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3 years ago

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.

You might be interested in

The day length in Manila, Philippines, varies over time in a periodic way that can be modeled by a trigonometric function.

iris [78.8K]

Answer:

L(t) = 727.775 -51.875cos(2π(t +11)/365)
705.93 minutes

Step-by-step explanation:

a) The midline of the function is the average of the peak values:

(675.85 +779.60)/2 = 727.725 . . . minutes

The amplitude of the function is half the difference of the peak values:

(779.60 -675.85)/2 = 51.875 . . . minutes

Since the minimum of the function is closest to the origin, we choose to use the negative cosine function as the parent function.

Where t is the number of days from 1 January, we want to shift the graph 11 units to the left, so we will use (t+11) in our function definition.

Since the period is 365 days, we will use (2π/365) as the scale factor for the argument of the cosine function.

Our formula is ...

L(t) = 727.775 -51.875cos(2π(t +11)/365)

b) L(55) ≈ 705.93 minutes

8 0

3 years ago

In ΔDEF, the measure of ∠F=90°, the measure of ∠D=66°, and EF = 32 feet. Find the length of FD to the nearest tenth of a foot.

Butoxors [25]

Answer:

14.2 ft

Step-by-step explanation:

tan 66° = 32/ FD

FD = 32 / tan 66° = 32 / 2.246 = 14.2

7 0

3 years ago

(10) Both red line and blue line trains left the station at 5:00 pm. If both

scoundrel [369]

Answer:

5:40

Step-by-step explanation:

This is a problem involving the least common difference.

If you know that the red and blue trains left at the same time at 5, you know that another red train will leave at 5:08. Another blue train at 5:10.

The way to solve this will be to write out the factors of 8 and 10 and find the smallest number that they overlap.

Red:

8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Blue:

10, 20, 30, 40

You see that after 40 mnutes, they are both leaving the station again. After 40 minutes, at 5:40, they are both leaving.

6 0

2 years ago

Esmerelda bought a bag of jelly beans. There were 24 green jelly beans, which made up 8%, percent of all the jelly beans in the

Margarita [4]

So, let's look at the problem once again.

8%, or 8/100 of the bag were green jelly beans.

Let's see what we can do to find out a number of other jelly beans, not including the green ones.

We know that 92% of jelly-beans are not green.

92% is 11.5 times more than 8%
(92/8)

24 (or 8%) times 11.5 = 276

276 - number of jelly beans that are not green.

276 plus 24 = 300.

Answer: 300 jelly beans were in one bag.

6 0

3 years ago

Please write step by step of how you got the answer. Thankyou

stealth61 [152]

Answer:

The solution in the attached figure

Step-by-step explanation:

step 1

Place the numbers -4, 4, 0, and -3 in the left side

Adds the numbers

$-4+4+0-3=-3$ ----> is correct