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3 years ago

What are the solutions to the equationx^2+14x=-130please do a step by step

Mathematics

1 answer:

Serjik [45]3 years ago

5 0

Answer:

The answer to your question is: x1 = - 7 + 9i x2 = -7 - 9i

Step-by-step explanation:

x² + 14x = - 130

x² + 14x + (7)² = -130 + (7)²

(x + 7)² = -81

x + 7 = ± √-81

i² = -1, then x + 7 = ±√ 81i²

x + 7 = ± 9i

x1 = -7 + 9i x2 = -7 - 9i

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Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

3 years ago

Write the equation of the circle whose center is (-5, -8) with diameter 12

lora16 [44]

Answer:

(x + 5)^2 + (y + 8)^2 = 6^2

Step-by-step explanation:

A circle formula: (x - h)^2 + (y - k)^2 = r^2

We are given diameter. To find the radius divide diameter by 2.

d = 12

12/2 = r = 6

H and K are given to be (-5 , -8)

(x - (-5))^2 + (y - (-8))^2 = 6^2

(x + 5)^2 + (y + 8)^2 = 6^2

I have plot this equation to confirm my answer is correct where the origin is (-5 , -8) and has a radius of 6.

3 0

1 year ago

I will give brainliest!

artcher [175]

1.2 which is 6/5 in fraction form

5 0

2 years ago

Read 2 more answers

The ratio of rabbits to guinea pigs in a shop is 2:7. The ratio of brown rabbits to grey rabbits is 2:3.What fraction of the ani

Arturiano [62]

Answer: 2/15
Explanation: 2/9 x 3/5 then simplify it

8 0

3 years ago

Diegos uncle sells computers. In addition to his wages, he gets paid 20% of the amount he sells

Ivahew [28]

Answer:

Answer:

Diego's uncle earned $600 because he told $3000 worth of computers.

Step-by-step explanation:

100% divided by 20% = 5

$600 x 5 = $3000

I hope this helps!

Step-by-step explanation:

4 0

2 years ago