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SSSSS [86.1K]
3 years ago
12

9/20

Mathematics
1 answer:
Stella [2.4K]3 years ago
4 0

<u>Question:</u>

Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0

<u>Answer:</u>

The number of real solutions for the equation x^{2}+5 x+7=0 is zero

<u>Solution:</u>

For a Quadratic Equation of form : a x^{2}+b x+c=0  ---- eqn 1

The solution is x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}  

Now , the given Quadratic Equation is x^{2}+5 x+7=0  ---- eqn 2

On comparing Equation (1) and Equation(2), we get

a = 1 , b = 5 and c = 7

In x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} , b^2 - 4ac is called the discriminant of the quadratic equation

Its value determines the nature of roots

Now, here are the rules with discriminants:

1) D > 0; there are 2 real solutions in the equation

2) D = 0; there is 1 real solution in the equation

3) D < 0; there are no real solutions in the equation

Now let solve for given equation

D= b^2 - 4ac\\\\D = 5^2 - 4(1)(7)\\\\D = 25 - 28 \\\\D = -3

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

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3 years ago
Use the information to solve the triangle. Round your answers to two decimal places. Hint: draw a sketch first to determine if y
Anestetic [448]

Answer:

A = 43°

b = 25.8 (3 sig. fig.)

c = 14.5 (3 sig. fig.)

Step-by-step explanation:

Using angle sum of triangle, we get A = 180 - 104 - 33 = 43°

Using sin law,

b/sin104 = 18.1/sin43

b = 25.8 (3 sig. fig.)

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7 0
3 years ago
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Step-by-step explanation:

4 0
3 years ago
Which represents where f(x) = g(x)?
son4ous [18]

Answer:

Option (1)

Step-by-step explanation:

Two functions 'f' and 'g' have been graphed in the picture attached.

Both the functions will be equal at the points where the values of these functions are equal.

Those points are the point of intersection of both the functions on the given graph.

At x = -4,

f(-4) = g(-4) = 4

At x = 0,

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Therefore, Option (1) will be the answer.

5 0
3 years ago
A chemist has one solution that is 20% alcohol and another that is 60% alcohol.
aleksley [76]

Answer:

solution 1= 40ml

solution 2= 160ml

Step-by-step explanation:

%alcohol= amount of alcohol/total solutionx100

0.52x200=104ml of alcohol present

0.2x L=0.2Lml of alcohol in solution one

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1st equation

0.2L+0.6M=104ml alcohol

times 10 to get whole

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2nd

same for this equation

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10L+10M=2000

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elimination method

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-

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M=160ml

2L+6 (160)=1040

2L=1040-960

2L=80

L=40ml

3 0
2 years ago
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