Pythagorean Theorem
a² + b² = c²
c = 13
a = 4
(Missing side) = b
4² + b² = 13²
16 + b² = 169
16 - 16
169 - 16 = 153
Square Root of 153 = 12.369
b = 12.369
The missing side is 12.369 (rounded to 12 as a whole number)
Answer:
C. 31.83 feet.
Step-by-step explanation:
We have been given that Trina has $1000 to purchase an open-top cylindrical dog pen in her backyard. She wants the height of the pen to be 5 feet.
First of all, we will find the surface area of dog pen using surface area of cylinder.
,where,
r = Radius of cylinder,
h = Height of cylinder.
Since the area of each square foot of pen costs $1, so in $1000 Trina can cover an area of 1000 square feet.
Now, we will set the surface area of cylinder equal to 1000 to solve for the radius.
Upon dividing both sides of our equation by 10 pi we will get,
Therefore, the radius of the dog pen is 31.83 feet and option C is the correct choice.
Answer:
(-15, 13)
Step-by-step explanation:
-3(8x + 9y = -3)
4( 6x + 7y = 1)
-24x - 27y = 9
24x + 28y = 4 (add both equations)
y = 13
6x + 7*13= 1
6x + 91= 1
6x = 1 -91
x = -91/6
x = -15
Elimination:
3x - 9y = 3
6x - 3y = -24
3x - 9y = 3
18x - 9y = -72
(subtract)
-15x = 75
÷ -15
x = -5
(3 × -5) - 9y = 3
-15 - 9y = 3
+ 15
-9y = 18
÷ -9
y = -2
Substitution:
6x - 3y = -24
+ 3y
6x = -24 + 3y
÷ 6
x = 4 + 0.5y
3(4 + 0.5y) - 9y = 3
12 + 1.5y - 9y = 3
12 - 7.5y = 3
- 12
-7.5y = -9
÷ -7.5
y = 1.2
x = 4 + (0.5 × 1.2)
x = 4 + 0.6
x = 4.6
So this one didn't fail as much, but I got different numbers. If you have to give in values, I'd give in the values from the elimination because I don't trust myself when it comes to the substitution
Answer:
250 batches of muffins and 0 waffles.
Step-by-step explanation:
-1
If we denote the number of batches of muffins as "a" and the number of batches of waffles as "b," we are then supposed to maximize the profit function
P = 2a + 1.5b
subject to the following constraints: a>=0, b>=0, a + (3/4)b <= 250, and 3a + 6b <= 1200. The third constraint can be rewritten as 4a + 3b <= 1000.
Use the simplex method on these coefficients, and you should find the maximum profit to be $500 when a = 250 and b = 0. So, make 250 batches of muffins, no waffles.
You use up all the dough, have 450 minutes left, and have $500 profit, the maximum amount.