geometry
algebra
surprise
SURPRISE (eXtRA)
100
the circumference of a circle is 32pi. find the radius
what is "16"
C/d=pi and C=32pi.so d=32. r=16
100
factor x^3-1000
(x-10)(x^2+10x+100)
100
does the point (0, 0) satisfy the inequality x-3y>9?
what is "no"
100
if you throw a 6 with a die, what is the total of the other 4 faces?
14
200
The length of a 73 degree arc of a circle is 15. What is the circumference of the circle?
what is "75"
a 72 degree arc is 72/360=1/5 of an entire circle. since this arc has length 15, the entire circumference of the circle has length 5(15)=75
200
Jayne drove 20mph to her grandparents' house. How fast must she drive on the return trip to average 30 mph for the round trip?
40mph
200
in trapezoid ABCD, AB is parallel to CD, angle A=150, and angle B=80. find measures of angles C and D
C=100, D=30
200
Lemniscate is the correct name for what symbol?
a. pi
b. sigma
c. infinity
c. infinity
300
Chord YZ of a circle with center O has length 12. The circumference of the circle is 24pi. What kind of triangle is YOZ? What is the radius of the circle? Find the length of arcYZ
To find the length of the arc, we must find angle YOZ. We start by figuring out lengths. Since circumference is 24pi, the diameter is 24 and radius is 12. Hence, OY=YZ=ZO, so triangle YOZ is equilateral. therefore, angle YOZ is 60 degrees, and our arc is 1/6 of the circle. the length of arc YZ is (1/6)(24pi)=4pi
300
solve for x:
5x^2+59x-12=0
x=1/5, -12
300
for what values of x does the product of
(x-1)(x+2)(x-5) equal 0?
what is 1, -2, 5
300
what does the term "crore" mean?
ten million
400
Chords AB and CD of circle O have the same length. arc AB=arc CD. prove that AB=CD
form two triangles by conecting A, B, C, and D to O. Since AB=CD, AO=CO, and BO=DO, we have triangel ABO similar to triangle CDO by SSS. Therefore, angle AOB=angle COD, so arcs AB and CD are congruent
400
I have 2 cartons of eggs. 20% of the eggs in the first carton are red, while 25% of the eggs in the second carton are red. If the second carton has 3 times as many eggs as the first, what percentage of my eggs are red? (6.32)
what is : 23.75%
Suppose there are x eggs in te first carton, so there are 3x eggs in the second. since 20% of the eggs in the first carton are red, 0.2x eggs in the first carton are red. since 25% of the eggs in the second basket are red, then the second carton as 3x eggs. there are (.25)(3x)=0.75x red eggs in the second carton. therefore, out of the total x+3x=4x eggs in the two cartons, we have 0.2x+0.75x=0.95x red eggs for a total percentage of
(0.95x/4x)=0.95/4=23.75%
400
the angle bisectors of triangle ABC are perpendicular segments from G to the sides of the triangle. why is GE=GD=GF?
since G is th equidistant from the sides of triangle ABC, then GE=GD=GF
400
How much dirt is in a hole 3.5 feet wide and 89 feet deep?
none. it's a hole.
500
Anna and Betty are 180 yards apart, at points A and B in the diagram, respectively. There is a semi-circular path from Anna to Betty. Chuck is at point C, the midpoint of this path. Anna must walk to Chuck and then to Betty. How much farther must Anna walk if she follows the path if she "cuts across", walking straight to C then straight to B?
what is "90pi-180sqrt2 yards"
triangle ACB is a 45-45-90 triangle
alt:
connect C to center of circle, O. since arc AC=arc CB=90 degrees, angle AOC=COB=90. segment OA, OB, and OC are all radii of the circle, so triangle AOC and BOC are 45-45-90 triangles. since AB=180 yards, we have AO=OB=OC=180/2=90 yards and AC=BC=COsqrt2 = 90 sqrt2 yards. Since arc AB is 1/2 a circle, its length is (AB)pi/2=90pi yards. So, Anna must walk 90pi- (AC+BC)=90pi-180sqrt2 yards farter if she follows the path
500
given that 55555^2=3086358025, calculate 55556^2 without a calculator. (11.2.2)
what is "3086469136"
the difference between (n+1)^2 and n^2 is n+(n+1). therefore, to find 55556^2 given 55555^2, we simply add 55555 and 55556 to 55555^2
500
the weight of an adult male grizzly bear in the US s approximately normally distributed with mean 500lb and standard deviation of 50lb. the weight of an average female grizzly bear in the US is also approximately distributed with mean 300lb and s.d. of 40lb. what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear weighing 530 lb?
what is "324lb"
500
24(5secxtanx4(secx)+12x5-2x3)dx=
lol