Answer:
Z = 45 degrees
Step-by-step explanation:
the angle is still an acute angle but it is not a right angle so it must be 45 according to my calculations. plz mark brainliest
Answer:
4+3=3+4
Step-by-step explanation:
The commutative property of addition says that, the order in which you add two real numbers does not matter.
Let 
, then
a+b=b+a
From the given options;
4+3=3+4
shows the commutative property of addition
Answer:
The distance added to each dimension is 2 yards.
Step-by-step explanation:
The initial dimensions of the rectangular fence is 8 yards by 4 yards.
The initial area of the rectangular fence = area of a rectangle
area of a rectangle = length x width
So that,
The initial area of the fence = 8 x 4
= 32
The initial area of the fence is 32 square yards.
But, with the new dimensions, area = 60 square yards.
(4 + x) x (8 + x) = 60
+ 12x + 28 = 60
+ 12x - 32 = 0
(x + 14) = 0 or (x - 2) = 0
x = -14 or x =2
Thus, x = 2
The distance added to each dimension is 2 yards.
Answer: the distance from one corner of the field to the other corner is 136 m
Step-by-step explanation:
The distance from one corner to the other corner is the diagonal and it
divides the field into two equal right angle triangles. The diagonal represents the hypotenuse of each right angle triangle. The length and width of the rectangle represents the adjacent and opposite sides of the right angle triangle. To determine the length of the diagonal, d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore
d² = 110² + 80²
d² = 12100 + 6400 = 18500
d = √18500
d = 136 meters
Answer: The price of an adult ticket = $6
The price of a student ticket = $12
Step-by-step explanation:
Let the price of an adult ticket be a
Let the price of a student ticket be b.
From the question,
5a + 14b = 198 ...... equation i
10a + 8b = 156....... equation ii
Multiply equation i by 10
Multiply equation ii by 5
50a + 140b = 1980 ...... equation iii
50a + 40b = 780 ....... equation iv
Subtract iv from iii
100b = 1200
b = 1200/100
b = 12
Put the value of b into equation ii
10a + 8b = 156
10a + 8(12) = 156
10a + 96 = 156
10a = 156-96
10a = 60
a = 6
The price of an adult ticket = $6
The price of a student ticket = $12
