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2 years ago

Can someone plz help with 21?? Thanks!

Mathematics

2 answers:

cluponka [151]2 years ago

7 0

Answer:

option 4

Step-by-step explanation:

$\frac{2}{3}$ ( $\frac{1}{4}$ x - 2) = $\frac{1}{5}$ ( $\frac{4}{3}$ x - 1) ← distribute parenthesis on both sides

$\frac{1}{6}$ x - $\frac{4}{3}$ = $\frac{4}{15}$ x - $\frac{1}{5}$

Multiply through by 30, the LCM of 6, 3, 15, 5

5x - 40 = 8x - 6 ( subtract 8x from both sides )

- 3x - 40 = - 6 ( add 40 to both sides )

- 3x = 34 ( divide both sides by - 3 )

x = - $\frac{34}{3}$ = - 11.333..

Romashka-Z-Leto [24]2 years ago

6 0

Answer:

4) -11.3...

Step-by-step explanation:

distribute both sides to get (1/6)x - (4/3) = (4/15)x - (1/5)

move the variables to one side and the constants to the other: ((4/15) - (1/6))x = (-(4/3) + (1/5))

simplify to get (1/10)x = (-17/15) multiply everything by 10 to get x=-34/3 or -11.33333333333333333...

You might be interested in

Find the circumference of the circle. Round to the nearest tenth if necessary.

NikAS [45]

Answer:

c.132

Step-by-step explanation:

so we are given the diameter which is 42m **the diameter is the straight line that passes through the middle of the circle**

but in order to find the circumference we need to find the radius **the radius is always half (1/2,0.5) of the diameter**

so we have to divide 42/2 which equals 21

now we need to set up the formula;

c=2πr/c=2xπxr **when unknown variables such as 'r' are next to another mathematical numeral such as the pi symbol you don't really have to but the multiplication symbol between them**

c=2π21

=131.946891451

and in your case, it seems we must round to the tenths place so the nine then "becomes a ten" and you're left with 132

good luck :)

i hope this helps

have a good one !!

6 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.

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