Answer:
A) 5.50x + 10y ≤ 800
B) yes
C) no
D) 80 pull buoys and 35 kick boards
Step-by-step explanation:
A) The sum of costs must not exceed the budget:
5.50x +10.00y ≤ 800
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B) 5.50(0) +10.00(50) = 500 ≤ 800 . . . . . yes, the coach could buy these
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C) 5.50(125) +10.00(25) = 937.50 > 800 . . . no, they cost too much
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D) The point (80, 35) is in the solution space. The coach could buy 80 pull buoys and 35 kick boards.
Answer:
y = 2x + 1 ;
y - 3 = - 3(x - 1) ; y = - 3x + 6 ;
Independent ;
(1, 3)
Step-by-step explanation:
Given the data:
Sidewalk 1:
x __ y
2 _ 5
0 _ 1
Sidewalk 2:
x __ y
1 _ 3
3 _ -3
Equation for sidewalk 1 in slope - intercept form:
Slope intercept form:
y = mx + c
c = intercept ; m = slope
m = (change in y / change in x)
m = (1 - 5) / (0 - 2) = - 4 / - 2 = 2
Y intercept ; value of y when x = 0
(0, 1) ; y = 1
Hence, c = 1
y = 2x + 1
Sidewalk 2:
Point slope form:
y - y1 = m(x - x1)
m = slope
m = = (-3 - 3) / (3 - 1) = - 6/2 = - 3
Point (x1, y1) = (1, 3)
y - 3 = - 3(x - 1)
To slope intercept form:
y - 3 = - 3(x - 1)
y - 3 = - 3x + 3
y = - 3x + 3 + 3
y = - 3x + 6
Since the slope of both lines are different, intersection will be at single point and will have a single solution. This makes it independent.
Using substitution method :
y = 2x + 1 - - - (1)
y = - 3x + 6 - - - (2)
Substitute (1) into (2)
2x + 1 = - 3x + 6
2x + 3x = 6 - 1
5x = 5
x = 1
From (1)
y = 2(1) + 1
y = 2 + 1
y = 3
Coordinate of the point of intersection = (1, 3)
Answer: Monitors A and B
Step-by-step explanation:
The similar monitors based on display resolution are those with similar ratios.
Take the ratios to their simplest forms to see which are similar.
Monitor A
= 640 : 480
= 16 : 12
= 4 : 3
Monitor B
= 800 : 600
= 8 : 6
= 4 : 3
Monitor C
= 1,280 : 800
= 32 : 20
= 8 : 5
<em>Monitors A and B are similar as they have the same display ratio. </em>
Answer:
(a) a=6 and b≠
(b)a≠6
(c) a=6 and b=
Step-by-step explanation:
writing equation in agumented matrix form
now 
now 
a) now for inconsistent
rank of augamented matrix ≠ rank of matrix
for that a=6 and b≠
b) for consistent w/ a unique solution
rank of augamented matrix = rank of matrix
a≠6
c) consistent w/ infinitely-many sol'ns
rank of augamented matrix = rank of matrix < no. of variable
for that condition
a=6 and b=[tex]\frac{11}{4}
then rank become 3 which is less than variable which is 4.
