EOC #16-30 Math III

The graph of the function is shown.

Place (click and drag) each interval into the column that describes the function on that interval. ​Increasing, Decreasing, Positive Negative, in that order. ​

​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ (a)   ​ ​ (b)   ​ ​ (c)   ​ ​ (d)  

A function is shown.

$$H\left(x\right)=4x^3-5x^2-23x+6$$

What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?

(a)  

Which function does not have the set of all real numbers as its domain?

An equation is shown below.

$$9^{-3x+2}=48$$

What is the value of x to the nearest ten-thousandth?

The diagram below shows an angle, θ, graphed in the xy-coordinate plane. Segment RT is the initial side of the angle, and segment RM is the terminal side. Segments RT and RM are radii of the unit circle centered at the origin R(0, 0).

The x-coordinate of point M is $$-\frac{1}{2}$$ . What is the measure of $$\theta$$ to the nearest thousandth of a radian?

A function, f(x)=Asin(Bx)+H, has the following properties:

~a period of 6,​

~a minimum value of 2,

~f(2.5)=5, and

~A, B, and H are all positive constants.

Place (click and drag) values in the appropriate cells below that create this function.​​ (a)   ​ (b)   ​ (c)  

The vertices of a triangle are at (0, 0), (6, 6), and (9, 3). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x?

In parallelogram MNPT, $$m\ \angle M\ =\left(6x+10\right)\degree$$ and $$m\ \angle N\ =\ \left(5x+10.5\right)\degree.$$ How many degrees is $$\angle T?$$

(a)  

In rectangle FGHI, diagonals $$\overline{FH}$$ and $$\overline{GI}$$ intersect at E.

~IE= 3x+4

~EG= 5x-6

What is the length of $$\overline{FH}$$ ?

Triangle PMT is shown,

What is the measure of segment PG?