Answer:
- -5, -18
- -5x -18x
- (x -3)(6x -5)
Step-by-step explanation:
a) The factors of 90 are ...
90 = (-1)(-90) = (-2)(-45) = (-3)(-30) = (-5)(-18) = (-6)(-15) = (-9)(-10)
The sums of these factors are -91, -47, -33, -23, -21, -19.
The factor pair with the sum of -23 is of interest here. Those factors are ...
-5, -18
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b) -23x = -5x -18x
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c) The rewritten expression is ...
6x^2 -5x -18x +15
(6x^2 -5x) -(18x -15) . . . . group into pairs
x(6x -5) -3(6x -5) . . . . . . .factor each pair
(x -3)(6x -5) . . . . . . . . . . factor out the common factor (6x -5)
Answer:
In cooking (recipes).
Step-by-step explanation:
If the serving size for a recipe is not adequate for the number of people you are serving, you will have to convert the amounts(measurements) of the ingredients to suit your needs. You will do this by first creating a ratio defining the relationship between the serving size of the given recipe to the number of people needed to be served. For example, if a recipe serves 4 people, and you need to serve 8, your ratio would simplify to 1/2. This means you must proportionally relate this ratio to the individual amounts of each ingredient.
A = l × w. Substitute 72 into A and fill in the rest of the equation.
w = l - 1. Plug l - 1 into w
72 = l × (l - 1). Multiply l by (l - 1)
72 = l^2 - l. Subtract 72 from each side.
0 = l^2 - l - 72. Factor.
0 = (l + 8) (l - 9). Set each term equal to zero.
(l + 8) = 0. Subtract 8 from each side.
l = -8. Length cant be a negative number so let's try the other term.
(l - 9) = 0. Add 9 to each side.
l = 9. The length is 9.
Earlier we stated that the width is one less than the length, therefore, the width is 9 - 1 = 8.
The width is 8 units.
Answer:
3 1/3 cups of flour
Step-by-step explanation:
20/4 = 5
20 servings is 5 times 4 servings, so you need 5 times the amount of ingredients.
5 * 2/3 = 10/3 = 3 1/3
Answer: 3 1/3 cups of flour
