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Answer:
a) a +b= 13, ab= 40
b) length= 8m, width= 5m
Step-by-step explanation:
Perimeter of rectangle= 2(length +width)
Area of rectangle= length ×width
a) Perimeter= 26m
2(a +b)= 26
Divide both sides by 2:
a +b= 26 ÷2
a +b= 13 ----- (1)
Area= 40m²
ab= 40 ----- (2)
b) From (1): a= 13 -b ----- (3)
Substitute (3) into (2):
(13 -b)(b)= 40
Expand:
13b -b²= 40
b² -13b +40= 0
Factorise:
(b -5)(b -8)= 0
b -5= 0 or b -8= 0
b= 5 or b= 8
Substitute into (3):
a= 13 -5 or a= 13 -8
a= 8 or a= 5
Since the length is usually the longer side of the rectangle, the length and the width of the rectangular garden is 8m and 5m respectively.
Answer:
Number of students can a van carry are 16 and number of students can a bus carry are 28 .
Step-by-step explanation:
The number of students a van carry be x .
The number of students a bus carry be y .
As given
The local amusement park is a popular field trip destination.
This year the senior class at High School A and the senior class at High School B both planned trips there.
The senior class at High School A rented and filled 6 vans and 10 buses with 376 students.
Equations becomes
6x + 10y = 376
As given
High School B rented and filled 3 vans and 2 buses with 104 students.
Equations becomes
3x + 2y = 104
Multiply 3x + 2y = 104 by 2 and subtracted from 6x + 10y = 376 .
6x - 6x + 10y - 4y = 376 - 208
6y = 168
y = 28
Putting the value of y in the equation 3x + 2y = 104 .
3x + 28 × 2 = 104
3x + 56 = 104
3x = 104 - 56
3x = 48
x = 16
Therefore the number of students can a van carry are 16 and number of students can a bus carry are 28 .
Answer:
Parallel
Step-by-step explanation:
The graphs of these two equations will never intersect. Hope this helps.