Answer:
Question #1
m∠4 + m∠7 = 180° - Given.
∠4 and ∠7 are supplementary angles - Definition of supplementary angles.
∠7 and ∠2 form a linear pair - Definition of linear pair.
∠7 and ∠2 are supplementary angles - Definition of linear pair.
m∠7 + m∠2 = 180° - Definition of supplementary angles.
m∠2 = m∠4 - Substitution property.
c ║ d - Converse of corresponding angles postulate.
Question #2
m∠3 = m∠8 - Given.
∠8 and ∠6 form a linear pair - Definition of linear pair.
∠8 and ∠6 are supplementary angles - Definition of linear pair.
m∠8 + m∠6 = 180° - Definition of supplementary angles.
∠3 and ∠6 are supplementary angles - Substitution property.
m∠3 + m∠6 = 180° - Definition of supplementary angles.
Question #3
p ║ q - Given.
∠1 ≅ ∠5 - Given.
∠1 ≅ ∠2 - Alternate interior angle theorem.
∠2 ≅ ∠5 - Substitution property.
~Hope this helps!~
Answer:
$ 3199.0
Step-by-step explanation:
Let the number of shares of ABC = x
and XYZ = y
writing each as a linear equation
32 x + 23 y = 10100 equation 1
1.2 x + 1.4 y = 540
1.4 y = 540 - 1.2 x
y = ( 540 - 1.2 x) / 1.4
substitute for y in equation 1
32 x + 23( 540 - 1.2 x) / 1.4 = 10100
32 x + 8871.43 - 19.71 x = 10100
collect the like terms
32 x - 19.71 x = 10100 - 8871.43
12.29 x = 1228.57
x = 1228.57 / 12.29 = 99.97
the amount of money to be invested in ABC shares = 99.97 × $ 32 = $ 3199.0
Answer:
a) A = kB
b) 20
c) 9
Step-by-step explanation:
A is directly proportional to B when A = 12, B = 3
a) find a formula for A in terms of B
A ∝ B
A = kB
Where k is constant of proportionality
when A = 12, B = 3
12 = 3k
k = 12/3
k = 4
b) find the value of A when B = 5
A = kB
k = 4
A = 4 × 5
A = 20
c) find the value of B when A = 36
k = 4
A = kB
B = A/k
B = 36/4
B = 9
Phil gets x dollars, but before he gets x dollars, he needs to pay 100 dollars to enter the tournament. Therefore the net winning is not x dollars but you should substract 100 dollars from x.
So, the expression of the net winning will be x-100
