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3 years ago

I really need help please anyone

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

7 0

-3/4 is the slope of the line

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A bookshelf has 276 books distributed evenly among 6 shelves. Find the unit rate of books per shelf

nexus9112 [7]

Answer:

46 books

Step-by-step explanation:

276/6=46 books per shelf

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3 years ago

3/4 divided by 12 help please

Harman [31]

Answer:

$\frac{1}{16}$

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A parabola can be drawn given a focus of (8,7) and a directrix of x = −2. What can be said about the parabola?

krek1111 [17]

Answer:

See below

Step-by-step explanation:

Given that the directrix is vertical, the parabola has to be horizontal because its axis is perpendicular to the directrix.

5 0

3 years ago

Write an equation in slope intercept form of a line that passes through (-2, 1) and (4,2).

fenix001 [56]

Answer:

$\displaystyle y = \frac{1}{6}x + 1\frac{1}{3}$

Step-by-step explanation:

First, find the <em>rate of change</em> [<em>slope</em>]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-1 + 2}{2 + 4} = \frac{1}{6}$

Now plug these coordinates into the Slope-Intercept Formula. It does not matter which ordered pair you choose:

2 = ⅙[4] + b

⅔

$\displaystyle 1\frac{1}{3} = b \\ \\ y = \frac{1}{6}x + 1\frac{1}{3}$

_______________________________________________

1 = ⅙[−2] + b

−⅓

$\displaystyle 1\frac{1}{3} = b \\ \\ y = \frac{1}{6}x + 1\frac{1}{3}$

** You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.

I am joyous to assist you anytime.

5 0

3 years ago

If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(

timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

2 years ago