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11Alexandr11 [23.1K]
3 years ago
14

Solve for a: a(a-3) =100

Mathematics
1 answer:
marissa [1.9K]3 years ago
5 0
a(a-3) =100\\
a^2-3a-100=0\\
\Delta=(-3)^2-4\cdot1\cdot(-100)=9+400=409\\
\sqrt{\Delta}=\sqr{409}\\
a_1=\dfrac{-(-3)-\sqrt{409}}{2\cdot1}=\dfrac{3-\sqrt{409}}{2}\\
a_2=\dfrac{-(-3)+\sqrt{409}}{2\cdot1}=\dfrac{3+\sqrt{409}}{2}
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Here to you!!!!!!!! now prove it
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Answer:

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teenagers wearing glasses =5

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2 years ago
Two workers paint lines for angled parking spaces. One worker paints a line so that m∠1=65. The other worker paints a line so th
scoundrel [369]

The image of the car park showing the 2 angles is attached.

Answer:

Their lines are parallel.

Step-by-step explanation:

From the attached image, we can see that ∠1 and ∠2 form a pair of alternate exterior angles. Thus; ∠1 = ∠2.

Now since they are congruent, it means that their lines will be parallel.

Thus, we can conclude that their lines are parallel.

3 0
3 years ago
A canoe in still water travels at a rate of 12 miles per hour. The current today is traveling at a rate of 2 miles per hour. If
VARVARA [1.3K]

Answer:

It’s 60miles

Step-by-step explanation:

We assume the trip is "d" miles and that the "extra hour" refers to the additional time that a current of 2 mph would add. That is, we assume the reference time is for a current of 0 mph.

The time with no current is ...

 time1 = distance/speed

 time1 = d/12 . . . . hours

With a current of 2 mph in the opposite direction, the time is ...

 time2 = d/(12 -2) = d/10

The second time is 1 hour longer than the first, so we have ...

 time2 = 1 + time1

 d/10 = 1 + d/12

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 d = 60 . . . . . . . . . subtract 5d

The one-way distance is 60 miles.

7 0
2 years ago
Paper plates cost $8 per package and plastic utensils cost $5 per package. Your supplier delivers 15 packages for a total cost o
Fittoniya [83]
To find the total of what you sold for each package, you'll need to write two equations. Know that x = paper plate packages and y = utensil packages.
First, x + y = 15 shows that there has to be fifteen packages, and 8x + 5y = 90 shows the $ made from selling a certain number of packages.
Next, you can solve by substitution, so change x + y = 15 to y = 15 - x.

To find our x, substitute the y in 8x + 5y = 90 to get
8x + 5(15 - x) = 90
Distribute: 8x + 75 - 5x = 90
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Divide the 3: x = 5

Now with our x, we can put 5 into the original equation x + y = 15 to get 5 + y = 15. Subtracting the 5, we get y = 10.

So, you have delivered 5 paper plate packages and 10 utensil packages.
8 0
3 years ago
If MP is a perpendicular bisector to LN, find each value (picture attached)
solong [7]

Answer:

x=4, MN= 37, LM= 37, y=7.

Step-by-step explanation:

If MP is a perpendicular bisector to LN, then NP and LP are equivalent.

(Solve for y)

2y+2= 16

(Move the +2 to the right side of the equation)

2y= 14

(Divide both sides by 2 to isolate the variable)

y=7

To find x and the measure of MN and LM, solve for x in the following equation:

7x+9 = 11x-7

(Move 7x to the right side of the equation)

9 = 4x-7

(Move -7 to the right side of the equation.)

16= 4x

(Divide both sides by 4 to isolate the variable.)

4= x

Plug x back into both equations to get the measure of MN and ML

MN=7(4)+9

MN= 28+9

MN= 37

LM= 11(4)-7

LM= 44-7

LM= 37

I hope this helps!

3 0
2 years ago
Read 2 more answers
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