Explorer Level (Pre Algebra)
Solve for x: 7x-10=25
5
Jabari and Allen are having a space race in their super fast spaceships. Allen gives Jabari a 15 minute head start. If Jabari travels 14 miles per minute and Allen travels 19 miles per minute, how long (in minutes) will it take Allen to catch up with Jabari?
42
Jabari flies 12 miles north and 9 miles east to get to Allen’s house. How many miles less would it take if Jabari flew straight to Allen’s house without any turns?
6
1. Solve for x if x5 y2 = x3(2√y)4
+- 4
In which quadrant does the terminal side of θ lie, in which cosθ < 0 and tanθ > 0?
III
Determine the slope of the line given by:
y + 4 = −1/2 (x − 1)
-1/2
Log rules are used to write: 6 log 2 + 2 log 3+ log 5 as 1+ log m, find the value of m.
288
Jabari and his friend, Allen, are playing with a base converter that converts numbers to a different base. Allen inputs numbers into the converter in base 8 and the converter outputs the number in base 10. If Allen inputs 127 into the converter, what is the output?
87
Allen is pressing random keys on a funny keyboard that Jabari has aboard his spaceship to annoy him. It has 12 distinct characters and 4 other characters that appear twice each. What is the probability that Allen picks a repeated character once.
2/5
Given f(x) = 3x+4 / 2 and
g(x) = 8 + 6x,
find f(g(x)).
14 + 9x
A rectangle with an area of 168 is inscribed in a circle. If the length of the rectangle is 3 more than 3 times the width, find the area of the circle in terms of π.
625/4π
How many trailing zeros are there in the value of 2023! ?
503
The point with polar coordinates (5,π/6) can be represented in the complex plane with the equation
z = a+bi. Find a+b.
5/ 2 + (5√3)/2
Jabari went to his local space store and saw his favorite laser toy on sale for 70% off. If the laser is now $54.39, what was the original price of the laser toy?
$181.30
A rectangle with a perimeter of 92 is inscribed in a circle. If the length of the rectangle is 2 less than 2 times the width, find the area of the circle in terms of pi.
289π
Allen visited Jabari and it took him 14.92 gallons of space fuel to get to his house. If his air conditioning takes up 0.25 gallon of fuel per mile, how many gallons per mile does his spaceship take, otherwise, if the distance to Jabari’s house is 14 miles?
Find the value of x in the system of equations: 8x+y = 162x and 9x−2y = 34
-6/7
Given a triangle with side lengths 7, 9, and 11, what is the tangent of the largest angle?
√195
A rectangular prism has a length one less than twice the width and a height three more than the length. If it has a width of 5 in, what is the surface area (in square inches) of the prism?
426
Find x given:
4x −2y + z = 13, x + 4y − 4z = −9,
and − x + 2y + 4z = 21
3
Find y given:
4x −2y + z = 13,
x +4y − 4z = −9,
and − x +2y + 4z = 21.
2
Find the sum of the real roots of the equation: 333x−2 +311x+2 = 322x+1 + 1
2/11