MCAS Mondays
The equation of line f is y=2 and the equation of line g is y=2x-1.
Write an equation of a line that is parallel to f that passes through P=(-2,-1).
y=-1
A right triangle has sides opposite, adjacent, and hypotenuse in relation to an angle theta. Please state the 3 trig functions as ratios of those three side lengths.
CAH
TOA
If you live in L.A., then you live in California.
Is the converse of this statement true?
No!
Triangle ABC is isosceles with AB=BC, and angle BAC=56 degrees. Find the remaining two angles of this triangle.
68
56
Construct a 45-45-90 triangle using the side length "x".
x-x-xsqrt(2)
Solve for s (Ms. Toupin will draw the construction on the board).
s=18
Standing 40 meters from the base of a flag pole, Nina used a protractor to measure an angle of elevation of 33 degrees to the top of the pole. How tall was the pole?
25.9 meters
Please solve the problem written on the board!
How do you know?
x=122
y=58
z=122
An airplane reaches an altitude of 9000 meters and then begins to descend at a constant rate of 625 meters per minute.
Write an equation that can be used to determine y, the altitude of the airplane after x minutes.
y=-625x+9000
Construct a 30-60-90 triangle where the shortest side length is "x".
x-xsqrt(3)-2x
Find the length of f (Ms.Toupin will draw the construction on the board).
13sqrt(3)
A mega chicken casts an eight-foot shadow. How high is the sun in the sky?
32 degrees.
What is the measure of each interior angle of an octagon?
135 degrees.
The lines defined by P=(4+5t, -1+2t) and Q=(4-2u,-1+5u) intersect perpendicularly. Justify this statement. What are the coordinates of the point of intersection.
(4,-1)
Find the altitude of an equilateral triangle with side lengths of 6.
3sqrt(3)
Give the following x values that make the equation true:
5x-1=x2+2x+1
x=1; x=2
Out for a walk in Boston, Ms. Toupin measures the angle of elevation to the distant Prudential Tower and gets 2.4 degrees. After walking two km directly towards the building, she finds that the angle of elevation has increased to 5 degrees. Calculate the height of the Pru (not accurate height).
x=3.839km
Solve for y (the problem is drawn on the board by Ms. Toupin)
y=55
Find the solution to the system of equations:
4x+9y=10
2x+3y=30
x=25
y=-10
WITHOUT CHECKING GOOGLE CLASSROOM: What have our three mathematicians of the month been this year?
Alan Turing, Vi Hart, and Benjamin Banneker
Each exterior angle of a regular polygon has a measure of 20 degrees. What is the number of sides of the polygon?
18 sides
Ms. Toupin and her dogs leave her house and go for a long walk. After going 6 km due east, they turn and go another 10km in the direction 30 degrees north of east. They plan to return along a straight path. How far from her house are they at this point? Use an angle to describe the direction that Ms. Toupin and her dogs should follow to get home again.
Walk is about 12.38 km home at 11 degrees southwest.
Prove the converse of:
If the diagonals of a quadrilateral bisect each other, then the figure is a parallelogram.
Proof using two parallel lines cut by a transversal- alternate interior angles must be equal. Then ASA since opposites sides of a parallelogram are congruent. Finish with CPCTC for diagonals are equal length (aka bisected).
Triangle LMN is similar to triangle XYZ. This diagram (drawn by Ms. T on the board) shows some of the dimensions, in units, of the triangles. Based on the diagram, what is the length in units of XZ?
24
What are three accomplishments of Benjamin Banneker's life?
So many to choose from!
*First ticking clock in US
*Planned Washington D.C.
*Wrote Scientific Almanac
*Wrote the first civil rights activism letter (to Thomas Jefferson)
*Predicting solar eclipses
etc. etc. etc.