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3 years ago

8

you have four chains of three links each. although it is difficult to cut the links, you wish to make a single loop with all 12

links. what is the fewest numbers of cuts you must make to accomplish this task

1 answer:

mel-nik [20]3 years ago

3 0

You have 4 parts that you want to combine so you need to make 3 cuts

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GIVING BRAINLEIST!!!!

kipiarov [429]

If i were going by guesses i’d say y=x. sorry if i’m wrong.

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3 years ago

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If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

<em><u>Solution:</u></em>

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

<em><u>Use the following log rules</u></em>

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

Next

$b) log_b 324$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

Next

$c) log_b\frac{8}{9}$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

Next

$d) \frac{log_b27}{log_b16}$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

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3 years ago

Put the following portions in order from least to greatest 30% 1/5 75% 5/6

sertanlavr [38]

Answer:

1/5,30%,75%,5/6

Step-by-step explanation:

first turn all of them in to decimals:

1/5=0.20

30%=0.30

75%=0.75

5/6=0.83

then put the decimals in order from least to greatest

done!

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3 years ago

Find the slope of the line passing through (-9,3), (-3,-5)

egoroff_w [7]

Answer:

-4/3

Step-by-step explanation:

Slope: (y2-y1)/(x2-x1)

(-5-3)/(-3+9) = -8/6 = -4/3

The slope is -4/3

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3 years ago

Geometry- I need an answer for x and y.

elixir [45]

Answer:

x = 13sqrt(3) ft = 22.5 ft

y = 13 ft

Step-by-step explanation:

The triangle is a 30-60-90 right triangle.

The ratio of the lengths of the sides is

short leg : long leg : hypotenuse = 1 : sqrt(3) : 2

From the ratio above we see that the hypotenuse is twice the short leg.

The long leg is sqrt(3) times the short leg.

y = short leg

x = long leg

26 ft = hypotenuse

y = 26 ft/2 = 13 ft

x = 13 ft * sqrt(3) = 13sqrt(3) ft = 22.5 ft

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3 years ago

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