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Viktor [21]
3 years ago
12

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

Mathematics
1 answer:
natulia [17]3 years ago
7 0

Answer:

8\ units< x < 18\ units

Step-by-step explanation:

we know that

The <u>Triangle Inequality Theorem</u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Applying the Theorem

case 1) 42+4x > 2x-6

4x-2x > -6-42

2x > -48

x > -24\ units

case 2) 42+(2x-6) >4x

42-6 >4x-2x

36 >2x

18 >x -----> rewrite

x

case 3) 4x+(2x-6) > 42

4x+2x > 42+6

6x > 48

x > 8\ units

therefore

8\ units< x < 18\ units

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ANSWER

g(f( - 1)) = \frac{1}{5 }

EXPLANATION

The given function is:

f(x) =  {x}^{2}

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g(f( - 1)) = \frac{1}{2{( - 1)}^{2} + 3 }

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Jenna drew irregular quadrilateral ABCD inscribed in circle P. She knows that: m∠3=2⋅m∠1, and m∠2=2⋅m∠4, and m∠2+m∠3=360°. What
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Answer:

The generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

Step-by-step explanation:

We are given the following from what she knows

m∠3=2⋅m∠1... 1

m∠2=2⋅m∠4 ... 2

m∠2+m∠3=360 ... 3

From what is given, we can substitute equation 1 and 2 into equation 3 as shown:

From 3:

m∠2+m∠3=360

Substituting 1 and 2 we will have:

2⋅m∠4 + 2⋅m∠1 = 360

Factor out 2 from the left hand side of the equation

2(m∠4+m∠1) = 360

Divide both sides by 2

2(m∠4+m∠1)/2 = 360/2

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Since the sum of two supplementary angles is 180°, hence the generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

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Step-by-step explanation:

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