Slope through two points

Find the slope of a line that passes through the points (3,−26)and (8,19).

X-intercept of a line

What is the x-intercept of the line y=2x−96?

The y-intercept

What is the y-intercept of the line with slope m=1 that passes through the point (19, 33)?

Minimario's diagonal

Let ABCD be a square with side length 2 and let X be a point outside the square such that XA=XB=2√. The length of the longest diagonal in pentagon AXBCD can be expressed as x√. What is the value of x?

Maximizing Rectangle Area

A rectangle has perimeter equal to 28. What is the maximum possible area of this rectangle?

Area of Inscribed Isosceles Triangle

ABC is an isosceles triangle with AB=BC. The circumcircle of ABC has radius 8. Given that AC is a diameter of the circumcircle, what is the area of triangle ABC?

Details and assumptions

The circumcircle of a triangle ABC passes through A,B,C.

Angles in a Acute Triangle

In acute triangle △ABC, ∠CAB=34∘ and E is the foot of the perpendicular from B to AC. A point H on line segment BE is chosen, and X is the foot of the perpendicular from H to AB. What is the measure (in degrees) of ∠EHX?

Calvin the Cat man

Calvin has 3 cats. The oldest cat Heathcliff is 16 years old. The mean age of the cats is 10. The median age of the cats is 8. What is the age of the youngest cat?

Possible Test Scores for a grade of B

You are taking a Math class, where your grade is determined by your performance in 5 tests. The maximum score on each test is 100. Your first 4 test scores have been 63,80,90 and 85. To receive a B in the class, the average of the five test scores must be greater than or equal to 80 and strictly smaller than 90. If only integer test scores are allowed, how many different test scores could you receive for the last test and get a grade of B?

Trip Expenses

A group of friends are planning a road trip. If they all contribute $24, then they would be $6 short of the total cost of the trip. If they all contribute $25, then they would have $3 more than the total cost of the trip. What is the total cost of the trip?

Pity the frog

A frog is stuck at the bottom of a man-made well which is 21 feet deep. Each day, the frog is able to climb up 5 feet. However, each night, the frog slides down 3 feet. On which day would the frog be able to escape this well?

Find that remainder!

What is the remainder when 4321 is divided by 321?