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3 years ago

The difference of the square of a number and 18 is equal to 3 times that number. Find the positive solution.

Mathematics

2 answers:

taurus [48]3 years ago

4 0

Ilya [14]3 years ago

3 0

Answer: x=6 or x=-3

Step-by-step explanation:

x^2-18=3x

x^2-3x-18=0

(x-6)*(x+3)=0

x-6=0 x+3=0

x=6 x=-3

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3 years ago

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2 years ago

A building makes a 90° angle with the ground. A ladder leans against the building, making a 110° exterior angle with the ground.

liberstina [14]

Answer:

A building makes a $90^{\circ}$ angle with the ground .The two interior angles are $70^{\circ}$ and $20^{\circ}$

Solution:

Given, a ladder which is against the building wall makes an exterior angle of $110^{\circ}$

And building makes a $90^{\circ}$ angle with the ground.

So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.

Now, we know that, sum of exterior angles and interior angles equals to $180^{\circ}$

Here, in the case of ground and ladder, exterior angle is $110^{\circ}$ and interior angle is unknown.

Exterior angle + interior angle = 180

110 + interior angle = 180

Interior angle = 180 – 110

Interior angle = $70^{\circ}$

We have found one of the two interior angles of right angle triangle.

We know that, sum of angles in a triangle is 180 degree

Known Interior angle + unknown interior angle + right angle = 180

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Unknown interior angle = 180 - 160

Unknown interior angle = $20^{\circ}$

Hence the two interior angles are $70^{\circ}$ and $20^{\circ}$

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3 years ago