Select the correct answer.

Consider the quadratic equation x2 = 4x - 5. How many solutions does the equation have?

JulijaS [17]

Answer:

no real solutions
2 complex solutions

Step-by-step explanation:

The equation can be rearranged to vertex form:

x^2 -4x = -5 . . . . . . . . . subtract 4x

x^2 -4x +4 = -5 +4 . . . . add 4

(x -2)^2 = -1 . . . . . . . . . show the left side as a square

x -2 = ±√-1 = ±i . . . . . . take the square root; the right side is imaginary

x = 2 ± i . . . . . . . . . . . . . add 2. These are the complex solutions.

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<em>Comment on the question</em>

Every 2nd degree polynomial equation has two solutions. They may be real, complex, or (real and) identical. That is, there may be 0, 1, or 2 real solutions. This equation has 0 real solutions, because they are both complex.

3 0

3 years ago

Using the slope formula, find the slope of the line through the given points. (7,4) and (5,6)

anyanavicka [17]

We can use the points (7, 4) and (5, 6) to solve.

Slope formula: y2-y1/x2-x1

= 6-4/5-7

= 2/-2

= -1

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Best of Luck,

Wolfyy :)

4 0

3 years ago

A student bikes 1/4 mile to school. After school, the student bikes 1/3 mile to a cousin’s house. Finally, the student bikes 7/1

gizmo_the_mogwai [7]

The miles the student biked in two weeks is 11 2/3 miles.

The distance the student bikes is given in fractions. Fractions are numbers that are made up of numerator and denominators. An examples of a fraction is 1/4. 1 is the numerator and 4 is the denominator.

In order to determine the distance biked in 2 weeks, the distance biked in a day has to be determined.

Distance biked in a day = (1/4 + 1/3 + 7/12)

14/12 = 1 2/12 = 1 1/6

Distance he would travel in 2 weeks

1 1/6 x 10

7/6 x 10 = 70 /6 = 11 2/3 miles

To learn more about fractions, please check: brainly.com/question/848992

5 0

3 years ago

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are

jasenka [17]

Answer:

The indicated confidence interval for the difference between the two population means is (-1.5159, 7.5159)

Step-by-step explanation:

Let the drying times of type A be the first population and the drying times of type B be the second population. Then

We have small sample sizes $n_{1} = 11$ and $n_{2} = 9$ , besides $\bar{x}_{1} = 71.5$ , $s_{1} = 3.4$ , $\bar{x}_{2} = 68.5$ and $s_{2} = 3.6$ . Therefore, the pooled

estimate is given by

$s_{p}^{2} = \frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(11-1)(3.4)^{2}+(9-1)(3.6)^{2}}{11+9-2} = 12.1822$

The 99% confidence interval for the true mean difference between the mean drying time of type A and the mean drying time of type B is given by

$(\bar{x}_{1}-\bar{x}_{2})\pm t_{0.01/2}s_{p}\sqrt{\frac{1}{11}+\frac{1}{9}}$ , i.e.,

$(71.5-68.5)\pm t_{0.005}(3.4903)\sqrt{\frac{1}{11}+\frac{1}{9}}$

where $t_{0.005}$ is the 0.5th quantile of the t distribution with (11+9-2) = 18 degrees of freedom. So

$3\pm(-2.8784)(3.4903)(0.4495)$ , i.e.,

the indicated confidence interval for the difference between the two population means is (-1.5159, 7.5159)

5 0

3 years ago

The points (2, 3) and (6, 11) lie on a line. What is the slope of this line?

AveGali [126]

Answer:

8/4

Step-by-step explanation:

to do slope is y2 - y1 over x2 - x1, so it would be 11 - 3 for 8, then 6 - 2, leaving 8/4.

3 0

3 years ago