Answer:
x = (1/2) (-9 ± √73)
Step-by-step explanation:
Using completing the square method
x²+9x+2=0
x²+9x = -2 (complete the square by adding (9/2)² to both sides)
x²+9x + (9/2)² = -2 + (9/2)²
( x + (9/2) )² = -2+ (9/2)²
( x + (9/2) )² = -2+ (81/4)
( x + (9/2) )² = 73/4
x + (9/2) = ± √(73/4)
x + (9/2) = ± √(73) / 2
x = -(9/2) ± √(73) / 2 (factorize out (1/2) )
x = (1/2) (-9 ± √73)
Answer:
Part 9) The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13
Part 10) The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot
Step-by-step explanation:
Part 9)
Let
x ----> number of items on Emily's grocery list
x ----> number of items on Bobby's grocery list
we know that
----> equation A
----> equation B
Solve by substitution
Substitute equation A in equation B

solve for x



Find the value of y

therefore
The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13
Part 10)
Let
x ----> the height of the taller bookshelf in feet
y ----> the height of the shorter bookshelf in feet
we have
----> equation A
Remember that

To convert inches to feet divide by 12
so

----> equation B
Solve the system by substitution
substitute equation A in equation B
solve for y
Find the value of x

therefore
The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot
Answer:
Step-by-step explanation:
The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.
Answer:
|–4| < |–8|, |–5| > 1, |–2| = |2|
Step-by-step explanation: