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Grace [21]
2 years ago
6

A dollar store sells items for $1 and $2. You plan to go there and spend at least $20. Let x stand for the number of one-dollar

items and let y stand for the number of two-dollar items. Write and graph a linear inequality that models the situation.

Mathematics
1 answer:
KonstantinChe [14]2 years ago
8 0

Answer:

5

Step-by-step explanation:

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If log10 y = 2. what does y equal?
lys-0071 [83]

Answer:

log_{10}  (100) = 2

Step-by-step explanation:

Here, the given expression is:

log_{10}  (y) = 2

Now, by logarithm rules, we know

if  log_{b}(x) = z

, then x =b^{z}

Comparing here, b = 10  and  z = 2

⇒ y  =   10^{2}  = 100

or, log_{10}  (100) = 2

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A. Use this diagram of a right triangle to derive and prove the Pythagorean Identity, based on sin θ and cos θ. Start with what
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2 years ago
What is the correct slope intercept form of the equation y + 16 = 3(x - 0) ?
Sindrei [870]

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y+16=3(x-0)

y+16=3(x)

y+16=3x

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3rd option

8 0
3 years ago
How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0
ziro4ka [17]

Answer:

\displaystyle x = \frac{\pi}{3} +k\, \pi or \displaystyle x =- \frac{\pi}{3} +2\,k\, \pi, where k is an integer.

There are three such angles between 0 and 2\pi: \displaystyle \frac{\pi}{3}, \displaystyle \frac{2\, \pi}{3}, and \displaystyle \frac{4\,\pi}{3}.

Step-by-step explanation:

By the double angle identity of sines:

\sin(2\, x) = 2\, \sin x \cdot \cos x.

Rewrite the original equation with this identity:

2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0.

Note, that 2\, (2\, \sin x \cdot \cos x) and (-2\, \sin x) share the common factor (2\, \sin x). On the other hand, 2\sqrt{3}\, \cos x and (-\sqrt{3}) share the common factor \sqrt[3}. Combine these terms pairwise using the two common factors:

(2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0.

Note the new common factor (2\, \cos x - 1). Therefore:

\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0.

This equation holds as long as either \left(2\, \sin x + \sqrt{3}\right) or (2\, \cos x - 1) is zero. Let k be an integer. Accordingly:

  • \displaystyle \sin x = -\frac{\sqrt{3}}{2}, which corresponds to \displaystyle x = -\frac{\pi}{3} + 2\, k\, \pi and \displaystyle x = -\frac{2\, \pi}{3} + 2\, k\, \pi.
  • \displaystyle \cos x = \frac{1}{2}, which corresponds to \displaystyle x = \frac{\pi}{3} + 2\, k \, \pi and \displaystyle x = -\frac{\pi}{3} + 2\, k \, \pi.

Any x that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

  • \displaystyle x = \frac{\pi}{3} + k \, \pi (from \displaystyle x = -\frac{2\,\pi}{3} + 2\, k\, \pi and \displaystyle x = \frac{\pi}{3} + 2\, k \, \pi, combined,) as well as
  • \displaystyle x =- \frac{\pi}{3} +2\,k\, \pi.
7 0
3 years ago
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