Olve for x. 3(3x - 1) + 2(3 - x) = 0 x = 3/7 x = -3/7 x = 1/3 x = -1/3

Mathematics

1 answer:

zloy xaker [14]3 years ago

8 0

Answer:

x = -3/7

Step-by-step explanation:

We are given the following equation for which we have to solve for x:

$3(3x - 1) + 2(3 - x) = 0$

So we will start by expanding the equation by multiplying the common factor with the brackets to get:

$9x-3+6-2x=0$

Arranging the like terms together (variables on one side of the equation and constants on the other side) to get:

$9x-2x=3-6\\\\7x=-3\\\\x=-\frac{3}{7}$

Therefore, x = -3/7.

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68° radius=4.2cm A sector of a circle is shown. Find its area, rounded to the nearest tenth.

andrezito [222]

Answer:

Step-by-step explanation:

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3 years ago

For the love of God help me !! I'm desperate for it tomorrow

Eduardwww [97]

Try to relax. Your desperation has surely progressed to the point where
you're unable to think clearly, and to agonize over it any further would only
cause you more pain and frustration.
I've never seen this kind of problem before. But I arrived here in a calm state,
having just finished my dinner and spent a few minutes rubbing my dogs, and
I believe I've been able to crack the case.

Consider this: (2)^a negative power = (1/2)^the same power but positive.

So:
Whatever power (2) must be raised to, in order to reach some number 'N',
the same number 'N' can be reached by raising (1/2) to the same power
but negative.

What I just said in that paragraph was: log₂ of(N) = - log(base 1/2) of (N) .
I think that's the big breakthrough here.
The rest is just turning the crank.

Now let's look at the problem:

log₂(x-1) + log(base 1/2) (x-2) = log₂(x)

Subtract log₂(x) from each side:

log₂(x-1) - log₂(x) + log(base 1/2) (x-2) = 0

Subtract log(base 1/2) (x-2) from each side:

log₂(x-1) - log₂(x) = - log(base 1/2) (x-2) Notice the negative on the right.

The left side is the same as log₂[ (x-1)/x ]

==> The right side is the same as +log₂(x-2)

Now you have: log₂[ (x-1)/x ] = +log₂(x-2)

And that ugly [ log to the base of 1/2 ] is gone.

Take the antilog of each side:

(x-1)/x = x-2

Multiply each side by 'x' : x - 1 = x² - 2x

Subtract (x-1) from each side:

x² - 2x - (x-1) = 0

x² - 3x + 1 = 0

Using the quadratic equation, the solutions to that are
x = 2.618
and
x = 0.382 .

I think you have to say that x=2.618 is the solution to the original
log problem, and 0.382 has to be discarded, because there's an
(x-2) in the original problem, and (0.382 - 2) is negative, and
there's no such thing as the log of a negative number.

There,now. Doesn't that feel better.

4 0

2 years ago

Ms. Mwanted to estimate the height of the Republic Plaza building in downtown Denver. She has an app on

Volgvan

Answer:

The height of the bullding is 717 ft

Step-by-step explanation:

Right Triangles

The trigonometric ratios (sine, cosine, tangent, etc.) are defined as relations between the triangle's side lengths.

The tangent ratio for an internal angle A is:

$\displaystyle \tan A=\frac{\text{opposite leg}}{\text{adjacent leg}}$

The image below shows the situation where Ms. M wanted to estimate the height of the Republic Plaza building in downtown Denver.

The angle A is given by his phone's app as A= 82° and the distance from her location and the building is 100 ft. The angle formed by the building and the ground is 90°, thus the tangent ratio must be satisfied. The distance h is the opposite leg to angle A and 100 ft is the adjacent leg, thus:

$\displaystyle \tan 82^\circ=\frac{h}{100}$