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3 years ago

2 x 3x= 2x2= +_=

Mathematics

1 answer:

Tpy6a [65]3 years ago

3 0

Answer:

1)6x

2)4

3)6x+4=2(3x+2)

Step-by-step explanation:

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a positive number is 5 times less than another positive number. Six times the lesser number plus 3 times the greater is 3. Find

IgorLugansk [536]

<h2>Greetings!</h2>

Answer:

One number is $\frac{5}{7}$ and the other number is $\frac{1}{7}$

Step-by-step explanation:

Let x be the smaller number and y be the bigger number.

x = x

y = 5x

6x + 3y = 3

6x + (3 * 5x) = 3

6x + 15x = 3

(÷3)

2x + 5x = 1

7x = 1

x = $\frac{1}{7}$

6x + 3y = 3

6( $\frac{1}{7}$ ) + 3y = 3

$\frac{6}{7}$ + 3y = 3

3y = 3 - $\frac{6}{7}$

3y = $\frac{15}{7}$

Divide both sides by 3 to get 1y:

y = $\frac{5}{7}$

So one number is $\frac{5}{7}$ and the other number is $\frac{1}{7}$

<h2>Hope this helps!</h2>

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You're trying to find constants $a_0,a_1,a_2$ such that $\hat y=a_0+a_1\hat x+a_2{\hat x}^2$ . Equivalently, you're looking for the least-square solution to the following matrix equation.

$\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}$

To solve $\mathbf{Ax}=\mathbf b$ , multiply both sides by the transpose of $\mathbf A$ , which introduces an invertible square matrix on the LHS.

$\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b$

Computing this, you'd find that

$\mathbf x=\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}\approx\begin{bmatrix}121.119\\-3.786\\-0.175\end{bmatrix}$

which means the first choice is correct.

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3 years ago

2 x 3x= 2x2= __+___=

2 x 3x= 2x2= +_=