A family's monthly income is $3531. The family spends 3 over 5 of this on food. How much is spent on food.

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

Select all of the following ordered pairs that are in the solution set of the inequality shown.

Irina-Kira [14]

Answer:

points on the boundary line: (0, 10), (20, 0)
solution points not on the boundary line: (100, 100)

Step-by-step explanation:

We cannot tell from the posted picture whether the boundary line is solid or dashed, so the answer above is split into two parts. If the boundary line is solid (x+2y≥20), all three listed points are in the solution set. If the boundary line is dashed (x+2y>20), only (100, 100) is in the solution set.

8 0

3 years ago

Read 2 more answers

What is the standard form of the quadratic function that has a vertex at (3,-2) and goes through the point (4,0)?

nydimaria [60]

Answer:

2x^2 - 12x + 16

Step-by-step explanation:

5 0

3 years ago

How to I put 87×10 into scientific notation

jasenka [17]

8.7 *10^2 is the answer

8 0

3 years ago

I am very stuck with this

Bingel [31]

Answer:

see explanation

Step-by-step explanation:

To multiply the vector by a scalar, multiply each of the elements by the scalar.

To add 3 vectors add the corresponding elements of each vector

2a + 3b + 4c

= 2 $\left[\begin{array}{ccc}2\\3\\\end{array}\right]$ + 3 $\left[\begin{array}{ccc}-4\\1\\\end{array}\right]$ + 4 $\left[\begin{array}{ccc}3\\2\\\end{array}\right]$

= $\left[\begin{array}{ccc}4\\6\\\end{array}\right]$ + $\left[\begin{array}{ccc}-12\\3\\\end{array}\right]$ + $\left[\begin{array}{ccc}12\\8\\\end{array}\right]$

= $\left[\begin{array}{ccc}4-12+12\\6+3+8\\\end{array}\right]$

= $\left[\begin{array}{ccc}4\\17\\\end{array}\right]$

8 0

3 years ago