An ice cream store sells 4 drinks, in 5 sizes, and 6 flavors. In how many ways can a customer order a drink

Which of the following is not a possible number of solutions when solving a system of equations containing a quadratic and a lin

Kobotan [32]

Answer:

3

Step-by-step explanation:

We have a system with two equations, one equation is a quadratic function and the other equation is a linear function.

To solve this system we have to clear "y" in both equations, and then equal both equations, then we will have a quadratic function and equal it to zero:

$ax^2+bx+c=0, a\neq 0$

Then to resolve a quadratic equation we apply Bhaskara's formula:

$x_{1}=\frac{-b+\sqrt{b^2-4ac} }{2a}$

$x_{2}=\frac{-b-\sqrt{b^2-4ac} }{2a}$

It usually has two solutions.

But it could happen that $\sqrt{b^2-4ac}$ then the equation doesn't have real solutions.

Or it could happen that there's only one solution, this happen when the linear equation touches the quadratic equation in one point.

And it's not possible to have more than 2 solutions. Then the answer ir 3.

For example:

In the three graphs the pink one is a quadratic function and the green one is a linear function.

In the first graph we can see that the linear function intersects the quadratic function in two points, then there are two solutions.

In the second graph we can see that the linear function intersects the quadratic function in only one point, then there is one solutions.

In the third graph we can see that the linear function doesn't intersect the quadratic function, then there aren't real solutions.

7 0

3 years ago

2sin^2 2x=2 In the domain [0,2pi) What can x equal ( in radians).

lions [1.4K]

Bear in mind that, when it comes to trigonometric functions, the location of the exponent can be a bit misleading, however recall that sin²(θ) is really [ sin( θ )]²,

$\bf 2sin^2(2x)=2\implies sin^2(2x)=\cfrac{2}{2}
\\\\\\
sin^2(2x)=1\implies [sin(2x)]^2=1\implies sin(2x)=\pm\sqrt{1}
\\\\\\
sin(2x)=\pm 1\implies sin^{-1}[sin(2x)]=sin^{-1}(\pm 1)$

$\bf \measuredangle 2x=sin^{-1}(\pm 1)\implies \measuredangle 2x=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}\\\\
-------------------------------\\\\
\measuredangle 2x=\cfrac{\pi }{2}\implies \measuredangle x=\cfrac{\pi }{4}\qquad \qquad \qquad \qquad \measuredangle 2x=\cfrac{3\pi }{2}\implies \measuredangle x=\cfrac{3\pi }{4}$

3 0

3 years ago

Riverside Elementary School is holding a school-wide election to choose a school color. Five eighths of the votes were for blue,

liberstina [14]

First read it little by little like I did : )

3 0

3 years ago

Read 2 more answers

Find the value of x and y from ordered pair. （x+y,2x-y）=（13,2）

Katarina [22]

Answer:

x=5, y=8