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Alex Ar [27]
3 years ago
12

Select and use the most direct method to solve 2x(x + 1.5) = -1. Describe and justify the methods you used to solve the quadrati

c equation
Mathematics
1 answer:
miskamm [114]3 years ago
5 0

Step-by-step explanation:

Given that,

A quadratic equation,

2x(x + 1.5) = -1

We need to solve the quadratic equation. Firstly we need to simplify the above equation to form it as ax^2+bx+c=0.

So,

2x^2+3x=-1\\\\2x^2+3x+1=0

Here, a = 2, b = 3 and c = 1

The roots of the given equation can be given by :

x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}

Putting all the values we get :

x=\dfrac{-b\pm \sqrt{b^2+4ac} }{2a}, \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\x=\dfrac{-3\pm \sqrt{3^2+4(2)(1)} }{2(2)}, \dfrac{-3\pm \sqrt{3^2-4(2)(1)} }{2(2)}\\\\x=\dfrac{-3+1}{4}, \dfrac{-3-1}{4}\\\\x=-\dfrac{1}{2}, -1

So, the roots of the given equation is -1/2 and -1.

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Answer:

20.26832436,-17.26832437

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3 years ago
How can you determine the difference between an arithmetic and geometric sequence if you are given the first 4 terms of the sequ
Bess [88]
Compute successive differences of the terms.

If they are all the same, the sequence is arithmetic and the common difference is the difference you have found.

If successive pairs of differences have the same ratio, the sequence is geometric and the common ratio is the ratio you have determined.


Example of arithmetic sequence:
  1, 3, 5, 7
Successive differences are 3-1 = 2, 5-3 = 2, 7-5 = 2. All the differences are 2, which is the common difference of the sequence.

Example of geometric sequence:
  1, -3, 9, -27
Successive differences are -3-1 = -4, 9-(-3) = 12, -27-9 = -36. These are not the same, so the sequence is not arithmetic. Ratios of successive pairs of differences are 12/-4 = -3, -36/12 = -3. These are the same, so the sequence is geometric with common ratio -3.
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3 years ago
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There are 25 computers in a math lab. There are 6 activity books for every 2 computers in the math lab. How many activity bookle
kondaur [170]

Answer:

b

Step-by-step explanation:

6 0
3 years ago
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A hockey season ticket holder pays $88.56 for her tickets plus $5.00 for a program each game. A second person pays $19.76 for a
Aleksandr-060686 [28]

Answer: x = 6

Step-by-step explanation: If you take 88.56 + 5x = 19.76x, an equation, you should first rearrange the variables to the left side of the equation: 5x - 19.76x = -88.56.

Next, you should combine your like terms. So, -14.76 = -88.56.

Then, divide both sides of the equation by the coefficient of variable. So, x = -88.56 / -14.76./

Lastly, calculate. Determine the sign for multiplication or division, so x = 88.56 / 14.76. Multiply both the numerator and denominator with the same integer. So, x = 8856 / 1476. Cross out the common factor, then you get your answer of x = 6

5 0
2 years ago
The ratio of boys to girls in a group is 5:3. If there are 18 more boys than girls, work out how
zmey [24]
<h3>Answer:  72 people total</h3>

45 boys, 27 girls

============================================================

Explanation:

g = number of girls

g+18 = number of boys, since there are 18 more boys than girls

For example, if g = 7, then g+18 = 7+18 = 25. In this example, we have 7 girls and 25 boys. The problem with this example is the ratio of boys to girls is 25:7 which is not equal to 5:3

We could use trial and error until we land on the solution, or we can use algebra as shown in the next section.

-------------------

The ratio of boys to girls is 5:3, meaning

(number of boys)/(number of girls) = 5/3

which turns into

(g+18)/g = 5/3

after we make the proper substitutions

Let's solve for g

(g+18)/g = 5/3

3(g+18) = 5g

3g+54 = 5g

54 = 5g-3g

54 = 2g

2g = 54

g = 54/2

g = 27

There are 27 girls.

This leads to,

g+18 = 27+18 = 45

So there are 45 boys

In total, we have 27+45 = 72 people

-----------------------------

Checking the answer:

The claim is that 45/27 is the same as 5/3

For now assume that claim is true. Set the fractions equal to each other and use cross multiplication like so

45/27 = 5/3

45*3 = 27*5

135 = 135

The third equation has the same thing on both sides, so it's a true equation. This must mean the first equation is true as well. Therefore, 45:27 and 5:3 are the same ratio and the answer is confirmed.

You could also use your calculator to note that

45/27 = 1.667

5/3 = 1.667

both decimal values are approximate.

8 0
3 years ago
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