All categories

2 years ago

What is the solution to the following equation 2x^2-3x 2=0?

1 answer:

8 0

Here you have a quadratic equation with one unknown variable (x). Since the equation is set equal to 0, we solve for it by factoring the left hand side of the equation and then apply the zero product property to solve for the unknown variable (x).

Factoring: 2x2 + 3x - 2 = 0

(2x - 1)(x + 2) = 0

Zero product property: (2x - 1)(x + 2) = 0

2x - 1 = 0 AND x + 2 = 0

+ 1 + 1 - 2 - 2

______________ _______________

2x = 1 x = -2

(2x) / 2 = (1) / 2

x = 1/2

Thus, the solution to this equation is: x = 1/2 and x = -2

You might be interested in

Match the real-world descriptions with the features they represent within the context of Melissa’s garden. Not all tiles will be

Leni [432]

Length of the tomato patch is 0

6 0

2 years ago

Quadrilateral WXYZ is on a coordinate plane. Segment XY is on the line x − 3y = −12, and segment WZ is on the x − 3y = −6. Which

Nostrana [21]

Answer:

Equation shown

Step-by-step explanation:

Eq(1): x-3y=-12

X=-12+3y

=-4+y

Eq(2): x-3y=-6

X=-6+3y

=-2+y

4 0

2 years ago

Read 2 more answers

If a hurricane was headed your way, would you evacuate? The headline of a press release states, "Thirty-four Percent of People o

IgorC [24]

Answer:

The 98% confidence interval would be given by (0.326;0.354)

Step-by-step explanation:

1) Notation and definitions

$X=63$ number of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

$n=6138$ random sample taken

$\hat p=0.34$ estimated proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

$p$ true population proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

2) Confidence interval

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by $\alpha=1-0.98=0.02$ and $\alpha/2 =0.01$ . And the critical value would be given by: