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2 years ago

The prime numbers which come between 5 and 15.

Mathematics

2 answers:

Marta_Voda [28]2 years ago

7 0

7,11,13

give brainliest

Evgen [1.6K]2 years ago

5 0

Hope it helps yah

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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

$\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}}
\\\\\\
\cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}}
\\\\\\
\cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}$

4 0

3 years ago

lily bought 6 skirts and 5 coats for a total of $452.62. if lily sister bought 3 skirts and 5 coats for $289.36, what was the pr

Vikentia [17]

Answer:

$26.02

Step-by-step explanation:

Let the price of a skirt be A and that of coat be B

Iilly bought 6 skirts and 5 coats for a total of $452.62

That’s

6A + 5B = 452.62

Also, Lilly’s sister bought 3 skirts and 5 coats for $289.36

That’s

3A + 5B = 289.36

We now have two equations

1 . 6A + 5B = 452.62

2. 3A + 5B = 289.36

Subtract equation two from equation one

We have

3A = 163.26

Divide both sides by 3

3A/3 = 163.26/3

A = 54.42

A = $54.42

Now substitute 54.42 for A in either equations to get B the price of a coat

Using equation one, we have

6A + 5B = 452.62

6 x 54.42 + 5B = 456.62

326.52 + 5B = 456.62

Subtract 326.52 from both sides

326.52 - 326.52 + 5B = 456.62 - 326.52

5B = 130.1

Divide both sides by 5

5B/5 = 130.1/5

B = 26.02

= $26.02

A coat cost $26.02

3 0

2 years ago

One angle of an isosceles triangle measures 100°. Which other angles could be in that isosceles triangle?

REY [17]

Answer:40 degrees

Step-by-step explanation:

4 0

3 years ago

Which of the following describes the correct process for solving the equation 3x+6=21 and arrives at the correct solution?

My name is Ann [436]

The correct solution is C

Subtract 6 from both sides of the equation
3x + 6 - 6 = 21 - 6
3x = 15

Then divide both sides by 3

$\frac{3x}{3} = \frac{15}{3}$

x = 5

4 0

3 years ago

Your answer should be a polynomial in standard form. (-1+2p)(3-4p)=(−1+2p)(3−4p)

saul85 [17]

$\\ \rm\Rrightarrow (-1+2p)(3-4p)=(-1+2p)(3-4p)$