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Anestetic [448]
3 years ago
14

Evaluate the discriminant of the equation. Tell how many solutions each equation has and whether the solutions are real or imagi

nary.
x^2 + 4x + 5 = 0
Mathematics
2 answers:
Novay_Z [31]3 years ago
6 0

Answer to Q1:

-4

Step-by-step explanation:

The formula to find discriminant is  

D= b²-4ac

Given equation is  

x²+4x+5=0

ax²+bx+c= 0 is general quadratic equation.

comparing given equation with general quadratic equation,we get

a= 1  ,b = 4 and c= 5

putting above values in the formula to find discriminant,we get

D= (4)²-4(1)(5)

D= 16-20

D= -4

Answer to Q2

Two  solution and imaginary

Step-by-step explanation:

Given equation is

x²-4x-5=0

The formula to find discriminant is D= b²-4ac

If D < 0 , the quadratic equation has two imaginary solutions.

If D > 0, the quadratic equation has two distinct real solutions.

If D = 0 , the quadratic equation has one solution.

x²+4x+5=0 has D=-4 which is less than zero.

hence, it has two imaginary solutions.


cupoosta [38]3 years ago
4 0

Answer:

D=-4<0, the equation has no real solutions, it has two imaginary solutions.

Step-by-step explanation:

The quadratic equation x^2 +4x+5=0 has coefficients

a=1,

b=4,

c=5.

The discriminant D is the expression

D=b^2-4ac.

Hence,

D=4^2-4\cdot 1\cdot 5=16-20=-4

Since the discriminant is negative, the equation has no real solutions, it has two imaginary solutions.

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enyata [817]
#7 is A
For # 5 & 6 is there a multiplication sign between the numbers or is supposed to be a power or something else?
7 0
3 years ago
Convert 0.533333... to a fraction.<br> (only the 3 is repeating)<br><br> Please show the work!!
amm1812
<span>Let x = 0.5333333333 ...

So 100x = 53.3333333333 ...
and 10x = 5.3333333333 ...
---------------------------------
90x = 53 – 5 = 48.

So x = 48/90 = 8/15 after reduction to lowest terms (by factor of 6)
0.3333... = ⅓. and that 0.5 = ½.

So 0.533333... = 0.5 + 0.0333333...0.5 + 0.3333.../10 = 1/2 + (1/3)/10 = 1/2 + 1/30 = 16/30 = 8/15</span>
6 0
3 years ago
Find the probability that the mean annual preciptiation will be between 32 and 34 inches. variable is normally distributed
liq [111]
Supposing, for the sake of illustration, that the mean is 31.2 and the std. dev. is 1.9.

This probability can be calculated by finding z-scores and their corresponding areas under the std. normal curve.  
                                                                     34 in - 31.2 in
The area under this curve to the left of z = -------------------- = 1.47 (for 34 in)
                                                                           1.9
                                                                      32 in - 31.2 in
and that to the left of 32 in   is               z = ---------------------- = 0.421
                                                                             1.9

Know how to use a table of z-scores to find these two areas?  If not, let me know and I'll go over that with you.


My TI-83 calculator provided the following result:

normalcdf(32, 34, 31.2, 1.9) = 0.267  (answer to this sample problem)

5 0
2 years ago
14. BUS TRIP A bus leaves at 10 A.M. to take students on a field trip to a
k0ka [10]

The bus is 54.5 miles far from the site at the time of 11:30A.M as per the given information in the question.

<h3>What is the slope of a line?</h3>

The slope of a line indicates how steep it is. Slope is defined mathematically as "climb over run" (change in y divided by change in x).

It is assumed that a bus moving at a constant speed departs at 10 a.m. towards a historic location, is 100 miles away by 10:25 a.m., and is 65 miles away at 11:15 a.m.

We must create a point-slope equation that connects the distance from the place to the time in minutes after 10:00 a.m. Then, around 11:30 a.m., we need to figure out how far the bus is from the site.

A line's point-slope is y₂-y₁)=m(x₂-x₁)

Since x denotes the amount of minutes after 10:00 a.m., 10:25 a.m. is represented by x=25 and 11:15 a.m. by x=75.

At 10:25 a.m., a distance of 100 miles from the place is represented by 75.

The point represents a distance of 100 miles from the site at 10:25 a.m. The point represents a distance of 65 miles from the site at 11:15 a.m.

By substituting the points (25, 100) and (75, 65) into the slope formula and simplifying we get,

m=(y₂-y₁)/(x₂-x₁)

m=(65-100)/(75-25)

m=-35/50

m=-0.7

Now choose one of the points and substitute that point and the slope into the slope-point form

y₋y₁=m(x-x₁)

By choosing (x₁, y₁)=(25, 100)

By choosing (x₂, y₂)=(75, 65)

Since 11:30 A,M is 90 minutes after 10:00A.M

By substituting x=90 in the equation we get the value of y,

y-100= -0.7(90-25)

y-100= -0.7(65)

y-100 =-45.5

y= 54.5

Hence, the bus is 54.5 miles from the site at the time of 11:30 A.M

y-100= -0.7(x-25)

OR

y-65= -0.7(x-75)

The bus is 54.5 miles from the site at 11:30A.M.

To know more about slope of a line, visit:

brainly.com/question/28771374

#SPJ9

6 0
1 year ago
The distance traveled (d) varies directly as the time (t) of
Helen [10]

Answer:

2.70 hours to travel 180 mi.

Step-by-step explanation:

The distance traveled (d) varies directly as the time (t) of travel, by the following formula:

s = \frac{d}{t}

In which s is the velocity.

It takes 63 min to travel 70 mi.

So i am going to find the velocity in miles per minute

s = \frac{70}{63} = 1.11

how many hours would it take to travel 180 mi?

I am first going to find the time in minutes, then divide by 60 to pass to hours.

s = \frac{d}{t}

st = d

t = \frac{d}{s}

t = \frac{180}{1.11}

t = 162.16

It takes 162.16 minutes = 162.16/60 = 2.70 hours to travel 180 mi.

6 0
2 years ago
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