Answers edited by CW

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• Cups A and B are cone shaped and have heights of #39 cm# and #25 cm# and openings with radii of #17 cm# and #13 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
  
• Four times the square of a non-zero number is equal to eight times the number. What is the number?
  
• How do you express #x^(1/2) / x^(1/3)# in radical form?
  
• Given an octagon inscribed in a square of side, #s# express the shaded area i terms of s? Hint the intersecting circles quarter circles have radius that are related to the diagonal of the square...
  
• How do you solve #3(6)^(2x-3)=648#?
  
• How do you find the area of #triangle RST# given t=15.7, s=15.7, #mangleR=98#?
  
• Kite ABCD has a longer diagonal AC with a length of 14 in. and a shorter diagonal BD with a length of 8 in. The diagonals intersect at point E. What is the length of BE?
  
• Find the ratio of the areas of the in-circle and circum-circle of an equilateral triangle?
  
• How do you evaluate #log_(1/3) (1/27)#?
  
• Given the radius of the circle inscribing the hexagon is #r# express the shaded area in terms of #r#?
  
• Question #ff501
  
• A triangle has corners at #(5 ,8 )#, #(3 ,9 )#, and #(4 ,7 )#. What is the area of the triangle's circumscribed circle?
  
• How do you solve #2cosx-1=0#?
  
• A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #9 # and the height of the cylinder is #6 #. If the volume of the solid is #135 pi#, what is the area of the base of the cylinder?
  
• The sum of the squares of two positive numbers is 53 and the difference of the squares of the numbers is 45. How do you find the number?
  
• Logan is flying a kite that is made up of three similar rectangles. The sides of the three rectangles are in the ratio 1:2:3. If the area of the smallest rectangle is 72 square inches, what are the areas of the other two rectangles?
  
• What is a "coming of age" novel? What does "coming of age" mean?
  
• How do you solve #3*6^(9r)=92.3#?
  
• Find the value of x for each of the given figures?
  
• The length of the table is #5# #m# greater than the width. The area is #84# #m^2#. What are the table dimensions?
  
• Question #69465
  
• A triangle has corners at #(2 , 1 )#, #(3 ,3 )#, and #(1 ,2 )#. What is the radius of the triangle's inscribed circle?
  
• Question #52a3e
  
• Circle A has a center at #(-4 ,2 )# and a radius of #3 #. Circle B has a center at #(2 ,-1 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?
  
• How do you evaluate #cos(tan^-1(1/2))# without a calculator?
  
• Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(11pi)/12 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?
  
• What is the surface area of a cylinder with a height of 9 cm and a base diameter of 10 cm?
  
• What is the distance between # (–7, 8) # and # (–5, 13) #?
  
• Question #3d939
  
• Given a square with side #s# calculate the area of the curved square, (purple shade area in the figure to the left)? The 2nd figure is to the right is sketched to help guide your thinking?
  
• How do you determine the number of possible triangles and find the measure of the three angles given #BC=12, AC=12sqrt2, mangleB=135#?
  
• You lean a 16 foot ladder against the wall. If the base is 4 feet from the wall, what angle does the ladder make with the ground?
  
• Find the area of the shade area plus the middle curved square, regions - 1, 2, 3, 4 and 5? All four circles are equal with radius r?
  
• How do you simplify #\sqrt { 225x ^ { 18} y ^ { 22} }#?
  
• Question #3144e
  
• A ranger spots a fire from a 73-foot tower in Yellowstone National Park. She measures the angle of depression to be 1°20'. How far is the fire from the tower?
  
• A rectangular field has an area of 266 square feet. The width of the garden is 14 feet. What is its length?
  
• In an isosceles trapezium diagonal is inclined at angle #45^@#with the parallel sides. The height of trapezium is 12cm. How will you find out the area of the trapezium without using trigonometry?
  
• Archimedes found found an interesting property of arbelos, that is the area of the circle whose diameter is AH and has common tangent line to the two smaller semicircles at point A is equal to the shaded area. Prove it?
  
• How do you solve #2 m + n = 0# and #m - 5 n = 22# using substitution?
  
• Circle A has a radius of #3 # and a center of #(3 ,9 )#. Circle B has a radius of #2 # and a center of #(1 ,4 )#. If circle B is translated by #<3 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
  
• Find the area of the shaded figures?
  
• How do you evaluate #log_4 128#?
  
• A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #9 #, #3 #, and #3 #, respectively. What is the rectangle's area?
  
• A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #96 #, what is the length of its longest diagonal?
  
• What is the sum of all the integers between #sqrt8# and #sqrt67#?
  
• How do you solve #\frac { 5} { 9} x = - 10#?
  
• There are 64 in a soccer tournament. Each team plays until it loses one game. There are no ties. How many games are played? You may want to draw a diagram to look for a pattern.
  
• Two circles have the following equations #(x -1 )^2+(y -4 )^2= 64 # and #(x +3 )^2+(y -4 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
  
• Question #01652
  
• How do you solve #6- 6y > 24#?
  
• What is the area, in square inches, of a regular octagon with 9-inch sides if the distance from the center to any vertex is 10 inches?
  
• Two circles have the following equations #(x +5 )^2+(y +6 )^2= 9 # and #(x +2 )^2+(y -1 )^2= 1 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
  
• How do you simplify #(\frac { 9^ { 6} } { 9} ) ^ { 2}#?
  
• A triangle has corners at #(2, 7 )#, #( 6, 3 )#, and #( 2 , 5 )#. If the triangle is dilated by # 2 x# around #(2, 5)#, what will the new coordinates of its corners be?
  
• Triangle has two sides that have lengths of 17 feet and 22 feet. Which ofthe following lengths could not represent the length of the third side?
  
• Circle A has a radius of #2 # and a center of #(1 ,7 )#. Circle B has a radius of #2 # and a center of #(8 ,1 )#. If circle B is translated by #<-4 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
  
• You are making 28 name badges for a committee. You complete 75% of these on Monday. How many do you have left to complete on Tuesday?
  
• What type of triangle is formed by joining the points D(7, 3), E(8, 1), and F(4,-1)?
  
• Question #e8728
  
• Mavis is 5 years older than her brother. Five years ago she was 2 times older than her brother. How old is each now?
  
• In a triangle, the measure of the first angle is three times that of the second angle. The measure of the third angle is 30 less than the measure of the second angle. What is the measure of each angle?
  
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