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likoan [24]
3 years ago
14

*A triangle has sides 42, 4x, and 2x−6. What is the possible range of x?

Mathematics
1 answer:
scoray [572]3 years ago
3 0

Answer:

<h2>The Possible range for x is : ]8 , 18[</h2>

Step-by-step explanation:

To can draw this triangle if:

4x - (2x - 6) < 42 < 4x + (2x - 6)

solve inequality 1 :

4x - (2x - 6) < 42 ⇔ 2x + 6 < 42 ⇔ 2x < 36 ⇔ x < 18 (1)

Solve inequality 2 :

42 < 4x + (2x - 6) ⇔ 42 < 6x - 6 ⇔ 48 < 6x ⇔ 8 < x (2)

from (1) and (2) we deduce that : 8 < x < 18

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6 0
3 years ago
An object is propelled upward from the top of a 300 foot building. The path that the object takes as it falls to the ground can
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Answer:

As per the statement:

The path that the object takes as it falls to the ground can be modeled by:

h =-16t^2 + 80t + 300

where

h is the height of the objects and

t is the time (in seconds)

At t = 0 , h = 300 ft

When the objects hit the ground, h = 0

then;

-16t^2+80t+300=0

For a quadratic equation: ax^2+bx+c=0         ......[1]

the solution for the equation is given by:

x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}

On comparing the given equation with [1] we have;  

a = -16 ,b = 80 and c = 300

then;

t= \frac{-80\pm \sqrt{(80)^2-4(-16)(300)}}{2(-16)}

t= \frac{-80\pm \sqrt{6400+19200}}{-32}

t= \frac{-80\pm \sqrt{25600}}{-32}  

Simplify:

t = -\frac{5}{2} = -2.5 sec and t = \frac{15}{2} = 7.5 sec

Time can't be in negative;

therefore, the time it took the object to hit the ground is 7.5 sec

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