What is the equation of a line that passes through (-1, 2) and (5, 2)?

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.

Lets simplify the given problem,

If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

1070 =[n - 2] x 180, where n = number of sides

$1070 =180n - 360180n =1070+360180n =1430n = 1430 / 180$

n = 7.94 number of sides. Since this is not a whole number, will simply round it up to 8.

Hence the number of sides is 8

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5 0

2 years ago

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Consider the cubic function f(x) = x^3 + ax^2 + bx + 4 where (a) and (b) are constants. When f(x) is divided by x-3, the remaind

Debora [2.8K]

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

8 0

3 years ago

The amount of time, in minutes, that a woman must wait for a cab is uniformly distributed between zero and 12 minutes, inclusive

murzikaleks [220]

Answer:

$P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b$

And using this formula we have this:

$P(X$

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Step-by-step explanation:

Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:

$X \sim Unif (a=0, b =12)$

And we want to find the following probability:

$P(X$

And for this case we can use the cumulative distribution function given by:

$P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b$

And using this formula we have this:

$P(X$

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

7 0

3 years ago