[数学 ]【新版】冲分救命题 -12081

In the xy-plane (not shown), a right triangle has its right angle at the origin and has its hypotenuse along the line y=7x-1. If none of the sides of the triangle are vertical, what is the product of the slopes of the three sides of the triangle?

[数学 ]【新版】冲分救命题 -12080

The sum of the consecutive odd integers from 3 to 97, inclusive, is equal to

[数学 ]【新版】冲分救命题 -12079

When 2(10100 ) + 1 is divided by 3, the remainder is r.

[数学 ]【新版】冲分救命题 -12078

n is a positive integer.

[数学 ]【新版】冲分救命题 -12077

When the positive integer x is divided by 42, the remainder is 19. What is the remainder when x is divided by 7?

[数学 ]【新版】冲分救命题 -12076

[数学 ]【新版】冲分救命题 -12075

.The length of a rectangular rug is 3 times its width, and the area of the rug is between 24 square feet and 63 square feet. Which of the following values could be the perimeter of the rug, in feet? Indicate all such values.

[数学 ]【新版】冲分救命题 -12074

In the triangle shown above, x

[数学 ]【新版】冲分救命题 -12073

[数学 ]【新版】冲分救命题 -12072

In the figure above the circle has center O, and AB and AD are tangent to the circle. If the degree measures of angles ABC and ADC are 20 and 40, respectively, what is the value of x+y?

[数学 ]【新版】冲分救命题 -12071

Square DEFG is inscribed in isosceles right triangle ABC. If the area of triangular region ABC is r, what is the area of triangular region AFE?

[数学 ]【新版】冲分救命题 -12070

The figure shows a right circular cone, where A is the center of the circular base. If the measure of angle ACB is 30°and the length of line segment BC is 2, what is the volume of the cone? (The volume of a right circular cone is one-third of the product of the height of the cone and the area of the circular base.) Give your answer to the nearest whole number.

[数学 ]【新版】冲分救命题 -12069

The solid shown consists of five cubes, each with a volume of 27,that are joined so that four pairs of faces coincide.

[数学 ]【新版】冲分救命题 -12068

The figure shown consists of three semicircles with diameters AB, BC, and AC, where B is the midpoint of AC. If the area of the shaded region is 48π, what is the length of AC?

[数学 ]【新版】冲分救命题 -12067

If the trapezoid above is composed of three equilateral triangles, each having area , what is the area of rectangular region ABCD?

[数学 ]【新版】冲分救命题 -12066

Let g be the function defined for all numbers x such that g(x)is the greatest integer that is less than or equal to x. If g(x)=-3, which of the following could be the value of x? Indicate all such values.

[数学 ]【新版】冲分救命题 -12065

campaign director can divide the campaign workers into 10 or 11 teams. When the workers are divided into 11 teams, each of 10 of the teams has x workers and 1 team has 6 workers. When the workers are divided into 10 teams, each of 9 of the teams has x+1 workers and 1 team has 5 workers. How many campaign workers are there?

[数学 ]【新版】冲分救命题 -12064

Signs A, B, and C are positioned on a 1,000-meter-long airplane runway. Sign A is 100 meters from the beginning of the runway and it followed by sign B and C in that order. The distance between sign B and sign C is 120 meters more than twice the distance from sign C to the end of the runway. The distance between sign A and sign B is 1/2 the distance between sign B and sign C. What is the distance, in meters, from sign C to the end of the runway?

[数学 ]【新版】冲分救命题 -12063

Signs A, B, and C are positioned on a 1,000-meter-long airplane runway. Sign A is 100 meters from the beginning of the runway and it followed by sign B and C in that order. The distance between sign B and sign C is 120 meters more than twice the distance from sign C to the end of the runway. The distance between sign A and sign B is 1/2 the distance between sign B and sign C. What is the distance, in meters, from sign C to the end of the runway?

[数学 ]【新版】冲分救命题 -12062

A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?