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3 years ago

What is the smallest number by which 864 must be multiplied with to make the quotient a perfect cube?

Mathematics

1 answer:

In-s [12.5K]3 years ago

3 0

Answer:

Number is two

Step-by-step explanation:

First of all we find the closest factors of 864 which are 32 x 27

Simply them we have

32 x 27 = 2^5 x 3³

Next we know that to be aperfect cube, each exponent needs to be equally divided by divisible by 3.

So If we multiply 864 x 2 we get

Then

1728 = 2^6 x 3³

So if we finally

Take the cube root of that is 2²* 3^1 = 4 x 3= 12

So 2² x 3^1

So if we equate the powers we have the answer as 2.

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Let a, b, c, and d be real numbers with a, c 6= 0. Prove that the lines y = ax+b and y = cx + d have the same x-intercept if and

Monica [59]

Step-by-step explanation:

We have got the lines :

$y=ax+b\\y=cx+d$

Both lines intercept the x-axis in the point :

$I = (i_{1} ,i_{2})$

In all point from x-axis the y-component is equal to 0.

$I=(i_{1},o)$

We replace the I point in the lines equations:

$0=a(i_{1})+b \\0=c(i_{1})+d$

From the first equation :

$0=a(i_{1})+b \\-b=a(i_{1})\\i_{1}=\frac{-b}{a}$

From the second equation :

$0=c(i_{1})+d\\ -d=c(i_{1})\\i_{1}=\frac{-d}{c}$

Then $i_{1}=i_{1}$

Finally :

$\frac{-b}{a}=\frac{-d}{c} \\\frac{b}{a}=\frac{d}{c} \\ad=bc$

y = ax + b and y = cx + d have the same x-intercept ⇔ad=bc

8 0

3 years ago

For f(x) = 2x +1 and g(x) = x^2-7, find (f/g) (x)

Rashid [163]

the answer is (f/g)(x) = 2(x^2 - 7) + 1
= 2x^2 - 14 + 1
= 2x^2 - 13

5 0

3 years ago

Which expression is equivalent to 150x² - 60x ?

Bas_tet [7]

Answer: The Answer is B

Step-by-step explanation:

You need to distribute 15x(10x - 4). 15x times 10x is 150x and since there is 2 x's your gonna square it. So then it would be 150x². next 15x times -4 is -60 and add your x. Your answer is 150x² - 60x.

8 0

3 years ago

Read 2 more answers

Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card

Viktor [21]

Answer:

a) i) No

ii) Probability of drawing a diamond and then spade without replacement is 0.0637.

b) i) Yes

ii) Probability of drawing a diamond and then spade with replacement is 0.0625

Step-by-step explanation:

Part a) Without replacement:

i) Are these events independent?

No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.

ii) Determine the probability of drawing a diamond and then a spade without replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond = 13/52

Probability of drawing a spade:

Total cards in deck after taking diamond = 52 -1 =51

Spades = 13

Probability of drawing a spade = 13/51

Probability of drawing a diamond and then spade = 13/52 * 13/51

= 169/2652

=0.0637

So, Probability of drawing a diamond and then spade without replacement is 0.0637

Part b) With replacements

i) Are these events independent?

Input Yes or No:

Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.

ii) Determine the probability of drawing a diamond and then a spade with replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond = 13/52

Probability of drawing a spade:

Total cards in deck after replacing diamond = 52

Spades = 13

Probability of drawing a spade = 13/52

Probability of drawing a diamond and then spade = 13/52 * 13/52

= 169/2704

=0.0625

So, Probability of drawing a diamond and then spade with replacement is 0.0625

7 0

3 years ago

You are asked to draw a triangle with the side lengths of 10 inches and 15 inches.

torisob [31]

Answer:

24 inches

Step-by-step explanation:

24 inches of it

4 0

3 years ago