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3 years ago

the perimeter of triangle ABC is 54. the triangle has side lengths AB =3×,BC=4×,and AC=5× find the length of each side

1 answer:

6 0

Firstly setup an equation to find the perimeter:

3x + 4x + 5x = 54, this is because perimeter is equal to sum of all side lengths

Then combine like terms:
12x = 54

Now use the division property of equality by dividing both sides by 12:
x = 4.5

So then, you will substitute the value of x for each value of the side lengths:
3(4.5) = 13.5 for AB, 4(4.5) = 18 for BC, and 5(4.5) = 22.5 for AC.

Hope this helps and let me know if you have any more questions!

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Answer:

$\frac{5}{ {x}^{2} + 7x - 30}$

Step-by-step explanation:

We can write a rational function.

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2 years ago

The equation of a circle is (x + 6)^2 + (y - 4)^2 = 16. The point (-6, 8) is on the circle.

pantera1 [17]

Answer:

y = 8 is the equation of tangent.

Step-by-step explanation:

The equation of the tangent to the circle at (-6,8) is of the form:

y = mx + c

where m is the slope of the tangent and c is the y-intercept.

The point (-6,8) lies on the circle and the tangent line as well.

Hence (-6,8) satisfies the line equation:

8 = m(-6) + c ⇒ c-6m = 8 -------------1

We know that slope of two perpendicular lines are related as:

$m_{1}\times m_{2}=-1$

At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.

Hence :

$m_{normal} \times m_{tangent}=-1$

We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{8-4}{-6+6}$

= ∞

Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0

Hence m=0

Putting m=0 in equation 1 we get:

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The equation of tangent line at (-6,8) is:

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3 years ago