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galben [10]
3 years ago
13

How do you simplify 2(m+5)+8(6m+1)

Mathematics
2 answers:
Sholpan [36]3 years ago
7 0
<span>2(m + 5) + 8(6m + 1) =
2m + 10 + 48m + 8 = 
50m + 18</span>
galina1969 [7]3 years ago
5 0
You must use distributive property to get 2m+10+48m+8 and then add all like terms. You get 50m+18 as your final answer.
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Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -
GaryK [48]

Consider all parabolas:

1.

y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

2.

y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

3.

y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

4.

y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

5.

y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

6.

y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

3 0
3 years ago
What is the sum of 3/10 and 17/100
alina1380 [7]
3/10 + 17/100

first make the 10 of the 3/10 turn into a 100 so it will make the 100 of the 17/100.
to make 10 turn into a 100 you multiply it by 10. if you're going to multiply the bottom number by 10 then you have to do the same thing with the top number:
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new equation:
30/100 + 17/100

now just add the top numbers and leave the 100's alone:
<span>30/100 + 17/100
</span>30+17=47
<span>30/100 + 17/100 = 47/100</span>
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3 years ago
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Lets look at the hours they are open from. 9 am - 4:30 pm which is 7 and a half hours a day. Now we multiply 7 1/2 by the number of days they are open, which will be 7 1/2 * 255 = 1,912.5. This means that the library is open 1,912 1/2 hours a year.

I hope I've helped! :)

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Answer:

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4 0
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