All categories

3 years ago

You can use the _______ of a quadratic equation to determine the number and type of solutions

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

7 0

Answer: Discriminant.

Step-by-step explanation:

1. The quadratic formula is:

$x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}$

2. And the discriminant is inside the square root:

$b^{2}-4ac$

2. Then, if the discriminant is negative, the quadratic equation does not have real solutions, it has two imaginary solutions. If the discriminant is zero the quadratic has one solution. If the discriminant is positive, the quadratic equation has two distinct solutions.

You might be interested in

Would love some help

natali 33 [55]

<h3>Answer: 90 cubic meters</h3>

Each triangle has a base of 10 and height of 3.6

area of triangle = 0.5*base*height = 0.5*10*3.6 = 18 square meters

multiply this with the height of the prism (5 meters) to get 18*5 = 90 cubic meters. I'm using the idea that,

volume of prism = (area of base face)*(height of prism)

The notation "m^3" is shorthand for "cubic meters"

We do not use the other dimensions of 9 m and 7 m.

7 0

3 years ago

Ad libitum [116K]

The transformation of a function may involve any change. The correct option is D.

<h3>How does the transformation of a function happen?</h3>

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

Up by d units: y = f(x) + d
Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k \times f(x)
Horizontal stretch by a factor k: y = f(\dfrac{x}{k})

Given the function f(x)=2ˣ, while the h(x)=-3(2ˣ), therefore, the function f(x) is a reflection and a translation of a function. Hence, the correct option is D.

Learn more about Transforming functions:

brainly.com/question/17006186

#SPJ1

4 0

2 years ago

It takes a ball an average of 0.09 seconds to knock down 4 dominoes, how long will it take to knock down 8 dominoes?

Elina [12.6K]

Answer: 0.18 seconds
step by step explanation: if it takes 0.09 seconds to knock down 4 dominoes, and you are trying to find out how long it will take to knock down 8 dominoes, you can see that 8/4=2, so you need to multiply 0.09 times 2 to get your answer, which is 0.18 seconds.

4 0

3 years ago

Statements that are true for a cylinder with radius r and height h.

vampirchik [111]

Answer:

Only the second and third statements are correct:

Doubling <em>r</em> quadruples the volume.

Doubling <em>h</em> doubles the volume.

Step-by-step explanation:

The volume of a cylinder is given by:

$\displaystyle V=\pi r^2h$

We can go through each statement and examine its validity.

Statement 1)

If the radius is doubled, our new radius is now 2<em>r</em>. Hence, our volume is:

$\displaystyle V=\pi (2r)^2h=4\pi r^2h$

So, compared to the old volume, the new volume is quadrupled the original volume.

Statement 1 is not correct.

Statement 2)

Using the previous reasonsing, Statement 2 is correct.

Statement 3)

If the height is doubled, our new height is now 2<em>h</em>. Hence, our volume is:

$V=\pi r^2(2h)=2\pi r^2h$

So, compared to the old volume, the new volume has been doubled.

Statement 3 is correct.

Statement 4)

Statement 4 is not correct using the previous reasonsing.

Statement 5)

Doubling the radius results in 2<em>r</em> and doubling the height results in 2<em>h</em>. Hence, the new volume is:

$V=\pi (2r)^2(2h)=\pi (4r^2)(2h)=8\pi r^2h$

So, compared to the old volume, the new volume is increased by eight-fold.

Statement 5 is not correct.

7 0

3 years ago

Kathy swam 3 laps in the pool this week. She must swim more than 12 laps.

Marysya12 [62]

Answer:10

Step-by-step explanation:

7 0

3 years ago