answer：First, I need to evaluate the expression (frac{x^2 - 3x - 4}{x - 4}) when (x = 5).I'll start by substituting (x = 5) into the numerator and the denominator separately.For the numerator:[5^2 - 3 cdot 5 - 4 = 25 - 15 - 4 = 6]For the denominator:[5 - 4 = 1]Now, I'll divide the results:[frac{6}{1} = 6]Therefore, the value of the expression when (x = 5) is 6.

answer：First, I need to determine the total number of walnut trees in the park after the workers plant additional trees.Currently, there are 107 walnut trees in the park.The workers will plant 104 more walnut trees today.To find the total number of walnut trees after planting, I will add the current number of trees to the number of trees that will be planted.So, 107 (current trees) plus 104 (newly planted trees) equals 211.Therefore, the park will have 211 walnut trees when the workers are finished.

answer：Okay, so I have this problem here about a parabola given by the equation ( x^2 = 2py ) where ( p > 0 ). The directrix of this parabola passes through the point ( (-1, -2) ), and I need to find the coordinates of the focus. The options are A: ( (0, 2) ), B: ( (4, 0) ), C: ( (0, 4) ), and D: ( (2, 0) ).First, I remember that for a parabola in the form ( x^2 = 4py ), the focus is at ( (0, p) ) and the directrix is the line ( y = -p ). Wait, but in this problem, the equation is ( x^2 = 2py ). Hmm, so that must mean that the standard form is slightly different. Maybe I need to adjust my understanding.Let me think. If the standard form is ( x^2 = 4py ), then comparing it to the given equation ( x^2 = 2py ), I can see that ( 4p ) in the standard form is equivalent to ( 2p ) here. So, does that mean that ( 4p = 2p )? That doesn't make sense because ( p ) can't be zero. Maybe I misapplied the standard form.Wait, perhaps the standard form is ( x^2 = 4py ), so if the given equation is ( x^2 = 2py ), then ( 4p_{text{standard}} = 2p_{text{given}} ). So, ( p_{text{standard}} = frac{2p}{4} = frac{p}{2} ). So, the focus would be at ( (0, p_{text{standard}}) = (0, frac{p}{2}) ) and the directrix would be ( y = -p_{text{standard}} = -frac{p}{2} ).Got it. So, in this case, the directrix is ( y = -frac{p}{2} ). The problem states that the directrix passes through the point ( (-1, -2) ). Since the directrix is a horizontal line, its equation is ( y = c ) for some constant ( c ). In this case, we have ( y = -frac{p}{2} ).Since the directrix passes through ( (-1, -2) ), this point must satisfy the equation of the directrix. So, plugging in the coordinates into the directrix equation: ( -2 = -frac{p}{2} ). Let me solve for ( p ).Multiply both sides by -1: ( 2 = frac{p}{2} ). Then, multiply both sides by 2: ( p = 4 ).Okay, so ( p = 4 ). Now, recalling that the focus is at ( (0, frac{p}{2}) ), which would be ( (0, frac{4}{2}) = (0, 2) ). So, the coordinates of the focus are ( (0, 2) ), which is option A.Wait, let me double-check. If ( p = 4 ), then the equation of the parabola is ( x^2 = 2 * 4 * y = 8y ). So, ( x^2 = 8y ). The directrix is ( y = -frac{p}{2} = -frac{4}{2} = -2 ). That makes sense because the directrix is ( y = -2 ), which passes through the point ( (-1, -2) ). The focus is at ( (0, 2) ), which is above the vertex at ( (0, 0) ). That seems correct.Just to make sure I didn't make any mistakes, let me go through the steps again. The given equation is ( x^2 = 2py ). The directrix is ( y = -frac{p}{2} ). The directrix passes through ( (-1, -2) ), so plugging in, ( -2 = -frac{p}{2} ). Solving gives ( p = 4 ). Therefore, the focus is at ( (0, frac{p}{2}) = (0, 2) ). Yep, that all checks out.I think I got it right. The focus is at ( (0, 2) ), which is option A.

answer：First, I need to determine the total number of rows across all four baking trays. Since there are five rows on each tray, multiplying the number of rows per tray by the number of trays gives the total number of rows.Next, I'll divide the total number of cookies by the total number of rows to find out how many cookies are in each row. This will provide the number of cookies per row on a baking tray.

answer：First, I need to express all variables in terms of ( d ) to simplify the expression ( frac{a cdot c}{b cdot d} ).Given that ( c ) is five times ( d ), I can write:[c = 5d]Next, since ( b ) is three times ( c ), substituting the value of ( c ) gives:[b = 3c = 3 times 5d = 15d]Then, ( a ) is four times ( b ), so substituting ( b ) gives:[a = 4b = 4 times 15d = 60d]Now, I substitute these expressions into the original fraction:[frac{a cdot c}{b cdot d} = frac{60d cdot 5d}{15d cdot d}]Simplifying the numerator and the denominator:[frac{60d cdot 5d}{15d cdot d} = frac{300d^2}{15d^2}]Finally, dividing both the numerator and the denominator by ( 15d^2 ) gives:[frac{300d^2}{15d^2} = 20]

answer：First, calculate the cost of each item category by multiplying the quantity by the unit price.Next, sum all the individual costs to determine the total amount before any discounts or taxes.Apply the 25% discount to the total amount to find the discounted total.Calculate the 8.5% tax on the discounted total to find the tax amount.Add the tax amount to the discounted total to get the final total amount Jimmy needs to pay.Finally, subtract the final total from the 150 bill to determine the change Jimmy will receive.