Answer:
Sample Space = {A, B, C, D, E, F}.
Sample space for choosing C to F = {C, D, E, F}.
Step-by-step explanation:
All six letters are included in the first set of possible outcomes.
Four letters (C to F) are included in the second set of possible outcomes.
Answer:
HL Theorem
Step-by-step explanation:
Here, we see that both triangles have a right angle, making them right triangles. We know that the hypotenuse must be equivalent, as it is the same line. Furthermore, we see that one of the legs from each triangle are equivalent. Therefore, we can use HL Theorem to prove these triangles are equal.
Answer:
the y-intercept is -1, or (0, -1)
Step-by-step explanation:
Identify the coordinates of the point where the line crosses the y-axis. They are (0, -1), and so the y-intercept is -1, or (0, -1).
2l+2w=24
l=3+w
The first equation comes from the perimeter formula. Since it is a rectangle, there are two lengths and two widths, which must all be added to get the perimeter. The second equation shows that the length is equal to the width plus three. In order to solve this equation, the substitution method should be used, since the one equation is already set equal to one of the variables (L)
2l+2w=24
l=3+w
2(3+w)+2w=24
Use distributive property to get rid of the parentheses
2(3+w)+2w=24
2(3)+2(w)+2w=24
6+2w+2w=24
Simplify like terms on the left side of the equation
6+2w+2w=24
6+4w=24
Subtract six from each side so that all of the w's are on one side
6+4w-6=24-6
4w=18
Divide each side by four to find the value of one w
4w/4=18/4
w=4.5
Plug 4.5 into the one equation to find the value of l
l=3+4.5
l=7.5
Put the numbers into the first equation and simplify:
2(7.5)+2(4.5)=24
15+9=24
24=24
So the length would be 7.5 inches, and the width would be 4.5 inches
