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Leya [2.2K]
3 years ago
15

Explain why a line and a parabola can have no more the two points of intersection.

Mathematics
1 answer:
galben [10]3 years ago
4 0
A parabola can be written with parameters: 
f(x)= ax^2 + bx + c

A line can be written 
f(x) = dx + e

where a, b, c, d, e are real numbers. 

Now when they intersect the two functions equal eachother. 
So: 

ax^2+bx+c = dx +e
rearrange: 
ax^2 +(b-d)x +c-e=0

Lets call b-d=f and c-e=g, (f, g are still real numbers)
We get: 
ax^2+fx+g=0
Now this is the standard form of 2nd degree polynomial. And we know that this can have 0,1,2 real solutions. 
Thus we have proven that they cannot have more than 2 points of intersection. 
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Solve.<br><br> 5x-2y&lt;10<br> I give Brainliest!
Anestetic [448]
<h2>Answer:</h2>

This is impossible to solve.

<h2>Step-by-step explanation:</h2>

For an equation or inequality to be solvable, there must be the same number of inequalities as variables. Here, there is an x and there is a y. This means that you need at least two inequalities to solve it.

You can, however, rearrange to get x or y on one side.

This can be done for x:

5x < 10 + 2y

x < 2 + 2/5y

Or it can be done for y:

5x < 10 + 2y

5x - 10 < 2y

2.5x - 5 < y

8 0
3 years ago
Find the volume of a right circular cone that has a height of 11.7 m and a base with a
yulyashka [42]

Answer:

volume of the cone = 247.98 cubic meter

Step-by-step explanation:

Height of the cone= 11.7 m

Circumference= 9 m

Radius= 9/2= 4.5 m

Volume of the cone;

            =\pi r^2\frac{h}{3}

As, \pi =\frac{22}{7}= 3.14

Putting the values in the formula:

Volume of the cone  is:

         =3.14*(4.5*4.5)*\frac{11.7}{3} \\\\=3.14*(4.5*4.5)*3.9\\\\=3.14*20.25*3.9\\\\=3.14*78.98\\\\=247.98m^3

The volume of the cone is 247.98 cubic meter

8 0
3 years ago
If it takes 5.7 gallons an hour how many cups will it take a minute
tino4ka555 [31]
1 gallon = 16 cups
1 hour   = 60 min

16 cups = 60 min
5 gallons =180 min/ 3 hrs

1 cup = 3.75 minutes
4 0
3 years ago
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How do you write 12,800 in scientific notation?
evablogger [386]

Answer:

Step-by-step explanation:

12,800 written as 1.28 x 104 in scientific notation

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I think I could be letter C
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