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2 years ago

Which quadratic equation is equivalent to (x – 4)2 – (x – 4) – 6 = 0?

Mathematics

2 answers:

Viktor [21]2 years ago

5 0

I hope choices must be given in the problem.

I am showing the method to find the equivalent equation of the above equation. You can match with your given choices.

First step is to expand the first term. So,

(x-4)² = (x - 4)(x - 4) Since a²= a*a

= x² - 4x - 4x + 4 * 4 By multiplying.

= x² -8x + 16 Combine the like terms.

So, (x - 4)² - (x -4) - 6

= x² - 8x + 16 - x + 4 - 6

= x² - 9x + 14 Combine the like terms.

So, equivalent equation of the above equation is x² - 9x + 14 = 0.

katovenus [111]2 years ago

3 0

Answer:

D: u2 – u – 6 = 0 where u = (x – 4)

Step-by-step explanation:

got it right on the test

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A church spire casts a shadow on the level ground. At the tip of the shadow, the tip of the spire lies 25° upward. Walking 100 m

malfutka [58]

Answer:

The height of the spire must be 69.24 m

Step-by-step explanation:

The information given are;

The initial angle of elevation of the tip of the spire from the tip of the shadow = 25°

The angle of elevation of the tip of the spire from the tip of the shadow after moving 100 m closer = 55°

The change distance moved closer to the church spire = 100 m

Let the base angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow be 25° and ∠x°

We have;

∠x° and the 55° angle of the ray from the tip of the spire to the tip of the shadow are supplementary angles (angle on a straight line)

Therefore;

∠x° = 180° - 55° = 125°

The calculated angle 125° above, the given 25° and the angle in between the two rays from the tip of the spire to the tip of the shadows are the interior angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow

Let the angle in between the two rays from the tip of the spire to the tip of the shadows = y

Therefore;

125° + y° + 25° = 180 (Angle sum theorem)

y° = 180° - (125° + 25°) = 30°

By sin rule, we have;

100/(sin (30°)) = (The length of the initial ray from the tip of the spire to the tip of the shadow before the shift)/(sin(125°))

Let the length of the initial ray from the tip of the spire to the tip of the shadow before the shift = l

100/(sin (30°)) = l/(sin(125°))

l = (sin(125°))×100/(sin (30°)) = 163.83 m

The height of the spire, by trigonometric ratio = sin(25°) × 163.83 m = 69.24 m

The height of the spire = 69.24 m.

4 0

2 years ago

Translate the sentence into an equation. Use n for the number.

Lyrx [107]

Answer:

x-3 =27

Step-by-step explanation:

4 0

1 year ago

Read 2 more answers

in the figure below line de is parallel to line f g with a transversal AG write and solve a system of liner equation to determin

Kay [80]

The complete question in the attached figure

we know that

angle y and angle (5y-18) are supplementary angles
then
y°+(5y-18)°=180°------> 6y=180+18------> y=198/6-----> y=33°
and
angle x and angle y are also supplementary angles
then
x+y=180--------> x=180-y-----> x=180-33-----> x=147°

the answer is
x=147°
y=33°