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Scilla [17]
3 years ago
9

If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?

Mathematics
1 answer:
kotegsom [21]3 years ago
7 0

Answer:

d. The equation has one solution and there is not enough information to determine the direction of the parabola.

Step-by-step explanation:

For a general quadratic equation

y = ax² +bx +c

the solution is

x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

The discriminant (D) is the part of the quadratic formula underneath the radical: b² - 4ac.

D tells us whether there are

  • two different real solutions
  • two identical real solutions ("one solution")
  • two complex solutions.

If D= 0,

x = \dfrac{-b}{2a}\pm0 = \mathbf{\dfrac{-b}{2a}}

and there are two identical solutions ("one solution").

The direction of the parabola depends on the sign of a.

That information is not given, so we cannot determine the direction of the parabola.

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Are the expressions 8a - 3b - (2a + 4b) and 6a + b equivalent?
Margaret [11]

Answer:

No.

Step-by-step explanation:

Let's start by simplifying the first expression:

8a-3b-(2a+4b)

Remove the parentheses:

8a-3b-(2a)-(4b)\\8a-3b-2a-4b

Combine like terms:

8a-2a-3b-4b\\6a-7b

6a-7b\neq 6a+b (Assuming that none of the variables are equivalent to 0)

3 0
2 years ago
Please help me solve this problem.
Tasya [4]

Let

x-------> total peanuts originally from the bag

we know that

1) Phillip took 1/3 of the peanuts from the bag--------> (1/3)*x

remaining=x-(1/3)*x-------> (2/3)*x

2) Joy took 1/4 of the remaining peanuts-------> (1/4)*[(2/3)*x]----> (1/6)*x

remaining= (2/3)*x-(1/6)*x------> (1/2)*x

3) Brett took 1/2 of the remaining peanuts------> (1/2)*(1/2)*x-----> (1/4)*x

remaining= (1/2)*x-(1/4)*x-------> (1/4)*x

4) Preston took 10 peanuts------> 10

(1/4)*x-10=71----> multiply by 4 both sides----> x-40=284----> x=324 peanuts

5) Total originally peanuts from the bag is equal to 324 peanuts

6) Phillip took (1/3)*x-----> (1/3)*324=108 peanuts

7) Joy took (1/6)*x------> (1/6)*324=54 peanuts

8) Brett took (1/4)*x------> (1/4)*324=81 peanuts

9) Preston took 10

so

check

108+54+81+10=253

remaining=324-253------> remaining=71-------> is correct

6 0
3 years ago
tanji creates a "square, circle" repeating pattern. Kenji creates a "Square, circle, trianglr, cricle" repeating pattern. if bot
RoseWind [281]

Both tanji & kenji have same number of circles i.e. 50 .

<u>Step-by-step explanation:</u>

Here we have , tanji creates a "square, circle" repeating pattern. Kenji creates a "Square, circle, triangle, circle" repeating pattern. if both tanji and kenji have 100 shapes in their patterns,  . We need to find that which pattern contains more circles .Let's find out :

<u>tanji creates a "square, circle" </u>

it's given that tanji has 100 shapes and he is repeating this pattern . In this pattern circle comes 1 every time out of 2 shapes :

Total number of times circle = \frac{100}{2}(1)

Total number of times circle = 50

<u>Kenji creates a "Square, circle, triangle, circle" </u>

it's given that tanji has 100 shapes and he is repeating this pattern . In this pattern circle comes 2 every time out of 4 shapes :

Total number of times circle = \frac{100}{4}(2)

Total number of times circle = 50

Both tanji & kenji have same number of circles i.e. 50 .

3 0
3 years ago
Write 7.75 x 10^-3 in standard notation​
Natasha_Volkova [10]

Answer:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

7.75 × 10^−3

4 0
3 years ago
Read 2 more answers
What is the answer???
Lapatulllka [165]
Is either I’m blind and can’t see or the letter are way too small
5 0
3 years ago
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