Answer:
Step-by-step explanation:
The quadratic equation in its standard form is:
Now, we are given 5 points of the parabola (if you graph a quadratic equation you will have a parabola), however we only need to choose three points to find the coeficients , and in the quadratic equation.
So, let's choose the first three points:
(-1,14):
(1)
(0,7):
(2)
(1,4):
(3)
Substituting (2) in (1) and (3):
(4)
(5)
At this point we have a system with two equations.
Adding (4) to (5):
(6)
Isolating :
(7)
Substituitng (7) in (3):
(8)
Isolating :
(9)
Now we have the three coeficients and we can write the quadratic equation:
Answer:
425/85*100 = 500 thus: 500-425 =75 Tickets.
Step-by-step explanation:
Answer:
75
Step-by-step explanation:
Markup:95%
find the selling price
The selling price should be $194.025.
Given that,
Based on the above information, the calculation is as follows:
= $194.025
Here we multiply the selling price with the markup percentage.
Therefore we can conclude that the selling price should be $194.025.
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Math item stem image
CLEAR CHECK
grams
The recommended daily amount of fiber is 30 grams.
Step-by-step explanation:
Quantity of fiber in one cup = 12 grams
It is 40% of our daily recommended amount.
Let,
x be the quantity of fiber recommended daily.
40% of x = 12
Dividing both sides by 0.4
The recommended daily amount of fiber is 30 grams.
Keywords: percentage, division
Learn more about percentages at:
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Linda made 72 more cards than Paul during the week.
Let :
Linda = x
Linda = x Paul = 1/3 of Linda's rate = x/3
Linda = x Paul = 1/3 of Linda's rate = x/3 Aaron = 2/3 = 2x / 3
Number of cards made by Aaron in a week = 72
This means :
2x/3 = 72
We can find x
2x = 72 × 3
2x = 216
Divide both sides by 2
x = 216 /2
x = 108
Hence, Number of cards made by Linda = 108
Recall :
Paul = x/3
Paul = 108 /3
Paul = 36 cards
Number of cards Linda makes more than Paul :
Linda's cards - Paul's cards
108 - 36 = 72 cards
Hence, Linda made 72 cards more than Paul.
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Answer:
Linda makes 72 more handmade cards than Paula
Step-by-step explanation:
First you need to find out how many handmade cards Linda makes by making a proportion.
The first ratio is 3 to 2 and since we are trying to find out how many cards Linda makes, it will be represented by x.
3 to 2 represents how many Linda makes to how many Aaron makes so the second ratio will be x to 72 since that's how many cards Aaron made.
Now you can put it into a proportion:
3/2 = x/72
Next you have to do Cross Product Property to find x
So 3*72 = 216
2*x = 2x
2x = 216
Now divide 2 by itself and then by 216 to find what x equals.
2/2 = 1
216/2 = 108
So Linda makes 108 handmade cards.
Now we need to find how many cards Paula made.
The ratio for how many Paula makes to how many Linda makes is 1 to 3
Since we are trying to figure out how many Paula made we need to represent it with x.
The second ratio will be x to 108 since 108 is how many cards Linda made.
Now you can put it into a proportion:
1/3 = x/108
Then you need to do Cross Product Property to find x
So 1*108 = 108
3*x = 3x
3x = 108
Now we need to divide 3 by itself to isolate x and then divide 3 by 108 to find what it equals.
3/3 = 1
108/3 = 36
So Paula makes 36 handmade cards.
Since the question is asking for how many more does Linda make than Paula you need to subtract 108 and 36.
So 108 - 36 = 72
Linda makes 72 more handmade cards than Paula.