When two dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Let x be the product of the numbers. Let P be the probability of the desired outcome. Compare the following charts and determine which chart shows the probability distribution for the product of the two numbers.
Chart A
x
2
3
4
5
6
7
8
9
10
11
12
Px
One-sixth
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 9 EndFraction
StartFraction 5 Over 36 EndFraction
One-sixth
StartFraction 5 Over 36 EndFraction
StartFraction 1 Over 9 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 36 EndFraction

Chart B
x
1
2
3
4
5
6
8
9
10
12
15
16
18
20
24
25
30
36
Px
StartFraction 1 Over 36 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 9 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 36 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 9 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 36 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 36 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 36 EndFraction

Chart C
x
2
3
4
5
6
8
10
12
15
18
20
24
30
Px
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 9 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 9 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 18 EndFraction

Chart D
x
1
2
3
4
5
6
8
9
10
12
15
16
18
20
24
25
30
36
Px
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction
StartFraction 1 Over 18 EndFraction

a.
Chart A
c.
Chart C
b.
Chart B
d.
Chart D

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

as, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

hope this : )

k

step-by-step explanation:

domit

if i put something wrong your not gonna like it so rather not say nothing.