Aschool wants to put on a dance recital middle school dancers have short programs that run 4 minutes long high school performers will dance longer with longer programs 7 minutes in length the entire program cannot have more than 10 dances in the entire recital must be over in less than 90 minutes what pair of inequalities best represents the number of short middle school dances m and the number of longer high school dances h that can be performed given these limitations

 The answer is

Step-by-step explanation: Given that a school wants to put on a dance recital. The programs of Middle school dancer will be short of 4 minutes each and programmes of High school performers will be long of 7 minutes each.

Number of middle school dances is "M" and number od high school dances is "H".

Since there cannot be more than 10 dances all together, so fisrt inequality can be written as

Also, the entire recital must take maximum 90 minutes, so the second inequality can be written as

Thus, the pair of inequalities is

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w