 ----> equation A

4x+9y=644 ---> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (44.52)

see the attached figure

therefore

The number of strawberry baskets sold was 44 and the number of raspberries baskets sold was 52

4 0
3 years ago
Please help me and thank you if you did help me
Luba_88 [7]
12 to 16 because all ratios are equivalent
7 0
4 years ago
Read 2 more answers
Write a fraction that is equivalent to 2/5
ANEK [815]

Answer: 4/10

Step-by-step explanation:

7 0
3 years ago
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