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3 years ago

Use the discriminant to determine the number and type of solutions for the given equation x^2+2x+6=0

1 answer:

7 0

The discriminant is the portion of the quadratic formula under the root sign: b²-4ac

A quadratic equation in standard form is ax²+bx+c=0. In your equation:
a=1, b=2, and c=6. Substituting them into the equation:

2²-4(1)(6)
=4-24
=(-20)

When the discriminant is negative there are two, imaginary solutions.

If the discriminant equals a positive, perfect square number (like 4, 9, 16, etc), there will be two, rational roots.
If the discriminant equals a positive, nonperfect square number (like 3, 15, 23, etc), there will be two, irrational roots.
If the discriminant equals 0, there will be one double root

A quadratic equation graphs a parabola. The graph of a quadratic with a positive discriminant will pass through the x-axis twice. If the discriminant is 0, it will touch the x-axis and 'bounce' back the way it came. If the discriminant is negative, it will not touch the x-axis.

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Domain and range of the function f(x)= 7x^5 PLEASE HELP I LITERALLY CANT DO IT

sineoko [7]

Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

The domain is all x values, and the range is all y values.

Domain:

The domain is all real numbers except where the slope is undefined (a vertical line). In this case, no number makes the expression undefined, so the domain is:

all real numbers

Interval notation: (-∞,∞)

all negative numbers and positive numbers (all real numbers)

Set-Builder Notation: {x | x ∈ R }

Range:

The range is the set of all valid values. Graph the line and check. Since all values of y are valid, the range is:

all real numbers

Interval notation: (-∞,∞)

all negative numbers and positive numbers (all real numbers)

Set-Builder Notation: {x | x ∈ R }

:Done

3 0

2 years ago

Two people are standing on opposite sides of a hill. Person A makes an angle of elevation of 65° with the top of the hill and pe

8090 [49]

Answer:

Option 3. 71 ft. is the distance between B and top of the hill.

Step-by-step explanation:

Let the height of the hill is h ft and the distance of A from the hill be x ft and distance from B to hill is y.

It is given distance between A and B is 45 ft. ∠BAO = 65° and ∠ABO = 80°.

We have to find the distance of B from the top of the hill.

Now from ΔACO $tan 65 = \frac{h}{45-x} = 2.14$

$h=2.14(45-x)$

From ΔBCO $tan80 = \frac{h}{x} = 5.67$

h = 5.67x

Now h = 5.67x = 2.14(45-x)

5.67x = 96.3 - 2.14x

2.14x + 5.67x = 96.3

7.81x = 96.3

x = 96.3/7.81 = 12.33 ft

Therefore $cos80 = \frac{x}{OB}$

$0.174 = \frac{12.33}{OB}$

$OB = \frac{12.33}{.174}=70.86=71ft.$

Therefore 71 ft is the distance between B and the top of the hill.

3 0

3 years ago

Needdd hellpppppssssssss

Ratling [72]

Answer:

Choice number one:

$\displaystyle \frac{5}{10}\cdot \frac{4}{9}$ .

Step-by-step explanation:

Let $A$ be the event that the number on the first card is even.
Let $B$ be the event that the number on the second card is even.

The question is asking for the possibility that event $A$ and $B$ happen at the same time. However, whether $A$ occurs or not will influence the probability of $B$ . In other words, $A$ and $B$ are not independent. The probability that both $A$ and $B$ occur needs to be found as the product of

the probability that event $A$ occurs, and
the probability that event $B$ occurs given that event $A$ occurs.

5 out of the ten numbers are even. The probability that event $A$ occurs is:

$\displaystyle P(A) = \frac{5}{10}$ .

In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:

$\displaystyle P(B|A) = \frac{4}{9}$ .