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3 years ago

Solve , -5x + 20 < 5

Mathematics

2 answers:

katovenus [111]3 years ago

7 0

Answer:

x>3

Step-by-step explanation:

julsineya [31]3 years ago

6 0

Let's solve your inequality step-by-step. −5x+20<5

Step 1: Subtract 20 from both sides. −5x+20−20<5−20−5x<−15

Step 2: Divide both sides by -5.‌ −5x−5‌<‌−15−5‌x>3

Answer: x>3

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Read 2 more answers

A business bought a lot of 2,500 lamps for 50,000 dollars and wants to sell them at 15 percent profit how much should each lamp

aev [14]

50,000 / 2500 = 20....he bought them for 20 bucks a piece. So if he wants to sell them at 15% profit, he would sell them for 20 + 0.15(20) = $ 23 bucks.

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3 years ago

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3 years ago

Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????) .

anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

We need to begin with the definition of tangent:

$tan (x) =\frac{sin(x)}{cos(x)}$

So we can replace into our formula and we got:

$tan(x-y) = \frac{sin(x-y)}{cos(x-y)}$ (1)

We have the following identities useful for this case:

$sin(a-b) = sin(a) cos(b) - sin(b) cos(a)$

$cos(a-b) = cos(a) cos(b) + sin (a) sin(b)$

If we apply the identities into our equation (1) we got:

$tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}$ (2)

Now we can divide the numerator and denominato from expression (2) by $\frac{1}{cos(x) cos(y)}$ and we got this:

$tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}$

And simplifying we got:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

And this identity is satisfied for all:

$(x-y) \neq \frac{\pi}{2} +n\pi$

8 0

3 years ago