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1 year ago

Given the trinomial 5x^2-2x-3, predict the type of solutions.

Mathematics

2 answers:

pishuonlain [190]1 year ago

3 0

Consider the trinomial $5x^2-2x-3.$

1. Find the discriminant:

$D=b^2-4ac=(-2)^2-4\cdot 5\cdot (-3)=4+60=64,\\ \\\sqrt{D}=8>0.$

2. Find the roots of given trinomial:

$x_{1,2}=\dfrac{-b\pm \sqrt{D}}{2a}=\dfrac{2\pm 8}{2\cdot 5}=1,-0.6.$

3. Conclusion: given trinomial has two different real roots.

Mnenie [13.5K]1 year ago

3 0

Given: 5x^2 - 2x - 3

Using a calculator to obtain the solutions to the given trinomial, the solutions obtained are 1 and -3/5. The values 1 and -3/5 are rational and real numbers. Therefore, the type of solutions obtained are rational and real.

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Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other

const2013 [10]

Answer:

The slope of diagonal PS is -1.

The slope of diagonal QR is 1.

The midpoint of PS is (2, 2).

The midpoint of QR is (2, 2).

Perpendicular and share the same midpoint.

6 0

1 year ago

Read 2 more answers

Learning Task 3. Find the equation of the line. Do it in your notebook.

Wewaii [24]

Answer:

1) The equation of the line in slope-intercept form is $y = 5\cdot x +9$ . The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ . The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) The equation of the line in slope-intercept form is $y = 3\cdot x +4$ . The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ . The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ . The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

Step-by-step explanation:

1) We begin with the slope-intercept form and substitute all known values and calculate the y-intercept: ( $m = 5$ , $x = -1$ , $y = 4$ )

$4 = (5)\cdot (-1)+b$

$4 = -5 +b$

$b = 9$

The equation of the line in slope-intercept form is $y = 5\cdot x +9$ .

Then, we obtain the standard form by algebraic handling:

$-5\cdot x + y = 9$

The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = 3$ , $y_{1} = 4$ , $x_{2} = -2$ , $y_{2} = 2$ )

$3\cdot m + b = 4$ (Eq. 1)

$-2\cdot m + b = 2$ (Eq. 2)

From (Eq. 1), we find that:

$b = 4-3\cdot m$

And by substituting on (Eq. 2), we conclude that slope of the equation of the line is:

$-2\cdot m +4-3\cdot m = 2$

$-5\cdot m = -2$

$m = \frac{2}{5}$

And from (Eq. 1) we find that the y-Intercept is:

$b=4-3\cdot \left(\frac{2}{5} \right)$

$b = 4-\frac{6}{5}$

$b = \frac{14}{5}$

The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{2}{5}\cdot x +y = \frac{14}{5}$

$-2\cdot x +5\cdot y = 14$

The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) By using the slope-intercept form, we obtain the equation of the line by direct substitution: ( $m = 3$ , $b = 4$ )

$y = 3\cdot x +4$

The equation of the line in slope-intercept form is $y = 3\cdot x +4$ .

Then, we obtain the standard form by algebraic handling:

$-3\cdot x +y = 4$

The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -3$ , $y_{1} = 0$ , $x_{2} = 0$ , $y_{2} = 6$ )

$-3\cdot m + b = 0$ (Eq. 3)

$b = 6$ (Eq. 4)

By applying (Eq. 4) on (Eq. 3), we find that the slope of the equation of the line is:

$-3\cdot m+6 = 0$

$3\cdot m = 6$

$m = 2$

The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ .

Then, we obtain the standard form by algebraic handling:

$-2\cdot x +y = 6$

The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -1$ , $y_{1} = -2$ , $x_{2} = 5$ , $y_{2} = 3$ )

$-m+b = -2$ (Eq. 5)

$5\cdot m +b = 3$ (Eq. 6)

From (Eq. 5), we find that:

$b = -2+m$

And by substituting on (Eq. 6), we conclude that slope of the equation of the line is:

$5\cdot m -2+m = 3$

$6\cdot m = 5$

$m = \frac{5}{6}$

And from (Eq. 5) we find that the y-Intercept is:

$b = -2+\frac{5}{6}$

$b = -\frac{7}{6}$

The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{5}{6}\cdot x +y =-\frac{7}{6}$

$-5\cdot x + 6\cdot y = -7$

The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

6 0

1 year ago

It takes Engineer Kweku three hours to drive to his brother’s house at an average speed of 50 miles per hour. If He takes the sa

11Alexandr11 [23.1K]

Answer:

2.5 hours

Step-by-step explanation:

The product of speed and time is distance. If the distance is the same, then time is inversely proportional to speed. At 60/50 = 6/5 times the speed, the return trip will take 5/6 times the time:

(5/6)(3 hours) = 2.5 hours . . . time for return trip

5 0

1 year ago

A flight of stairs is supported by two columns, as shown in the diagram.

dangina [55]

Answer:

12 feet

Step-by-step explanation:

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2 years ago

Which statement describes a process to solve sqrt b+20 - sqrt b=5?

babunello [35]

Answer:

Step-by-step explanation:

The equation is:

√b+20 - √b = 5

The first step is we will add √b to both sides:

√b+20 -√b +√b = 5 +√b

√b+20 = 5+√b

Now take square at both sides:

(√b+20)^2 = (5+√b)^2

b+20 = 25+10√b+b

Now combine the like terms:

b+20-25-b=10√b

-5 = 10√b

Divide both the terms by 10

-5/10 = 10√b/10

-1/2=√b

Take square at both sides:

(-1/2)^2 = (√b)^2

1/4 = b

So in this type of question we add radical terms to both sides and square both sides twice....

7 0

1 year ago