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gizmo_the_mogwai [7]
2 years ago
6

Suppose we want to choose 7 objects, without replacement, from 10 distinct objects.

Mathematics
1 answer:
Citrus2011 [14]2 years ago
7 0

Answer:

= 604800

Step-by-step explanation:

10 permute 7

the order matters

10 x 9 x8 x7 x6 x5 x4

hope this helps

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Solve The Equation <br> 4x×9y=7<br> 4x-9y=9
hoa [83]

Answer:

\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}

Step-by-step explanation:

\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}

4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}

8 0
3 years ago
You have 50 tickets to ride the ferris wheel and the roller coaster. if you ride 12 times total, using 3 tickets for each ferris
EastWind [94]
Hey! :)

you went on the roller coaster 7 times and the ferris wheel 5 times

Hope this helps! :)
4 0
3 years ago
Read 2 more answers
What is the width of a rectangle with an area of 5/8 in. squared and a length of 10 inches?
Ad libitum [116K]
5/8=10×w this is my equation then i divide by 10 on both sides
w=6.25
6 0
3 years ago
Shannon wants to buy cupcakes for her friend's birthday party. The bakery she goes to sells cupcakes for $3.50 each. The bakery
Aleks [24]
So I think it would be $35 because if you multiply $3.50 by ten then it would be $35
6 0
3 years ago
Read 2 more answers
Can anyone help me out on this
Licemer1 [7]

Answer:

y=x+10

Step-by-step explanation:

y=mx+b

y=1x+b

1 because for every 10 it goes to the right, it goes up 10 as well.

b=10 because the function crosses the y-axis at 10

so

y=x+10

4 0
3 years ago
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