The expression −5 ≤ x ≤ 34 is an inequality expression
<h3>How to draw the number line</h3>The expression is given as:
−5 ≤ x ≤ 34
This can be split as follows:
−5 ≤ x and x ≤ 34
The inequalities used in the expression are less than or equal to.
This means that the endpoints of the inequality are inclusive of the values of x.
So, the value of x starts from -5, and it ends at 34
See attachment for the number line
Read more about number lines at:
(x, y) = (7, -5)
<h3>Step-by-step explanation:</h3>It generally works well to follow directions.
The matrix of coefficients is ...
Its inverse is the transpose of the cofactor matrix, divided by the determinant. That is ...
So the solution is the product of this and the vector of constants [-6, -50]. That product is ...
... x = (3·(-6) +(-4)(-50))/26 = 7
... y = (5·(-6) +2·(-50))/26 = -5
The solution using inverse matrices is ...
... (x, y) = (7, -5)
Answer:
2. The airplane will crash into the ground after 5 seconds.
3. The domain of the function is [0,30] and range of the function is .
Step-by-step explanation:
2.
Ariana initial attempt is modeled by the function,
where, h is the height in feet and x is the time in seconds of the paper airplanes path.
If airplane crash into the ground, then ,
Equate each factor equal to 0.
Therefore the airplane will crash into the ground after 5 seconds.
3.
The height of the rocket in meters is modeled by the function shown below, where t is time in seconds.
The value of t must be positive because time can not be negative.
Find the zeros of the function.
The leading coefficient is negative, so the it is a downward parabola. Since the zeros of the function are 0 and 30, therefore the function is negative before 0 and after 30.
The height can not be negative, so the domain of the function is
The vertex of a downward parabola is the maximum point.
Vertex of a parabola,
Put t=15 it in the equation.
The range of the function is
Therefore the domain of the function is [0,30] and range of the function is .