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3 years ago

find the positive value of k that would make he left side of the equation a perfect square trinomial x^2-kx+64

Mathematics

1 answer:

Nataliya [291]3 years ago

6 0

Answer: 16

Explanation:

x² - kx + 64

Since we are looking for a perfect square, then we need to take the square root of 64 to find the factors: √64 = 8

So, the factors are: (x - 8)(x - 8)

Foil (or distribute) to get: x² - 16x + 64 The k-value is 16

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Cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.

umka21 [38]

Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

- If angle x is in the first quadrant, then the equivalent angles to it are

# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x

tan (180 - x) = -tan x)

# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x

tan (180 - x) = tan x)

# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

tan (- x) = -tan x)

* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x

∵ cos² x + sin² x = 1

∴ R.H.S = 1

∴ L.H.S = R.H.S

∴ cos x cos (-x) -sin x sin (-x) = 1

8 0

3 years ago

Use an algebraic equation to find the measure of each angle that is represented in terms of x.

GuDViN [60]

The measure of each angle is 117°

Explanation:

Given that the two angles are (11x-26)° and (7x+26)°

We need to determine the measure of each angle.

Measure of angles:

From the figure, it is obvious that the two angles are vertically opposite angles.

By definition, we know that, the vertically opposite angles are always equal.

To determine the measure of each angle, we shall first find the value of x.

Thus, we have,

$11x-26=7x+26$

$4x-26=26$

$4x=52$

$x=13$

Thus, the value of x is 13

Now, substituting $x=13$ in the angle (11x-26)°, we get,

$(11(13)-26)^{\circ}=(143-26)^{\circ}$

$=117^{\circ}$

The measure of the angle is 117°

Similarly, substituting $x=13$ in the angle (7x+26)°, we get,

$(7x+26)^{\circ}=(7(13)+26)^{\circ}$

$=117^{\circ}$

The measure of the angle is 117°

Hence, the measure of each angle is 117°

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