Jack played the first 3/5 of a basketball game. Then he played the final 1/10 of the game

Mathematics

1 answer:

____ [38]3 years ago

5 0

Answer:

He played 7/10 of the game

Step-by-step explanation:

3/5=6/10

6/10+1/10=7/10

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a rectangular field is to be covered on three sides leaving a side of length 20m uncovered. if the area of the field is 600m2. h

Leona [35]

Answer:

580m^2

Step-by-step explanation:

600m^2 -20m=580m^2

8 0

3 years ago

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

Emma has money in two savings accounts. One rate is 7% and the other is 8%. If she has $450 more in the 8% account and the total

hodyreva [135]

Answer:

420

Step-by-step explanation:

3 0

4 years ago

Find the value of 9!

katrin2010 [14]

Answer: 362880

The exclamation mark means factorial notation. The rule is we start with the given number, then count down til we get to 1, multiplying all along the way. In this case, we start with 9, then multiply with 8, 7, 6, etc til we get to 1, like so...

9! = 9*8*7*6*5*4*3*2*1 = 362880

Some calculators have a factorial button built in. The button should be labeled with an exclamation mark.

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4 years ago

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Sarah's family has an apple orchard The family sells 8 baskets of apples for every 3 jars of applesauce. How many baskets of app

Lina20 [59]

They would sell 320 baskets if they sold 120 jars of apple sauce. They sell 440 total baskets and jars. You have it right.

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3 years ago