All categories

3 years ago

Solve the following equation by completing the square. 1/4x^2+x+1/4=0

Mathematics

1 answer:

fenix001 [56]3 years ago

8 0

Answer:

D. X=-2+sqrt(3) or -2-sqrt(3)

$x_{1} =-2+\sqrt{3} \\x_{2} =-2-\sqrt{3}$

Step-by-step explanation:

Quadratic Equation given:

$\frac{1}{4} x^2+x+\frac{1}{4}=0$

In order to get rid of the fractions, multiply both sides by 4.

$\frac{1}{4}x^2\cdot \:4+x\cdot \:4+\frac{1}{4}\cdot \:4=0\cdot \:4$

We get:

$x^2+4x+1=0$

$x^2+4x+4-4+1=0$

Completing the square:

$(x+2)^2-4+1=0\\$

$(x+2)^2-3=0$

$(x+2)^2=3$

$x+2=\pm\sqrt{3}$

$x=-2\pm\sqrt{3}$

$x_{1} =-2+\sqrt{3} \\x_{2} =-2-\sqrt{3}$

You might be interested in

I think of a number times it by 2 and minus 2 my answer is nine

Vikki [24]

Answer:

5.5

Step-by-step explanation:

5.5 times 2 equals 11 minus 2 equals 9

4 0

2 years ago

Read 2 more answers

The principal of Fremont High School is putting together a table that lists student attendance at four types of events held at t

Ghella [55]

Answer:

Step-by-step explanation:

The answer is 2050

5 0

3 years ago

If the endpoints of the diameter of a circle are (10, 12) and (0, 2), what is the standard form equation of the circle? A) (x +

attashe74 [19]

So the equation of a circle is (x - h)² + (y - k)² = r² where (h,k) are the coordinates of the center of the circle and r is the radius. The diameter of a circle is a line that goes from one point of the circle to the other through the center of the circle. Well the center would be midway through the diameter so use midpoint formula to find the center which is (h,k) Mid point formula is both given x's added together divided by 2 for h and both y coordinates added together divided by 2 to find k
(10+0)/2
10/2= 5
(12+2)/2
14/2 = 7
so the center of the circle is (5,7) now use distance formula using the center and one of the points to the radius
√((5-10)²+(7-12)²)
√(-5²+ -5²)
√(25 + 25)
√50 is the radius
Now plug all found information into circle equation
(x-5)² + (y-7)² =50 note the end is 50 because the circle equation is radius squared and since the radius is √50, radius² is 50.
Answer is c

8 0

4 years ago

Read 2 more answers

Solve the system using substitution. 5x-y=73 and 2y=x

galina1969 [7]

Answer:

Point form:( $\frac{146}{9} \\\\$ , $\frac{73}{9}$ )

Equation form: x= $\frac{146}{9}$ , y= $\frac{73}{9}$

Step-by-step explanation:

Plz mark brainliest.

7 0

3 years ago

A pharmacist receives a shipment of 21 bottles of a drug and has three of the bottles tested. If five of the 21 bottles are cont

blagie [28]

Answer:

The probability is 0.8722

Step-by-step explanation:

There are 21 bottles

5 of them are contaminated.

there are 21 - 5 = 16 non-contaminated bottles.

So, if we grab a bottle at random, the probability that this bottle is contaminated will be equal to the quotient between the number of contaminated bottles and the total number of bottles, this is:

p = 5/21

Now we want to find the probability that, for 3 tested bottles, that less than two (0 or 1 ) are contaminated.

Let's see each case on its own.

0 bottles:

The probability of getting a non-contaminated bottle in the first try is equal to the quotient between the number of non-contaminated bottles and the total number of bottles, this is:

p₁ = 16/21

For the second bottle is the same, but because one non-contaminated bottle was drawn before, now there are 15 non-contaminated bottles and 20 bottles in total, so now the probability is:

p₂ = 15/20

and similarly, for the third bottle the probability is:

p₃ = 14/19

The joint probability is the product of the individual probabilities, we get:

P = p₁*p₂*p₃ = (16/21)*(15/20)*(14/19) = 0.4211

Now the case that one bottle is contaminated.

Let's assume that the first one is contaminated.

The probability of getting a contaminated bottle in the first draw is equal to the quotient between the number of contaminated bottles and the total number of bottles, so:

p₁ = 5/21

For the second bottle, we want a non-contaminated one, there are 16 non-contaminated bottles and 20 bottles left, so here the probability is:

p₂ = 16/20

and for the third bottle we have the probability:

p₃ = 15/19

The joint probability is:

p = p₁*p₂*p₃ = (5/21)*(16/20)*(15/19)

Also notice that we only looked at the case where the first bottle is contaminated, we also have the case where the second one is contaminated and the case where the third one is contaminated, so there are 3 permutations, then the probability of having one contaminated bottle is:

Q = 3*p = 3*(5/21)*(16/20)*(15/19) = 0.4511

Then the probability of having less than two contaminated bottles is:

probability = P + Q = 0.4211 + 0.4511 = 0.8722

8 0

3 years ago