Start by simplifying each expressions by factoring
There are 4 king and 4 eight cards inside 52 one deck of cards. The case asks for a king card and then an eight card.
To draw the king card, you have 4/52 probability.
To draw the eight card, you have 4/51 probability ( since the king card not replaced).
The total probability would be: 4*4/ 52*51= 4/663
Step-by-step explanation:
the easiest approach with a given point and the slope of the line is the point-slope form :
y - y1 = a(x - x1)
where "a" is the slope, and (x1, y1) is a point on the line.
so, we get
y - -8 = 4(x - -3)
y + 8 = 4(x + 3)
if we need the slope-intercept form
y = ax + b
we now simplify the point-slope form
y + 8 = 4x + 4×3 = 4x + 12
y = 4x + 4
To solve for x:
Move all the terms containing "x" to the left side of the equation. Do this by adding x to both sides.
2x+x=3x. The new equation is:
3x-1/2=3
Now, move all terms not containing "x" to the right side of the equation. Do this by adding 1/2 to both sides.
3x=3+1/2 The new equation is:
3x=3 1/2, or 3.5
The final step is to isolate x. To do so, divide each side by 3.
3x/3 = 3 1/2 /3 The new equation is:
x=1 1/6
Answer:
A. 2·x² + 16·x + 32 ≥ 254
Step-by-step explanation:
The given dimensional relationship between the dimensions of the photo in the center of the cake and the dimensions of the cake are
The width of the cake = The width of the photo at the center of the cake, x + 4 inches
The length of the cake = 2 × The width of the cake
The area of the cake Wanda is working on ≥ 254 in.²
Where 'x' represents the width of the photo (at the center of the cake), let 'W' represent the width of the cake, let 'L' represent the length of the cake, we get;
W = x + 4
L = 2 × W
Area of the cake, A = W × L ≥ 254
∴ A = (x + 4) × 2 × (x + 4) = 2·x² + 16·x + 32 ≥ 254
The inequality representing the solution is therefore;
2·x² + 16·x + 32 ≥ 254
