Expand the following: 3(16x-24)

Mathematics

1 answer:

Fynjy0 [20]3 years ago

6 0

Answer:

48x-72

Step-by-step explanation:

u multiply 3 by 16x then multiply 3 by 24 and bring down your minus sign

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Please write an equation

Katen [24]

Answer:

y = $\frac{3}{4}$ x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m = $\frac{5-2}{4-0}$ = $\frac{3}{4}$

The line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = $\frac{3}{4}$ x + 2 ← equation of line

4 0

2 years ago

Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Maurinko [17]

The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .