TWO MOVES TO FIT IN THE CLEAR SHAPE

Which statement about the following equation is true? 2x2-9x+2-1

Furkat [3]

Complete Question:

Which statement about the following equation is true?

$2x^2-9x+2 = -1$

A) The discriminant is less than 0, so there are two real roots

B) The discriminant is less than 0, so there are two complex roots

C) The discriminant is greater than 0, so there are two real roots

D) The discriminant is greater than 0, so there are two complex roots

Answer:

C) The discriminant is greater than 0, so there are two real roots

Step-by-step explanation:

The given equation is $2x^2-9x+2 = -1$ which by simplification becomes

$2x^2 - 9x + 3 = 0$

For a quadratic equation of the form $ax^2 + bx + c = 0$ , the discriminant is given by the equation, $D = b^2 - 4ac$

If the discriminant D is greater than 0, the roots are real and different

If the discriminant D is equal to 0, the roots are real and equal

If the discriminant D is less than 0, the roots are imaginary

For the quadratic equation under consideration, a = 2, b = -9, c = 3

Let us calculate the discriminant D

D = (-9)² - 4(2)(3)

D = 81 - 24

D = 57

Since the Discriminant D is greater than 0, the roots are real and different.

3 0

3 years ago

During the grand opening of the T-Shirt Shack at the Madera County Emu Farm, four of the emus broke through the fence and attack

Irina-Kira [14]

Given :

p = 0.68

margin of error, E = 0.1

99% confident interval

alpha, α = 1 - 0.99

= 0.01

$\frac{\alpha }{2}=\frac{0.01}{2} = 0.005$

∴ $z_{\alpha/2}=z_{0.005}=2.5758$ (z-critical value)

Sample size = $z_{\alpha/2} \times \frac{p(1-p)}{E^2}$

$=(2.5758)^2 \times 0.68 \times \frac{(1-0.68)}{0.1^2}$

$= 6.63475 \times 0.68 \times \frac{0.32}{0.01}$

= 144.37

= 145 (rounded off)

Therefore, there are 145 businesses does she need to sample to meet this criteria.

6 0

3 years ago

The water level in a lake was 22 inches below normal at the beginning of March. The water level decreased by 3 1/6 inches in Mar

Vinvika [58]

At the beginning it was 22 inches below normal (-22).
Then it decreased by 3 1/6 (-19/6).
Then increased by 1 6/7 (+13/7)

-22 - 19/6 + 13/7
-924/42 - 133/42 + 78/42
-1057/42 + 78/42
-979/42
-23 13/42

It was 23 13/42 inches below normal after April.

8 0

3 years ago

A random sample of 35 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the popul

love history [14]

Answer:

(47.3, 54.1)

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{10.4}{\sqrt{35}} = 3.4$

The lower end of the interval is the sample mean subtracted by M. So it is 50.7 - 3.4 = 47.3

The upper end of the interval is the sample mean added to M. So it is 50.7 + 3.4 = 54.1

The answer is (47.3, 54.1).

6 0

3 years ago

Someone anybody please help

babymother [125]

This is a system of equations problem that can be solved using one of three methods: graphing, substitution, or elimination. I'll be using substitution.

In substitution:
1) Solve one equation for either variable. I'll use the first equation because its easier to solve for one of the variables. I'll be solving for y because that will allow us to solve for the value of x faster.
 $x+y=60$
$y=60-x$

2) Substitute what you get into the other equation:
$20x + 5y = 600$
$20x + 5(60-x) = 600$

3) Solve your new equation in step 2 for the variable, x.
$20x + 5(60-x) = 600$
$20x + 300-5x = 600$
$15x + 300 = 600$
$15x = 300$
$x=20$

There are D) 20 $20 bills in her drawer.

3 0

3 years ago