Answer:
x = 8
y = 21
Step-by-step explanation:
(7x + 12)° and (12x - 28)° are alternate interior angles. Alternate interior angles are congruent. Therefore:
(7x + 12)° = (12x - 28)°
Solve for x
7x + 12 = 12x - 28
Collect like terms
7x - 12x = - 12 - 28
-5x = -40
Divide both sides by -5
-5x/-5 = -40/-5
x = 8
(12x - 28)° + (9y - 77)° = 180° (linear pair)
To find y, plug in the value for x = 8.
12(8) - 28 + 9y - 77 = 180
96 - 28 + 9y - 77 = 180
Combine like terms
- 9 + 9y = 180
Add 9 to both sides
-9 + 9y + 9 = 180 + 9
9y = 189
Divide both sides by 9
9y/9 = 189/9
y = 21
Answer:
(7m + 10) yards of cloth was used
Step-by-step explanation:
This is a multiplication problem. Firstly, we are told that she sew m shirts and she used 2 yards of cloth for each of the shirts. The total amount of materials used here is m * 2 = 2m yards
She also sew another (m + 2) Shirts using 5 yards of materials for each of the shirts. The total amount of materials used is thus 5(m + 2) which equals (5m + 10) yards
The total amount of cloth used altogether is thus 2m + (5m + 10) = (7m + 10) yards of cloth
Answer:
If A ⊆ B, then A ⊂ B.
If A = B, then A ⊆ B.
If A = B, then A ⊂ B.
Step-by-step explanation:
In set theory '⊂' is the symbol of proper subset and '⊆' is the symbol of subset of a set.
In option (a),
If A ⊆ B
⇒ A ⊂ B or A = B
Thus, If A ⊆ B, then A ⊂ B.
Option a is true.
(b) If A ⊂ B
⇒ A is the subset of B
That is, all elements of A are also the element of B,
But we can not say A = B
Thus, option b is not true.
(c) If A = B
⇒ A ⊂ B and A ⊃ B or A ⊆ B and B ⊆ A ( Because every set is the subset of itself )
⇒ A ⊆ B.
Option c is true.
(d) If A = B,
⇒ A ⊂ B
Option d is true.
(e) If A ⊂ B,
Then we can not say that,
A = B or A ≠ B
Thus, option e is not correct.
Answer:
9 minutes
Step-by-step explanation:
12 divided by 1.5 is 9.
Answer:
24
Step-by-step explanation:
