

Which positive real number is equal to the quarter of its cube root?

If the points with coordinates (a , b) and (c , d) lie on the the line with equation 2 y + 3 x = 4 and a  c = 3, then what is the value
of d  b?

Given the system of equations $$\dfrac{1}{3}x^2  \dfrac{1}{3}y^2 = 7 $$
$$0.01x + 0.01y = 0.05$$
What is x  y?

Function f is given by f(x) = x ^{2} + a x + b, where a and b are real numbers. What are the values of a and b if the division of f(x) by x  1 gives a remainder equal to 2 and the division of f(x) by x + 2 gives a remainder equal to  5?

What are the values of the real numbers a, b and c if the equation  4 x(x + 5)  3(4x + 2) = a x ^{2} + b x + c is true for all values of x?

What is the simplified form of the expression x  10 + x  12 for values of x such that 10 < x < 12?

A function is defined by the formula y = (2x  1) / (x + 3). What is the value of x for y =  1 / 4?

Which of the graphs below may be that of equation 3 x + 3 y = 3?
.

Which of the graphs below may be that of equation 2 y  2 (x  2)^{2}  2 = 0?
.

What is the solution set for the equation x  3 = √x + 17?

Find the solution set for the equations x ^{2} = 7  x   10

Write the inequality 3/2 ≤ x ≤ 5/2 using one inequality symbol only.

What is the solution set for the equations (x  2)(x^{2}  7 x + 13)  x + 2 = 0?

If f is a function, which of the functions defined below must have a graph symmetric with respect the y axis?
a) g(x) = (f(x))^{2}
b) h(x) = f(x)
c) i(x) = f(x^{2})
d) j(x) = f(x)

Find all values of k for which the the equation  2 x  4  2 = k + 1 have two solutions?

Find the value of x if (x + 2)^{2} + 2(x + 2) + y =  2 and y  2 = x.

Find the ratio r = \( \dfrac{f(x + h)  f(x)}{h} \) in terms m if f(x) = m x + b , where m and b are constant real numbers.

What is the solution set for the equations \( \dfrac{2}{w + 2} = \dfrac{4}{w+3}  \dfrac{1}{3} \)?

The equations of the two parabolas shown below are of the form: y = x ^{2} + A x + B and y =  x ^{2} + M x + N. The two parabolas are tangent (touches at one point) and A  M = 2. What is the value of B  N?
.

If the lines with equations A x + B y = C and M x + N y = P are perpendicular and M / N = 5, what is the value of A / B ?

Solve for x in terms of K, L, M, N and P the equation $$\dfrac{K x  L}{M x  N } = P $$.

The square root of a real number plus twice the same number is equal to 10. What is the number?

The graph of f(x) = x^{2} + a and the line y = x  2 are shown. The two graphs intersect at a point that is on the x  axis. Find a.
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For what values of x is the function $$f(x) = \dfrac{x+2}{\sqrt{x24}} $$ not a real number?

What is the value of 0.25 x + 0.15 y if 5 x + 3 y = 2?

If the complex number (8  16i) / (2  2i) is written in the form a + ib , where i = √(1), then what is the value of b?

Given the system of equations 0.2 (x + y)^{2} = 4 and 0.5 (x  y)^{2} = 3, find the value of the product xy.

There are 200 liters of water in a tank which started leaking at the rate of 0.25 liters per minute for about one hour. Then the rate at which water is leaking from the tank increases to 0.4 liter per minute. What is the quantity q of water left in the tank t hours after the tank started leaking with t > 1?

Zoe has to write an essay of 30 pages. On average, she writes 11 pages every 2 hours and 35 minutes. Hour many hours would it take Zoe to finish the essay?Round answer to the nearest hour.

A new car was bought at $50,000. The price of the car decreased at a rate of $4000 a year for the first two years and it has been decreasing continuously at a constant rate of $6,000 since. Write a formula for the price P in $ as a function of time t in years with t = 0 corresponding 2 years after the car was bought.
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