Answer:
Step-by-step explanation:
Given that you and a friend play a game where you each toss a balanced coin.
If the upper faces on the coins are both tails, you win $1;
if the faces are both heads, you win $2;
if the coins do not match (one shows a head, the other a tail), you lose $1 (win (−$1)).
Let Y be the amount won
Then Y can take values as 1,2 and -1
The above is the probability distribution for Y.
Answer: x = 22
Explanation:
1) Corresponding sides and correspoding angles of congruent triangles are equal.
2) When you name two congruent triangles the order of the vertices signal which sides and angles are congruents.
That triangle ABC is congruent to triangle DEF means that these are the corresponding parts, which are congruent to each other:
- ∠A and ∠D are congruent
- ∠B and ∠ E are congruent
- ∠C and ∠F are congruent
- Segment AB and segment DE are congruent
- Segment BC and segment EF are congruent
- Segment AC and segment DF are congruent
In the figures, it is given that the segment DF measures (1/2)x - 1 and the corresponding segment AC measures 10 units.
Hence, you set this equation: (1/2)x - 1 = 10
Solving for x:
- (1/2)x = 10 + 1
- (1/2)x = 11
- x = 2(11)
- x = 22 ← answer
Answer : (0,3) U (3, ∞)
We need to find the interval(s) over which the function is decreasing
We look at the intervals of x where the graph is decreasing
Decreasing interval of the graph is the part where the graph goes down
We look at the part where the graph changes direction
In the middle inverted U shaped graph , the graph changes direction and start decreasing at x=0
the graph is decreasing till x=3
so first decreasing interval is x=0 to 3. we write it as (0,3)
After x=3 the graph starts decreasing and it goes to infinity
So the second decreasing interval is 3 to infinity . We write it as (3, ∞)
Now combine both intervals by a 'U' union
(0,3) U (3, ∞)
False because that proves the triangles are similar, not congruent
Answer:
The smallest side is 7inches
Step-by-step explanation:
Let the shorter side be y.
The medium side is 4 more than the short side i.e
Meduim side = 4 + y
The longest side is 5 times the length of the shortest side i.e
Logest side = 5y.
Perimeter of the triangle = 53 inches
But the perimeter of a triangle is the Sum of all sides i.e
P = small + medium + large
53 = y + (4+y) + 5y
53 = y + 4 + y + 5y
Collect like terms
53 — 4 = 7y
49 = 7y
Divide both side by 7
y = 49/7
y = 7inches
Therefore the smallest side is 7inches
