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3 years ago

The sum of two numbers is 4. The larger number is 12 more than three times the smaller number. What are the numbers?

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

8 0

Step-by-step explanation:

So, we will take one of the numbers = x

And the other is 12 more than 3 times it, so = 3x + 12

So they said if we add them, we will get 4

So x + (3x + 12) = 4

4x + 12 = 4

4x = 4 - 12

4x = - 8

x = - 8 ÷4

x = - 2

So one of the numbers x = - 2

The other is 3x + 12

So x = - 2

3x +12 = 3(-2) + 12

= 6

So the 2 numbers = 6 and - 2

Lets check!

6 + (-2) = 4

So it's right!

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grin007 [14]

Answer:

Dimensions of printed poster are

length is 32 cm

width is 48 cm

Step-by-step explanation:

Let's assume

length of printed poster is x cm

width of printed poster is y cm

now, we can find area of printed poster

so, area of printed poster is

$=xy$

we are given that area as 1536

so, we can set it to 1536

$xy=1536$

now, we can solve for y

$y=\frac{1536}{x}$

now, we are given

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm

so, total area of poster is

$A=(8+x+8)\times (12+y+12)$

$A=(x+16)\times (y+24)$

now, we can plug back y

$A=(x+16)\times (\frac{1536}{x}+24)$

now, we have to minimize A

so, we will find derivative

$A'=\frac{d}{dx}\left(\left(x+16\right)\left(\frac{1536}{x}+24\right)\right)$

we can use product rule

$A'=\frac{d}{dx}\left(x+16\right)\left(\frac{1536}{x}+24\right)+\frac{d}{dx}\left(\frac{1536}{x}+24\right)\left(x+16\right)$

$=\frac{d}{dx}\left(x+16\right)\left(\frac{1536}{x}+24\right)+\frac{d}{dx}\left(\frac{1536}{x}+24\right)\left(x+16\right)$

now, we can simplify it

$A'=-\frac{24576}{x^2}+24$

now, we can set it to 0

and then we can solve for x

$A'=-\frac{24576}{x^2}+24=0$

$-\frac{24576}{x^2}x^2+24x^2=0\cdot \:x^2$

$-24576+24x^2=0$

$x=32,\:x=-32$

Since, x is dimension

and dimension can never be negative

so, we will only consider positive value

$x=32$

now, we can solve for y

$y=\frac{1536}{32}$

$y=48$

so, dimensions of printed poster are

length is 32 cm

width is 48 cm

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Firlakuza [10]

Answer:

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Step-by-step explanation:

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3 years ago

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vladimir1956 [14]

Answer:

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Step-by-step explanation:

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Soloha48 [4]

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yulyashka [42]

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Step-by-step explanation:

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