Below are suppose the be the questions:
a. factor the equation
<span>b. graph the parabola </span>
<span>c. identify the vertex minimum or maximum of the parabola </span>
<span>d. solve the equation using the quadratic formula
</span>
below are the answers:
Vertex form is most helpful for all of these tasks.
<span>Let </span>
<span>.. f(x) = a(x -h) +k ... the function written in vertex form. </span>
<span>a) Factor: </span>
<span>.. (x -h +√(-k/a)) * (x -h -√(-k/a)) </span>
<span>b) Graph: </span>
<span>.. It is a graph of y=x^2 with the vertex translated to (h, k) and vertically stretched by a factor of "a". </span>
<span>c) Vertex and Extreme: </span>
<span>.. The vertex is (h, k). It is a maximum if "a" is negative; a minimum otherwise. </span>
<span>d) Solutions: </span>
<span>.. The quadratic formula is based on the notion of completing the square. In vertex form, the square is already completed, so the roots are </span>
<span>.. x = h ± √(-k/a)</span>
Answer:
Step-by-step explanation:
Amount of water in tank 1 = amount of water in tank 2
30t +25 = -20t + 1000
Add 20t to both sides
30t + 20t + 25 = -20t + 20t + 1000
50t + 25 = 1000
Subtract 25 from both sides
50t + 25 - 25 = 1000 - 25
50t = 975
Divide both sides by 50
t = 975/50 = 39/2
t = 19 minutes 30 seconds
After 19 1/2 minutes both tanks will have 610 liters of water
Answer:
Ratio of goat to total number of animals at the zoo = 2 : 5
Step-by-step explanation:
Chickens = 2
Deer = 4
Donkeys = 3
Goats = 6
Total animals at the zoo = 15
what is the ratio of goats to the total number of animals at the zoo?
Ratio of goat to total number of animals at the zoo = 6 : 15
= 6/15
= 2/5
Ratio of goat to total number of animals at the zoo = 2 : 5
The recipe calls for 5/8 cups butter and Angie wants to triple the recipe.
Therefore, if Angie is tripling the recipe, she is multiplying all of the ingredients in the recipe by 3.
So for the butter, this would be:
5/8 * 3 = 15/8
Next, we should turn this improper fraction into a mixed number so that we can compare it to the amount of butter that Angie has.
15/8 = 1 7/8
1 7/8 > 1 1/4
Thus, Angie DOES NOT have enough butter to triple the recipe.
We need a picture of the graph
