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Soloha48 [4]
3 years ago
6

Consider the quadratic function f(x)=2x^2-8x-10

Mathematics
1 answer:
Slav-nsk [51]3 years ago
6 0

Answer:

f(x) = 2x² - 8x - 10.

This is a parabola open upward (since a>0) with an axis of symmetry = -b/2a:

a) axis of symmetry: x = -(-8)/(2*2) = 8/4 = 2. Then x = 2, which is the x component of the vertex

b) for x =  2, f(x) = f(2) = - 18 (component of y of the vertex)

c) VERTEX(2, - 18)

d) DISCRIMINENT: b² - 4.a.c = 64 - 4*2*(-10) = 144

Hope this helps! :)

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Plot triangle ABC on graph paper with points A(2,2). B(-2, -2) and C(8, -2).
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Answer:

  a) The new triangle is a reflection of the original across the origin. All angles, segment lengths, and line slopes have been preserved: the transformed triangle is congruent with the original.

  b) The new triangle is a reflection of the original across the origin and a dilation by a factor of 2. Angles have been preserved: the transformed triangle is similar to the original. The transformation is NOT rigid.

Step-by-step explanation:

1. The transformed triangle is blue in the attachment. It is congruent with the original. The transformation is "rigid," a reflection across the origin. All angles and lengths have been preserved, as well as line slopes.

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2. The transformed triangle is orange in the attachment. It is similar to the original, in that angles have been preserved and lengths are proportional. It is a reflection across the origin and a dilation by a factor of 2. Line slopes have also been preserved. A dilation is NOT a "rigid" transformation.

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Step-by-step explanation:

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If f(x)=3^2 and g(x)=4x^3+1 , what is the degree of (f*g)(x)?
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Question included in the image - geometry problem.
iren [92.7K]

Answer:

y = 116°

Step-by-step explanation:

Given that <em>L₁ </em>|| <em>L</em>₂:

The <u>exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite and non-adjacent remote interior angles.  

Also, ∠y° and ∠2x° are <u>same-side interior angles</u> formed by the intersection of the <em>hypotenuse</em> of the triangle that acts as a transversal to the parallel lines, <em>L₁ </em>and <em>L</em>₂.  Given that ∠y° and ∠2x° are <u>same-side interior angles</u>, then it means that they are the supplements of each other, such that the sum of their measures is 180°.  

Now that we have established these definitions, we can proceed with the solution.

<u>Equation 1</u>:  ∠y° + ∠2x° = 180° ⇒ Same-side interior angles

<u>Equation 2</u>:  ∠y° =  ∠x° + ∠84°  ⇒ exterior angle theorem

Substitute the value of m∠y° from Equation 2 into Equation 1 to solve for the value of x:

∠y° + ∠2x° = 180°

∠x° +  ∠84° + 2x° = 180°

Combine like terms:

∠3x° + ∠84° = 180°

Subtract ∠84° from both sides:

∠3x° + ∠84° - ∠84° = 180° -∠84°

∠3x° = 180° - ∠84°

∠3x° = 96°

Divide both sides by 3 to solve for x:

\frac{3x}{3} = \frac{96}{3}

∠x° = 32°

Substitute the value of x into Equation 2 to solve for y:

∠y° =  ∠x° + ∠84°

∠y° =  ∠32° + ∠84°

∠y° =  116°

Verify whether the values for x and y are correct by substituting their values into Equation 1 and 2:

<h3>Equation 1:</h3>

∠y° + ∠2x° = 180°

116° + 2(32)° = 180°

116° + 64° = 180°

180° = 180° (True statement).

<h3>Equation 2:</h3>

∠y° =  ∠x° + ∠84°

116° = 32° + 84°

116°  = 116°  (True statement)

Therefore, the correct answer is: y = 116°.

5 0
2 years ago
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