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3 years ago

What is the solution of quadratic system of equations ?

Mathematics

1 answer:

kobusy [5.1K]3 years ago

8 0

Answer:

(- 1, 1) and (- 5, - 35)

Step-by-step explanation:

since both equations express y in terms of x, equate the right sides

x² + 15x + 15 = - x² + 3x + 5 ( subtract - x² + 3x + 5 from both sides )

2x² + 12x + 10 = 0 ( divide all terms by 2 )

x² + 6x + 5 = 0 ← in standard form

(x + 1)(x + 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 5 = 0 ⇒ x = - 5

substitute these values into either of the 2 equations and solve for y

x = - 1 : y = (- 1)² + 15(- 1) + 15 = 1 - 15 + 15 = 1 ⇒ (- 1, 1 )

x = - 5 : y = (- 5)² + 15(- 5) + 15 = 25 - 75 + 15 = - 35 ⇒ (- 5, - 35 )

None of the given options

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2 years ago

Please see the picture and answer what does a= b=

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3 years ago

Whats its the result Of 25099.506/4.45?

777dan777 [17]

$\dfrac{25099.506}{4.45} \ \text{Divide}$

Shift the decimal points of both 25099.506 and 4.45 to the right by 2 decimal places.

(This is needed to convert 4.45 to 445, since long division must divide by a whole number.)

$\text{Set up the long division.}
$

$\text{Calculate 2509 divided by 445, which is 5 with a remainder of 284.}$

 $\text{ Bring down 9, so that 2849 is large enough to be divided by 445.}$

$\text{Calculate 2849 divided by 445, which is 6 with a remainder of 179.} 
$

$\text{Bring down 5, so that 1795 is large enough to be divided by 445.}$

$\text{Calculate 1795 divided by 445, which is 4 with a remainder of 15.}$

$\text{Bring down 06, so that 1506 is large enough to be divided by 445.
}$

$\text{Calculate 1506 divided by 445, which is 3 with a remainder of 171.}$

$\text{Bring down 0, so that 1710 is large enough to be divided by 445.}$

$\text{Calculate 1710 divided by 445, which is 3 with a remainder of 375.}$

$\text{Bring down 0, so that 3750 is large enough to be divided by 445.}$

$\text{Calculate 3750 divided by 445, which is 8 with a remainder of 190.}$

$\text{Bring down 0, so that 1900 is large enough to be divided by 445.}$

$\text{Calculate 1900 divided by 445, which is 4 with a remainder of 120.}$

$\text{Bring down 0, so that 1200 is large enough to be divided by 445.}$

$\text{Calculate 1200 divided by 445, which is 2 with a remainder of 310.}$

Therefore, 25099.506 ÷ 4.45 ≈ 5640.33842

8 0

3 years ago

A random sample of 25 statistics examinations was selected. The average score in the sample was 76 with a variance of 144. Assum

Mazyrski [523]

Answer:

99% confidence interval for the population average examination score is between a lower limit of 69.2872 and an upper limit of 82.7128.

Step-by-step explanation:

Confidence interval = mean +/- margin of error (E)

mean = 76

variance = 144

sd = sqrt(variance) = sqrt(144) = 12

n = 25

degree of freedom (df) = n - 1 = 25 - 1 = 24

confidence level (C) = 99% = 0.99

significance level = 1 - C = 1 - 0.99 = 0.01 = 1%

t-value corresponding to 24 df and 1% significance level is 2.797

E = t×sd/√n = 2.797×12/√25 = 6.7128

Lower limit = mean - E = 76 - 6.7128 = 69.2872

Upper limit = mean + E = 76 + 6.7128 = 82.7128

99% confidence interval is (69.2872, 82.7128)

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3 years ago

I have 2 questions.

frosja888 [35]

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3 years ago

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