The correct answer is the 3rd option.
The component form of a vector is to write in the form (x, y) the x and y component of a vector.
Since the vector starts at (0, 0) and ends at (5, -8) We can rest the start point to the end point to get the components of the vector:
![\begin{gathered} x\text{ component:} \\ 5-0=5 \\ y\text{ component}\colon \\ -8-0=-8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5Ctext%7B%20component%3A%7D%20%5C%5C%205-0%3D5%20%5C%5C%20y%5Ctext%7B%20component%7D%5Ccolon%20%5C%5C%20-8-0%3D-8%20%5Cend%7Bgathered%7D)
The component for is:
![\langle5,-8\rangle](https://tex.z-dn.net/?f=%5Clangle5%2C-8%5Crangle)
The magnitude of a vector is its' module, we calculate it by:
![\mleft\Vert u\mleft\Vert=\sqrt[]{x^2+y^2}\mright?\mright?](https://tex.z-dn.net/?f=%5Cmleft%5CVert%20u%5Cmleft%5CVert%3D%5Csqrt%5B%5D%7Bx%5E2%2By%5E2%7D%5Cmright%3F%5Cmright%3F)
Where x and y are the components of the vector. In this case:
![\mleft\Vert u\mleft\Vert=\sqrt[]{5^2+(-8)^2}=\sqrt[]{25+64}=\sqrt[]{89}\mright?\mright?](https://tex.z-dn.net/?f=%5Cmleft%5CVert%20u%5Cmleft%5CVert%3D%5Csqrt%5B%5D%7B5%5E2%2B%28-8%29%5E2%7D%3D%5Csqrt%5B%5D%7B25%2B64%7D%3D%5Csqrt%5B%5D%7B89%7D%5Cmright%3F%5Cmright%3F)
The whole answer is:
![u=\langle5,-8\rangle;\mleft\Vert u\mleft\Vert=\sqrt[]{89}\mright?\mright?](https://tex.z-dn.net/?f=u%3D%5Clangle5%2C-8%5Crangle%3B%5Cmleft%5CVert%20u%5Cmleft%5CVert%3D%5Csqrt%5B%5D%7B89%7D%5Cmright%3F%5Cmright%3F)
Which is option 3.
Answer: D x > -2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Step-by-step explanation:
It’s 10.
Answer:
4
Step-by-step explanation:
solve for x by simplifying both sides of the equation then isolating the variable
Answer:
see explanation
Step-by-step explanation:
(i)
+
= 1 ( multiply through by 6 to clear the fractions )
2x + 3y = 6 ( subtract 2x from both sides )
3y = - 2x + 6 ( divide through by 3 )
y = -
x + 2
(ii)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope ( gradient ) and c the y- intercept )
y = -
x + 2 ← is in slope- intercept form ( that is part (i)
with gradient m = - ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)