A negative number plus another negative number equals a positive number. True False

A spinner with 6 equally sized slices has 1 blue slice, 2 red slices, and 3 yellow slices. The dial is spun and stops on a slice

Darya [45]

Answer:

1/2

Step-by-step explanation:

Step one:

given data

sample space

1 blue slice,

2 red slices, and

3 yellow slices

sample size= 1+2+3= 6

Required:

The probability that the dial stops on a blue or red slice

1. The probability that the dial stops on a blue = 1/6

2. The probability that the dial stops on a red= 2/6= 1/3

Hence The probability that the dial stops on a blue or red= 1/6+1/3

= 1+2/6

=3/6

=1/2

4 0

3 years ago

1.Write the equation for an ellipse with vertices (–4, 2), (2, 2), (–1, –2) and (–1, 6).

Nimfa-mama [501]

The general equation of an ellipse:
$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1
$

we have vertices (–4, 2), (2, 2), (–1, –2) and (–1, 6).⇒⇒⇒ red points
by graphing the points ⇒⇒⇒ attached figure 1
the majority axis is the line connecting (–1, –2) and (–1, 6) and has a distance = 8
the minority axis is the line connecting (–4, 2), and (2, 2) and has a distance = 6
(h,k) represents the center of ellipse which is the intersection between axes
∴(h,k) = (-1,2)
and a = 3 , b = 4
∴ the equation of the ellipse is

$\frac{(x+1)^2}{9} + \frac{(y-2)^2}{16} =1
$
=========================================================

A hyperbola with vertices (9, 3) and (5, 3) ⇒⇒⇒⇒ blue points
and with foci (11, 3) and (3, 3). ⇒⇒⇒⇒ red points
by graphing the points ⇒⇒⇒ attached figure 2
so, the hyperbole axis is horizontal
(h,k) represents the center of hyperbola = (7,3) ⇒⇒⇒ green point
a = distance between center and any of vertices = 7 - 5 = 2
c = distance between center and any of foci = 7 - 3 = 4
∵ c² = a² + b²
∴ b² = c² - a² = 16 - 4 = 12
the general equation of the hyperbole :
 $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} =1
$
the equation of the hyperbole will be
 $\frac{(x-7)^2}{4} - \frac{(y-3)^2}{12} =1
$