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Bas_tet [7]
3 years ago
14

Simplify the following inequality 3x + 12 ≥2(4x + 3) −21 Help I need the answer ASAP

Mathematics
1 answer:
Vlada [557]3 years ago
3 0

Answer:

x ≤ 27/5

Step-by-step explanation:

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How do you find a vector that is orthogonal to 5i + 12j ?
Rashid [163]
\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies  -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
-------------------------------\\\\

\bf \boxed{5i+12j}\implies 
\begin{array}{rllll}
\ \textless \ 5&,&12\ \textgreater \ \\
x&&y
\end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5}
\\\\\\
slope=\cfrac{12}{{{ 5}}}\qquad negative\implies  -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12}
\\\\\\
\ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}

if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.

so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.

so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.

or using a unit vector for those above, then

\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}}&#10;\\\\\\&#10;\cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}}&#10;\\\\\\&#10;\cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}
4 0
3 years ago
You need to borrow $15,000 to buy a car, and you determine that you can afford monthly payments of $325. The bank offers three c
Klio2033 [76]

Answer:

the 5yr/ $270mth

Step-by-step explanation:

$15k × 8% = $1200 interest

$15k + $1200 = $16,200.00

$16500 ÷ 60months (5years) = $270/mth pymt

4 0
3 years ago
79,81,84,88,100,88,82 what is the mean of these numbers
Ivahew [28]

Answer:

86

Step-by-step explanation:

4 0
3 years ago
What is the slope of the line that goes through (0,0) (5,1)
GalinKa [24]
Hey there!

In order to solve this problem, we can use the slope given two points formula:

y2-y1/x2-x1

Now, we can plug in our points to get:

1-0/5-0 = 1/5

Your answer is 1/5, or B.

Hope this helps!
8 0
3 years ago
Read 2 more answers
0.4 to the 6th power
kaheart [24]
.4^6 = .004096 Hoped this helps.
6 0
3 years ago
Read 2 more answers
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