Equations, Expressions, and Inequalities Q&A: Get Expert Help and Learn from Real-World Examples

Find all homomorphisms ? : Z/6Z ? Z/15Z.

There are some bicycles and tricycles beside a garden The garden attendant counted a total of 64 bicycles and tricycles.

Simplify the following exponential expression completly.
$$\frac{10x^5{y}^{\cdot <!--\; \cdot \; -->}2x^{-<!--\; -\; -->2}}{5xy}$$

The sum of the digits of a certain two-digit number is 8. When you reverse its digits you increase the number by 18. Find the number.

A system of linear equations is called homogeneous if all of the constant terms are zero. The trivial solution is obtained by assigning the value of zero to each of the variables.
a) Can a homogenous system of linear equations have no solutions?
b) Find all the values of for which the following homogeneous system has a non-trivial solution (has infinitely many solutions). Find the general solution for x,y,z and in this case.
x-2y+z=0
x+ay-3z=0
-x+6y-5z=0

Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $12,000/day to operate, and it yields 50 oz of gold and 3000 oz of silver each of x day. The Horseshoe Mine costs $14,000/day to operate, and it yields 75 oz of gold and 1000 oz of silver each of y day. Company management has set a target of at least 650 oz of gold and 18,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost?
(x,y):
what is the minimum cost?

Event B happened after event A and before event C. The elasped time between event A and event C was 10^9 seconds and the elasped time between event B and event C was 10^3 seconds. Which of the following is closet to the elapsed time, in seconds, between event A and event B? The answer is 10^9 seconds, why?

Apt a recent meeting of MLA (Math Lovers Anonymous|with its patented 12-step programme), the 12 math-lovers in the room were each asked to choose an integer between 0 and 100. The mean choice was 60. However, if it weren't for the choices of Al and Len, the group as a whole would have had a mean choice of 70. If Len's choice had been 35, what integer did Al choose?

Add. Write your answer as a mixed number in simplest form.
$5\frac{3}{4}+3\frac{2}{7}$

1. 1. Solve the system of equations
x + 8y = 8
2x - 9y = -9
2. 2. If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why.
3x - 6y = 3
9x - 18y = 6
3. 3. If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. -4x + 6y = -5
18y = -15 + 12x
4. 4. Solve the system of equations. x + y = -1
x - y = 11
5. 5. Determine whether the given ordeblack pair is a solution to the system of equations.
(1, -2)
4x + y = 2
3x + 4y = -5
6. 6. Solve the system of equations. 4x + y = -13
6x + 5y = -9

Simplify
$\frac{\frac{3}{8}-<!--\; -\; -->1}{\frac{7}{4}+1}$

$x=\frac{3}{4},y=-<!--\; -\; -->\frac{2}{3}$ Evaluate the variable expression x + y for the given values of x and y.

$(256{)}^{0.16}\times <!--\; \times \; -->(256{)}^{0.09}=?$

Suppose that the functions s and t are defined for all real numbers x as follows. s(x) = 2x - 4 t(x) = 6x. Write the expressions for (s + t)(x) and (s*t)(x) and evaluate(s - t)(-1)

(s+t)(x)=
(s*t)(x)=
(s-t)(-1)=

how many years, to the nearest year, will it take money to quadruple if it is invested at 6% compounded annually?

$\frac{1}{3}(\frac{5}{6}+\frac{1}{2})\sim <!--\; \sim \; -->(\frac{1}{3}+\frac{5}{6})+2$

Determine if the quadratic equation has a maximum value or minimum value...then determine the value
2x^2+12x-7

3/10x35/18

If f(x)=ax^2+bx+c is a quadratic function for which f(0)= -4, f(6) = -6, and f(9) = 2, find coefficients a, b, and c.

The Nuttall Company sells 4 ounce bags of cashews. The quality control department only accepts bags of cashews that contain at least 48 cashews but no more than 52 cashews. If a bag of cashews having x cashews is accepted, what is an expression that describes all the possible values of x?