Answer is a number
True or False
Includes a 0
Modeling
Next Step?
100
The slope of the line y=2x+10
m=2
100
The lines y=3x+5 and y=3x-5 are parallel because they both have 5s.
False. They are parallel because they both have slope 3.
100
What is the measure of every angle in a rectangle?
90 degrees.
100
The angle of elevation of the sun is 40 degrees. A shadow from a tree is 20 feet long. Draw a picture that would help find the height of the tree.
100
0.457=x/8
Multiply both sides by 8!
x= 0.457*8=3.656
200
If cos(20)=x/15, find x.
x=14.095
200
The cosine of an angle is the length of the shortest side divided by the hypotenuse.
False.
Cosine= adjacent / hypotenuse. Based on the angle, the adjacent side may not be the shortest.
200
Find the slope of the line between (4,0) and (10, 5).
m=(5-0)/(10-4)=5/6
200
A 1200m long zipline is anchored to the ground from a 300m cliff. What is the angle of depression from the cliff down to the zipline anchor?
14.5 degrees. The angle of depression is equal to the angle of elevation from the anchor. So opp=300 and hyp=1200.
sin(\theta)=300/1200=0.25 so
\theta = \sin^(-1)(0.25)=14.5^\circ
200
x^2+10x+y^2-12y=-2
Take 10/2, square it, add to both sides (so, add 25 to both sides).
Take -12/2, square it, add to both sides (so, add 36 to both sides).
x^2+10x+25+y^2-12y+36=-2+25+36
300
If an angle in a right triangle has opposite side 30 and adjacent side 40, then what is the measure of the angle to the nearest degree?
37 degrees.
\tan(\theta) =30/40 so \theta=\tan^(-1) (30/40)=36.87^\circ
300
If a quadrilateral has two pairs of parallel lines, it can't be a square.
False! It may be a square, IF, adjacent sides have opposite reciprocal slope to make all angles right angles, AND if all sides have the same length
300
In a right triangle with hypotenuse 50 and one side with length 30, what is the length of the third side?
40 units.
a^2+b^2=c^2
30^2+b^2=50^2 so b^2=2500-900=1600 which means
300
If I set up a rotating sprinkler at the point (1,3) in the plane, and its arm is 4 feet long, What equation of a circle would show me the points the sprinkler arm will reach?
(x-1)^2+(y-3)^2=16 because 16=4^2!
300
know: adjacent=25 , angle = 31.
Want: opposite
tan(31) = x/25
Evaluate tan(31).
Then multiply both sides by 25!
400
Every line perpendicular to the line through the points (4,8) and (7, -7) has this slope.
What is 1/5?
Since the original line has slope m= (-7-8)/(7-4)=-15/3=-5 we need the opposite reciprocal slope for the perpendicular line, which is -1/m= (-1)/(-5)=1/5
400
The length of the segment between (2,7) and (-1, 3) is 5.
True. \sqrt( \(x_1-x_2)^2+(y_1-y_2)^2 = \sqrt( \(2--1)^2+(7-3)^2 = \sqrt(3^2+4^2)=\sqrt25=5
400
Find the center and radius for
x^2+40x+y^2+100=0
x^2+40x+400+y^2=300 so
(x+20)^2+(y-0)^2=300
Center is (-20, 0) and radius is \sqrt 300
400
A ladder leans against a wall.
The ladder is 30 feet long. The angle the ladder makes with the wall is 27 degrees. How far away is the base of the ladder from the base of the wall?
\sin (27)= x/30 since the angle between the ladder and the wall will be opposite the ground.
0.454=x/30 so x=0.454*30=13.62 feet
400
I have calculated that the lengths of AB, BC, CD, and AD are all the same.
I also know the slopes of AB and CD are both 4/3.
What is the next step if I need to show that ABCD is a square?
Show the slopes of BC and AD are both -3/4, so they are opposite reciprocal to the other slopes.
That makes the sides meet at right angles, so you've got a rectangle with all sides the same, which is a square.
500
When we complete the square for the circle with equation, first we will subtract 40 from both sides, then we will add what number to both sides?
x^2+y^2-18y+40=0
81.
Explanation: Since we have just x^2 we don't have to complete the square on this part, but the y^2-18y needs to be completed. -18/2=-9. (-9)^2=81, so we add 81 to both sides. Our final equation is x^2+(y-9)^2=41 so the center is (0, 9) and radius is \sqrt41
500
If cos (x)=0.4 and sin(y)=0.4 then x+y=90.
True! In any triangle, the cosine of one acute angle is the sine of the other one, so if one angle has the same cosine as the other's sine, the two angle measures will add to 90 degrees.
500
What is the angle of elevation to the top of a 500m building from a person sitting on the ground 800m away from the front of the building?
\tan^{-1)(500/800)=32^\circ
500
Draw a right triangle with a 34 degree angle and adjacent side of 20.
Then find the length of the hypotenuse.
Hypotenuse = 24.12
500
I have points A (1,7) B( 4, 12) , C(7, 5) and D(10, 10).
I found the slope of AB is 5/3. What is my next step if I want to show ABCD is a parallelogram?
Show that side CD is parallel to AB by computing its slope.
(10-5)/(10-7)=5/3 also!
Now check the slopes for BC and AD.