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3 years ago

WORTH 20 POINTS!!!! PLZZZ HELPP!!!!!!!!

1 answer:

8 0

0 = 230 - 45x
Add 45x to both sides
45x = 230
Divide both sides by 45
x = 230 / 45
Simplify
x = 46 / 9
The solution represents the x intercept, which is where the graph intersects the x axis.

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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

PLEASE HELP

Makovka662 [10]

The answer is -3 on apex:)

4 0

3 years ago

Read 2 more answers

What is 15 divided by 6

Rainbow [258]

Set up the long division.

6|15

Calculate 15 ÷ 6, which is 2 with a remainder of 3.

26|15123

Answer
2 with a remainder of 3

Answer (Mixed Fraction)
2 $\frac{3}{6}$
5 Simplify $\frac{3}{6}$ to $\frac{1}{2}$ 
2 $\frac{1}{2}$
Done
Decimal Form: 2.5

7 0

3 years ago

Help please if u can answer!:)

pentagon [3]

Answer:

ANGLE K IS 75 DEGREES

All the interior angles of a triangle ADD up to 180 degrees

lets add the angles!

6x-11+8x-29+3x-1

add like terms. all the x terms add up and all the constants as well

8x+6x+3x = 17x

-29-1-11 = -41

17x-41= 180 (-41 + 41 = 0 we do this to remove -41 from the left side of the equation to isolate x)

41+180 = 221

17x=221

221/17 = 13

x=13

so..

8 * 13 - 29 is the angle..

8*13 = 104

and 104-29 = 75

Angle K is 75 degrees! hope that helps..

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Which expressions below equal a rational number? Choose all that apply. 4/5 + 3/8; sqrt(100) + sqrt(5); 7sqrt(5) - sqrt(245); (4

masha68 [24]

Answer:

Step-by-step explanation:

<h3>Rational number</h3>

$1) \dfrac{4}{5}+\dfrac{3}{8}\\\\\dfrac{4}{5} \ \text{is a rational number} \ and \ \dfrac{3}{8} \ \text{is a rational number}\\\\\dfrac{4}{5}+\dfrac{3}{8} \ \text{is also a rational number}$

$b) \sqrt{100}+\sqrt{5} = 10+\sqrt{5}\\\\\sqrt{5} \ \text{is a irrational number}. \\\\ \text{Rational number added to irrational number will result in an irrational number}\\\\10 + \sqrt{5} \ is \ not \ a \ rational \ number.$

$7\sqrt{5}-\sqrt{245}=7\sqrt{5}-\sqrt{7*7*5}$

$= 7\sqrt{5}-7\sqrt{5}\\\\=0\\\\\text{\bf $ 7\sqrt{5}-\sqrt{245}$ ia a rational number}$

$(4\sqrt{7})*(2\sqrt{7})=4*2*\sqrt{7*7}\\$

= 4*2*7

= 56

$4\sqrt{7}*2\sqrt{7} \ \text{\bf is a rational number}$

8 0

2 years ago