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3 years ago

Five times a number k minus 9 is two thirds of a number j. solve for j

Mathematics

1 answer:

cupoosta [38]3 years ago

5 0

5k - 9 = 2/3 j, j = 3/2(5k-9)

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Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value.

Lelechka [254]

Answer:

1) $\frac{(-2)^{-5}}{(-2)^{-10}}=-32$

2) $2^{-1}.2^{-4} = \frac{1}{32}$

3) $(-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}$

4) $\frac{2}{2^{-4}} = 32$

Step-by-step explanation:

1) $\frac{(-2)^{-5}}{(-2)^{-10}}$

Solving using exponent rule: $a^{-m}=\frac{1}{a^m}$

$\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32$

So, $\frac{(-2)^{-5}}{(-2)^{-10}}=-32$

2) $2^{-1}.2^{-4}$

Using the exponent rule: $a^m.a^n=a^{m+n}$

We have:

$2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}$

We also know that: $a^{-m}=\frac{1}{a^m}$

Using this rule:

$2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}$

So, $2^{-1}.2^{-4} = \frac{1}{32}$

3) $(-\frac{1}{2} )^3.(-\frac{1}{2} )^2$

Solving:

$(-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}$

So, $(-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}$

4) $\frac{2}{2^{-4}}$

We know that: $a^{-m}=\frac{1}{a^m}$

$\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32$

So, $\frac{2}{2^{-4}} = 32$

3 0

3 years ago

Help me with this helpppppppppppppp worth 20 points

MariettaO [177]

I think its 2/12 but not 100% sure

5 0

3 years ago

Read 2 more answers

A 250 m train travels through a 2km tunnel at 27 km/hr. How long is it from the time the front of the train enters the tunnel, t

olga55 [171]

Answer:

5 min

Step-by-step explanation:

time taken=distance required to travel/speed of train

total distance train have to cover to just left the tunnel is (lenght of tunnel+length of train) =2km+250m

=2250m

speed of train is 27km/hr

multiply 5/18 to convert in m/s

i.e, (5/18)×27=7.5m/s

now time taken =2250m/(7.5m/s)

=300s

and,300s =5min

4 0

3 years ago

You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues and enter your answer belo

zalisa [80]

Answer:

184

Step-by-step explanation:

in the number 128 the number eight is right it should be to the right then in the number157 one is right it should be to the left in 841 8and 1 are in the wrong position 8 - right 1 - left then in the number 624 the number 4 is right but in the wrong position it should be in the middle the answer is digit 1,8,4

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2 years ago

What is the slope of the line through (-2,-6)and (2,2)

STALIN [3.7K]

Answer:

Y2-y1/x2-x1

=2-(-6)/2-(-2)

=8/4

Step-by-step explanation:

Given two points of a line to find the slope we use the formula; y2-y1/x2-x1 Hence the answer above.

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3 years ago