What is the point y=3x-13

The equation for a parabola has the form y = ax^2 + bz + c, where a, b, and c are constants and aメ0. Find an equation for the pa

vova2212 [387]

Answer:

a = 2, b = -9, c = 3

Step-by-step explanation:

Replacing x, y values of the points in the equation y = a*x^2 + b*x +c give the following:

(-1,14)

14 = a*(-1)^2 + b*(-1) + c

(2,-7)

-7 = a*2^2 + b*2 + c

(5, 8)

8 = a*5^2 + b*5 + c

Rearranging:

a - b + c = 14

4*a + 2*b + c = -7

25*a + 5*b + c = 8

This is a linear system of equations with 3 equations and 3 unknows. In matrix notation the system is A*x = b whith:

A =

1 -1 1

4 2 1

25 5 1

x =

a

b

c

b =

14

-7

8

Solving A*x = b gives x = Inv(A)*b, where Inv(A) is the inverse matrix of A. From calculation software (I used Excel) you get:

inv(A) =

0.055555556 -0.111111111 0.055555556

-0.388888889 0.444444444 -0.055555556

0.555555556 0.555555556 -0.111111111

inv(A)*b

2

-9

3

So, a = 2, b = -9, c = 3

5 0

2 years ago

Dwayne has a wrench set with the socket sizes of 1, 1/2, 1/4, 1/8, 1/16 what would the next size be?

lukranit [14]

Notice that the denominator is a multiplied by 2 for each fraction.

1/1•2 = 1/2

1 /2•2 = 1/4

1/4•2 = 1/8

1/8•2 = 1/16

1/16•2 =1/32

The next size is 1/32.

8 0

2 years ago

Use the drop-down menus to complete the statements about Euler's life after he lost his sight. After the cataract took Euler's s

mote1985 [20]

About 450 books and articles Euler completed after he lost his sight entirely.

<h3>Who was Leonhard Euler?</h3>

Leonhard Euler was a mathematician from Switzerland. He introduced the fundamentals of graph theory and topology.

His main field of work includes number theory, mechanics, fluid mechanics, and many more.

The life span of Euler was between 1707 and 1783. In the last few years of his life, he lost the eye sight. But the eye sight loss doesn't affect him from doing his work. In his lifespan, he published around 886 books and articles on various fields or science, mathematics and engineering.

After the total blindness, he published more than 450 books and articles.

For more details about Euler, refer to the link:

brainly.com/question/573685

8 0

1 year ago

A construction company is considering submitting bids for contracts of three different projects. The company estimates that it h

julsineya [31]

Answer:

a. $P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

b. $E(x) = 0.3$

c. $S(x)=0.5196$

d. $E=5,000$

Step-by-step explanation:

The probability that the company won x bids follows a binomial distribution because we have n identical and independent experiments with a probability p of success and (1-p) of fail.

So, the PMF of X is equal to:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

Where p is 0.1 and it is the chance of winning. Additionally, n is 3 and it is the number of bids. So the PMF of X is:

$P(x)=\frac{3!}{x!(3-x)!}*0.1^{x}*(1-0.1)^{n-x}\\$

For binomial distribution:

$E(x)=np\\S(x)=\sqrt{np(1-p)}$

Therefore, the company can expect to win 0.3 bids and it is calculated as:

$E(x) = np = 3*0.1 = 0.3$

Additionally, the standard deviation of the number of bids won is:

$S(x)=\sqrt{np(1-p)}=\sqrt{3(0.1)(1-0.1)}=0.5196$

Finally, the probability to won 1, 2 or 3 bids is equal to:

$P(1)=\frac{3!}{1!(3-1)!}*0.1^{1}*(1-0.1)^{3-1}=0.243\\P(2)=\frac{3!}{2!(3-2)!}*0.1^{2}*(1-0.1)^{3-2}=0.027\\P(3)=\frac{3!}{3!(3-3)!}*0.1^{3}*(1-0.1)^{3-3}=0.001$

So, the expected profit for the company is equal to:

$E=-10,000+50,000(0.243)+100,000(0.027)+150,000(0.001)\\E=5,000$

Because there is a probability of 0.243 to win one bid and it will produce 50,000 of income, there is a probability of 0.027 to win 2 bids and it will produce 100,000 of income and there is a probability of 0.001 to win 3 bids and it will produce 150,000 of income.

5 0

2 years ago

Find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)<br>

elena55 [62]

Answer:

Hello

Step-by-step explanation:

The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1

and the disk ? (inside of a circle) of center (0,0) and radius 2

$dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\$

3 0

2 years ago