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2 years ago

Add: -5g^2+(-9g^2-8)

Mathematics

1 answer:

Amiraneli [1.4K]2 years ago

3 0

Answer:

$\boxed{-14g^2 - 8}$

Step-by-step explanation:

$-5g^2 + (-9g^2 - 8)$

$= - 5g^2 - 9g^2 - 8$

$= -14g^2 - 8$

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WHAT IS X³-27 SIMPLIFIED

Eduardwww [97]

Answer:

It is (x - 3)³ - 9x(3 - x)

Step-by-step explanation:

Express 27 in terms of cubes, 27 = 3³:

$= {x}^{3} - {3}^{3}$

From trinomial expansion:

${(x - y)}^{3} = (x - y)(x - y)(x - y) \\$

open first two brackets to get a quadratic equation:

${(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)$

expand further:

${(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}$

take y to be 3, then substitute:

$( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)$

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Please help. My son and I don't get it

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2 years ago

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Paul was thinking of a number. Paul adds 10, then divides by 2 to get an answer of -13. What was the original number?

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Step-by-step explanation:

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2 years ago

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The difference of two numbers is 16 the greater number is five less than four times a small number find the two numbers

Elis [28]

Answer:

The numbers are 23 and 7

Step-by-step explanation:

1. Set up the equations

Let x = the greater number

and y = the smaller number. Then

(1) x - y = 16

4y = 4 times the smaller number and

4y - 5 = 5 less than 4 times the smaller number. Then

(2) x = 4y - 5

You have a system of two equations:

$\begin{cases}(1) & x - y = 16\\(2) & x = 4y - 5\end{cases}$

2. Solve the equations

$\begin{array}{lrcll}(3) & 4y - 5 - y & = & 16 &\text{Substituted (2) into (1)}\\& 3y - 5 & = & 16 &\text{Simplified}\\ & 3y & = & 21 &\text{Added 5 to each side}\\(4) &y & = & \mathbf{7} &\text{Divided each side by 3} \\& x - 7 & = & 16 & \text{Substituted (4) into (1)}\\& x& = & \mathbf{23} & \text{Added 7 to each side}\\\end{array}$

The larger number is 23; the smaller number is 7.

3. Check

$\begin{array}{rclcrcl}23 - 7& = & 16 & \qquad &23&=&4(7) - 5\\16 & = & 16 & \qquad &23& = &28 - 5\\&&& \qquad &23& = &23\\\end{array}$

OK.

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3 years ago