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3 years ago

Is 5(2x-3y) and 10x-3y equivalent?

Mathematics

1 answer:

stiks02 [169]3 years ago

3 0

Answer:

Step-by-step explanation:

Apply the distributive property to 5(2x - 3y):

Multiply 5 by each term inside the parentheses.

5(2x - 3y) = 10x - 15y

The other expression is 10x - 10y.

The terms 10x in both expressions are equal.

Since the term -15y is not equal to the term -10y, the expressions are not equivalent.

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A number is chosen at random from the integers 10 to 30 inclusive. Find the probability that the number is a multiple of 3.

kirill [66]

Answer:

For each part, find how many numbers have the stated characteristic, then divide by 21.

e.g. multiples of 5:

these would be 10, 15, 20, 25, and 30

so prob (a multiple of 5 ) = 5/21

Do the others the same way

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3 years ago

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3 years ago

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spayn [35]

Yo sup??

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3 years ago

Evaluate the following

IRINA_888 [86]

(a) $[\frac{9}{2.6} - \frac{2.5^{2} }{2.5} ]^{2}$

Answer:

$[\frac{9}{2.6} - \frac{2.5^{2} }{2.5} ]^{2}$

= $[\frac{9}{2.6} - \frac{2.5*2.5 }{2.5} ]^{2}$

= $[\frac{9}{2.6} - \frac{2.5}{1} ]^{2}$

*canceling 2.5 in numerator and denominator*

$= [\frac{9-(2.5)(2.6)}{2.6} ]^2\\*Using L.C.M of 2.6 and 1 which comes out to be '2.6'= [\frac{9-(6.5)}{2.6} ]^2\\= [\frac{2.5}{2.6} ]^2\\*multiplying and dividing by '10'= [\frac{2.5*10}{2.6*10} ]^2\\= [\frac{25}{26} ]^2\\= \frac{25^2}{26^2}\\= \frac{625}{676}\\= 0.925$

Properties used:

Cancellation property of fractions

Least Common Multiplier(LCM)

The least or smallest common multiple of any two or more given natural numbers are termed as LCM. For example, LCM of 10, 15, and 20 is 60.

(b) $[[\frac{3x^{a}y^{b}} {-3x^{a} y^{b} } ]^{3} ] ^{2}$

Answer:

$[[\frac{3x^{a}y^{b}} {-3x^{a} y^{b} } ]^{3}] ^{2}\\$

*using $[x^{a}]^b = x^{ab}$ *

$= [\frac{3x^{3a}y^{3b}} {-3x^{3a} y^{3b} }] ^{2}$

*Again, using $[x^{a}]^b = x^{ab}$ *

$= \frac{3x^{2*3a}y^{2*3b}} {-3x^{2*3a} y^{2*3b} } \\= (-1)\frac{3x^{6a}y^{6b}} {3x^{6a} y^{6b} }\\[\tex]*taking -1 common, denominator and numerator are equal*[tex]= -(1)\frac{1}{1}\\= -1$

Property used: 'Power of a power'

We can raise a power to a power

(x^2)4=(x⋅x)⋅(x⋅x)⋅(x⋅x)⋅(x⋅x)=x^8

This is called the power of a power property and says that to find a power of a power you just have to multiply the exponents.

3 0

3 years ago

How many times larger is 2 x 1012 than 5 x 106?

vfiekz [6]

Answer: It is 3.81886792453 times larger

Step-by-step explanation: 2 x 1012 is 2024

5 x 106 is 530

so take 2024 and divide it by 530 and you get 3.81886792453

in case you were wondering this rounds to 3.82

hope this helps and mark me brainliest if you can

6 0

3 years ago