m∠FDE = 52°
Solution:
Given data:
DE ≅ DF, CD || BE, BC || FD and m∠ABF = 116°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠ABF + m∠CBF = 180°
116° + m∠CBF = 180°
m∠CBF = 64°
If CD || BE, then CD || BF.
Hence CD || BE and BE || FD.
Therefore BFCD is a parallelogam.
<em>In parallelogram, Adjacent angles form a linear pair.</em>
m∠CBF + m∠BFD = 180°
64° + m∠BFD = 180°
m∠BFD = 116°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠BFD + m∠DFE = 180°
116° + m∠DFE = 180°
m∠DFE = 64°
we know that DE ≅ DF.
<em>In triangle, angles opposite to equal sides are equal.</em>
m∠DFE = m∠DEF
m∠DEF = 64°
<em>sum of all the angles of a triangle = 180°</em>
m∠DFE + m∠DEF + m∠FDE = 180°
64° + 64° + m∠FDE = 180°
m∠FDE = 52°
Answer:
y - 13 = 5(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Given y = 5x - 3 in slope- intercept form
with slope m = 5, then
m = 5 and (a, b) = (- 2, 13)
y - 13 = 5(x - (- 2)), that is
y - 13 = 5(x + 2) ← in point- slope form
Answer:
(a)Charlie is right
(b)$0
Step-by-step explanation:
(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.
In the game, the possible outcomes are: HH, HT, TH and TT.
Charlie wins when the outcome is HH, TT
- P(Charlie Wins)=2/4
- P(Charlie Losses)=2/4
Lucy wins when the outcome is HT or TH
- P(Lucy Wins)=2/4
- P(Lucy Losses)=2/4
Therefore, the game is fair. Charlie is right.
(b)
If the outcome is HH, Lucy pays $3.
If the outcome is HT or TH, Lucy gets $2.
If the outcome is TT, Lucy pays $1.
The probability distribution of Lucy's profit is given below:
Expected Profit
Lucy's expected profit from the game is $0.
The answer is A, because the Y-intersect starts at -2
Answer:
Step-by-step explanation:
In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. ... 8 is in ones place and its place value is 8. Understanding the place value of digits in numbers helps in writing numbers in their expanded form.
