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lesya [120]
4 years ago
8

Find the equation of the parabola that passes through the points: (0,5) (1,7) (-2,19)

Mathematics
2 answers:
Ymorist [56]4 years ago
3 0

Answer:

y= 3x^2 - x+5

Step-by-step explanation:

hope that helps

Lubov Fominskaja [6]4 years ago
3 0

Answer:

y=3x^{2} -x+5

Step-by-step explanation:

The general form of a parabola is

y=ax^{2} +bx+c

Now, we have three points, where each of them gives values for (x,y). We can use them to create a system of three equations with three unknown variables

5=c\\7=a(1)^{2} +b(1)+c\\19=a(-2)^{2} +b(-2)+c

Then, we replace the value of c in the second and third equation to find create an equation with only two variables

7=a+b+5\\19=4a-2b+5

2=a+b\\14=4a-2b

Then, we multiply the first equation by 2, and sum both equations

4=2a+2b\\14=4a-2b

18=6a\\a=\frac{18}{6}\\ a=3

Finally, we use this value to find b

2=a+b\\2=3+b\\b=2-3\\b=-1

Therefore, the equation of the parabola is

y=ax^{2} +bx+c\\y=3x^{2} -x+5

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If a car dealership buy as car for $9000, and wants to make a 45% profit, how much do they need to sell the car for? ​
Degger [83]

Answer:

A car dealership needs $13050 to sell the car to earn the 45% profit if a car dealership buys a car for $9000.

Step-by-step explanation:

Car cost = $9000

Profit percentage = 45% profit

Thus,

Profit amount = 45% of 9000

                       = 45/100 × 9000

                       = 0.45 × 9000

                       = $4050

In order to determine how much a car dealership needs to sell the car to earn the 45% profit, all we need is to add the profit amount i.e. $4050, and the car cost i.e. $9000.

i.e.

Car cost + Profit amount = $9000 + $4050

                                         = $13050

Therefore, a car dealership needs $13050 to sell the car to earn the 45% profit if a car dealership buys s car for $9000.

6 0
3 years ago
Evaluate the following expression. [4 + (12 - 2) ÷ 5] ÷ 7
Anika [276]

Answer:

[4 + (12 - 2) ÷ 5] ÷ 7

[4 + 6 / 5] / 7

[10 / 5] / 7

2 / 7

= 2/7 or 0.28571428571

7 0
3 years ago
Read 2 more answers
Identify the subsets of real numbers to which the number 25√ belongs.
Radda [10]
It would be rational
8 0
3 years ago
Read 2 more answers
PLEASE HELP URGENT
ad-work [718]
Pick - d. 51 minutes
8 0
3 years ago
PLEASE HELP THIS IS A TIMED QUESTION ON A QUIZ!!!
pantera1 [17]

Answer:

  • a)  11, d) 25, e) 14, b) 25, c) 28, f) 33

Step-by-step explanation:

<h3>Given</h3>
  • ΔBDF, with H is the centroid of BDF, DF = 50, CF = 42, and BH = 22
<h3>To find</h3>
  • HE , DE , CH, EF,  HF, BE
<h3>Solution</h3>

As per definition of the centroid, the points C, E and G are midpoints of respective sides and the length of short and long distances from the centroid have ratio of 1/3 and 2/3 of median

  • a) HE =  1/2BH = 1/2(22) = 11
  • d) DE =  1/2DF = 1/2(50) = 25
  • e) CH =  1/3CF = 1/3(42) = 14
  • b) EF =  DE = 25
  • c) HF =  2/3CF = 2/3(42) = 28
  • f) BE =BH + HE = 22 + 11 = 33
3 0
3 years ago
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