High School Math
What are the coordinates of the intersection point(s) of the circle with the equation x²+y²=10 and the line with the equation 3x-y=-10?
(-3,1)
Consider point P with coordinates (2,-3). If point P is rotated 90° in a counter clockwise direction about the origin what are the coordinates of the image point P?
(3,2)
Adolescent weight (in pounds) are distributed with a mean of 135 and a stranded deviation of 5. If an adolescent has a weight of 122 pounds what is the standardized score (z-score) that corresponds to his weight?
-2.6
The system of equations 2x+ y+ 3z= -2 5x+ 2y = 5 2y+ 3z= -13 has a unique solution. What is the sum of the values of x, y, and z that make the solution of the system of equations?
-3
What is the simplified form of the expression 3i√2 × √-12 ?
-6√6
Consider the vector u= 9i-12j. What is the unit vector that is orthogonal to u?
-⁴/₅i-³/₅j
A golfer has a mean score of 68.04 with a stranded deviation of 2.4. Assume that his score on each round is independent of his score on any other round and that his scores are approximately normally distributed. To the nearest hundredth what is the probability that his scores on each of two consecutive rounds will be no more than 66?
.039
Let ƒ(x) = In x/x. What is ƒ'(x)?
1-In x/x²
If the volume of a sphere is 288π, what is the diameter of the sphere?
12
In the expanded form of the expression (3x+y)⁴ what is the coefficient of the term with the product xy³?
12
The sum of the lengths of the edges of a cube is 144 inches. In inches what is the length of a diagonal of the cube?
12 inches
The lengths of the bases of a trapezoid are 10 and 24. What is the length of the median of the trapezoid?
17
Consider the graph of a periodic function ƒ(x). What are the amplitude and the period, respectively of the function ƒ?
2 and π/2
Consider the ellipse with the polar equation r= 5/3+2sinθ. What is the eccentricity of the ellipse?
2/3
An airplane is flying in a horizontal path and at a height of 12,000 feet when the pilot sees a water tower on the ground. The angle of depression from the airplane to the base of the tower has a measure of 25°.To the nearest foot what is the length of the line of sight from the airplane to the base of the tower/
28,394 feet
What is an equation of the line that passes through the point with coordinates (6,2) and is perpendicular to the line with equation 3x+2y=2?
2x-3y=6
Evaluate the definite integral ∫⁶₁√x+3 dx.
38/3
The perimeters of two equilateral triangles are 6 km and 9√3 km. What is the ratio of the areas of the two triangles?
4:27
How many solutions of the equations sinθ=0 exist on the interval where 0≤θ≤4π?
5
The rate of growth of the population in a bacteria colony is proportional to the size of the population at a particular time. If the population doubles every five hours, how much time is required for the population to triple?
7.925hours
If A=[⁵₂ ⁻⁶₄], what is the inverse A⁻¹ of the matrix A?
A⁻¹=¹/₃₂[⁴-₂ ⁶₅]
What is the solution set of the inequality (x+1/6)<x-(3x-2/4)?
S={x|x>-4}
Researchers recently found evidence of a linear relationship between the weight of a truck (x, in pounds) and the distance (y in feet) that is required for a truck traveling at 40 miles per hour to come a complete stop after the driver applies the brakes. The equation of the least-squares regression line for predicting the distance based on the truck's weight is y-26+.05x. Which of the following statements in an appropriate interpretation of the value .05 in the equation?
The predicted stopping distance increases by .05 foot for each increase for one pound in the weight of a truck
What is the polar equation of the curve with the rectangular equation x+y-2=0 ?
r=2/cosθ+sinθ
What is ∫x-3/x dx?
x-3 In x+C
Solve the equation, log(3x+7) + log(x-2) =1
x=⁸/₃
Assume that x y and z represent positive numbers. If log z= ¹/₃log x+ log y what is z in terms of x and y?
y³√x
Suppose that z caries directly as the square of x and inversely as y. If z=8 when x=4 and y=6 what is z when x=6 and y=12?
z=9
Consider the equation xy²-3x=y³. When x=⁻½ and y=1 what is y'?
⁻½
