Answer:
y = 15.75x + 25 is the linear equation
$88 would be the total cost
Step-by-step explanation:
First, create the equation using y = mx + b, where x is the number of hours:
y = 15.75x + 25 will be the equation, since the charge is $15.75 per hour and the flat fee is $25
There are 4 hours in between 8:30 AM and 12:30 PM, so to find the cost, plug in 4 as x and simplify:
y = 15.75x + 25
Plug in 4 as x:
y = 15.75(4) + 25
y = 63 + 25
y = 88
So, the total cost would be $88
9514 1404 393
Answer:
D. 12
Step-by-step explanation:
There are a number of ways to find the area of this rectangle. Perhaps the most straightforward is to find the lengths of the sides and multiply those. The distance formula is useful.
d = √((x2 -x1)^2 +(y2 -y1)^2)
Using the two upper-left points, we find the length of that side to be ...
d = √((3 -0)^2 +(3 -0)^2) = √(9 +9) = √18 = 3√2
Similarly, the length of the lower-left side is ...
d = √((-2 -0)^2 +(-2 -0)^2) = √(4+4) = √8 = 2√2
Then the area of the rectangle is ...
A = LW
A = (3√2)(2√2) = 3·2·(√2)^2 = 3·2·2 = 12
The area of rectangle ABCD is 12.
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Other methods include subtracting the area of the corner triangles from the area of the bounding square:
5^2 -2(1/2)(3·3) -2(1/2)(2·2) = 25 -9 -4 = 12
Solve for x:x/5 - 2 = x/2 + 3
Put each term in x/5 - 2 over the common denominator 5: x/5 - 2 = x/5 - (10)/5:x/5 - (10)/5 = x/2 + 3
x/5 - (10)/5 = (x - 10)/5:(x - 10)/5 = x/2 + 3
Put each term in x/2 + 3 over the common denominator 2: x/2 + 3 = x/2 + 6/2:(x - 10)/5 = x/2 + 6/2
x/2 + 6/2 = (x + 6)/2:(x - 10)/5 = (x + 6)/2
Multiply both sides by 10:(10 (x - 10))/5 = (10 (x + 6))/2
10/5 = (5×2)/5 = 2:2 (x - 10) = (10 (x + 6))/2
10/2 = (2×5)/2 = 5:2 (x - 10) = 5 (x + 6)
Expand out terms of the left hand side:2 x - 20 = 5 (x + 6)
Expand out terms of the right hand side:2 x - 20 = 5 x + 30
Subtract 5 x from both sides:(2 x - 5 x) - 20 = (5 x - 5 x) + 30
2 x - 5 x = -3 x:-3 x - 20 = (5 x - 5 x) + 30
5 x - 5 x = 0:-3 x - 20 = 30
Add 20 to both sides:(20 - 20) - 3 x = 20 + 30
20 - 20 = 0:-3 x = 30 + 20
30 + 20 = 50:-3 x = 50
Divide both sides of -3 x = 50 by -3:(-3 x)/(-3) = 50/(-3)
(-3)/(-3) = 1:x = 50/(-3)
Multiply numerator and denominator of 50/(-3) by -1:Answer: x = (-50)/3
You can have 24 different combinations for bowls of ice cream.
Answer:
24
Step-by-step explanation:
