Any number that is divisible by 3 is also divisible by 6. Find a counterexample to show that the conjecture is false

Find the discriminant, and determine the number of real solutions. then solve x^2 +8x+20=0

vodomira [7]

Answer:

Part 1) The quadratic equation has zero real solutions

Part 2) The solutions are

$x_1=-4+2i$ and $x_2=-4-2i$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

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

in this problem we have

$x^{2}+8x+20=0$

so

$a=1\\b=8\\c=20$

The discriminant is equal to

$D=(b^{2}-4ac)$

If D=0 -----> the quadratic equation has only one real solution

If D>0 -----> the quadratic equation has two real solutions

If D<0 -----> the quadratic equation has two complex solutions

Find the value of D

$D=8^{2}-4(1)(20)=-16$ -----> the quadratic equation has two complex solutions

Find out the solutions

substitute the values of a,b and c in the formula

$x=\frac{-8(+/-)\sqrt{8^{2}-4(1)(20)}} {2(1)}$

$x=\frac{-8(+/-)\sqrt{-16}} {2}$

Remember that

$i=\sqrt{-1}$

$x=\frac{-8(+/-)4i} {2}$

$x_1=\frac{-8(+)4i} {2}=-4+2i$

$x_2=\frac{-8(-)4i} {2}=-4-2i$

8 0

4 years ago

140 is 9% of what???

Len [333]

Answer:

The correct answer is B) 1555.6

Step-by-step explanation:

In order to find this, we must divide the part by the percentage. This will give us the total out of 100%

140/.09 = 1555.6

7 0

3 years ago

What is the circumference of a circle with radius 3 cm to the nearest hundredth

Ksju [112]

Answer:

see below

Step-by-step explanation:

The circumference of a circle is given by

C = 2*pi*r

C = 2* pi *3

C = 6 pi

The value depends on whether you use 3.14 for pi or the pi button

3.14 = 18.84

pi button 18.85

3 0

3 years ago

Read 2 more answers

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard devi

alexira [117]

Answer: 0.8490

Step-by-step explanation:

Given : The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches.

i.e. $\mu=30$ and $\sigma=0.9$

Let x denotes the lengths of aluminum-coated steel sheets.

Required Formula : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For n= 36 , the probability that the average length of a sheet is between 29.82 and 30.27 inches long will be :-

$P(29.82$

∴ Required probability = 0.8490

3 0

3 years ago

A=9,b=-24 Evaluate a +b for the given valus

aliina [53]

Step-by-step explanation:

A + b

Putting value of a and b

9 + (-24)

9 - 24

= - 15

7 0

3 years ago