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Sonja [21]
2 years ago
9

Solve equation by using the quadratic formula.

Mathematics
1 answer:
Sati [7]2 years ago
5 0

Answer: 1:  x=3, x=1

2:  x= -5

3:  There are 2 real solutions.

4:  There are 2 real solutions.

5:  There are no real solutions.

6.  There is 1 real solution.

7.  

8.  x= -6, x = -2

9.  x = -1/6, x=1

10.  

Explanation:

1.  The quadratic formula is

Substituting our known information we have:

2.  Rewriting the quadratic in standard form we have x²+10x-25=0. Substituting this into the quadratic formula gives us:

3.  The discriminant is b²-4ac.  For this problem, that is 20²-4(-4)(25)=400--400=800.  Since this is greater than 0, there are 2 real solutions.

4.  The discriminant in this problem is 7²-4(2)(-15)=49--120=49+120=169.  This is greater than 0, so there are 2 real solutions.

5.  The discriminant in this problem is 1²-4(-2)(-28)=1-224=-223.  Since this is less than 0, there are no real solutions.

6.  If the discriminant of a quadratic is 0, then by definition there is 1 real solution.

7.  Rewriting the quadratic we have 3x²-4x-2=0.  Using the quadratic formula we have:

8.  Factoring this trinomial we want factors of 12 that sum to 8.  6*2 = 12 and 6+2=8, so those are our factors.  This gives us:

(x+6)(x+2)=0

Using the zero product property we know that either x+6=0 or x+2=0.  Solving these equations we get x= -6 or x= -2.

9.  Factoring this trinomial we want factors of 6(-1)=-6 that sum to -5.  (-6)(1)=-6 and -6+1=-5, so this is how we "split up" the x term:

6x²-6x+1x-1=0

We group together the first two and the last two terms:

(6x²-6x)+(1x-1)=0

Factor the GCF out of each group.  In the first group, that is 6x:

6x(x-1)+(1x-1)=0

In the second group, the GCF is 1:

6x(x-1)+1(x-1)=0

Both terms have a factor of (x-1), so we can factor it out:

(x-1)(6x+1)=0

Using the zero product property, we know either x-1=0 or 6x+1=0.  Solving these equations we get x=1 or x=-1/6.

10.  Substituting our information into the quadratic formula we get:

Step-by-step explanation:

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fiasKO [112]

Answer:

1. $686.94

2. $735.03

3. $10707.55

4. $17631.94

5. $19635.72

Step-by-step explanation:

1st Question:

The interest rate is 7% for each year. This means that each year the person has to pay 7% more than the previous amount. So we need to multiply the initial amount by (0.07+1=1.07) in order to get the interest for the first year. if we want to find the second year's interests then we will have to multiply 2 (1.07)'s and so on.

in this case our function is: 600*(1.07)^t=P(t)

when t=2 P(2)=600*(1.07)^2=$686.94

2nd Question:

Function: 600*(1.07)^t=P(t)

when t=3 P(3)=600*(1.07)^3=$735.03

3rd Question:

initial value=$8500

1+0.08=1.08

Function: 8500*(1.08)^t=P(t)

t=3

P(3)=8500*(1.08)^3=$10707.55

4th Question:

initial value=$12000

1+1.08=1.08

t=5

Function: P(t)=12000*(1.08)^t

P(5)=12000*(1.08)^5=$17631.94

5th Question:

Function: 14000*(1.07)^t=P(t)

P(5)=14000*(1.07)^5

P(5)=$19635.72

4 0
2 years ago
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