Theorem of cosine:
a²=b²+c²-2bc(cos α) ⇒cos α=-(a²-b²-c²) / 2bc
In this case:
a=15 cm
b=10 cm
c=5 cm
cos α=-(15²-10²-5²) / 2*10*5
cos α=-100 / 100
cos α=-1
A=arc cos -1=180º This is impossible, because:
A+B+C=180º; then B=C=0º This is impossible for make a triangle (B>0 and C>0 if we want to make a triangle).
Therefore: it is not possible can make a triangle with side lengths of 5 cm, 10 cm and 15 cm.
Answer:
x = 1, y = 1
Step-by-step explanation:
3x - 4y = -1
5x + 2y = 7
If we multiply the whole second equation by 2, we get:
10x + 4y = 14
Adding this to the first equation:
10x + 4y + 3x - 4y = 14 - 1
13x = 13
x = 1
Applying this to the second equation:
5 (1) + 2y = 7
2y = 2
y = 1
The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length and W is the width. Because we don't know either the length or the width we can't solve the problem...too many unknowns. BUT we do have some information that will help with this problem. We are told that the length is 2 feet longer than the width, so we can use that: L = W+2. Now we can make the substitution into the formula along with the value for the perimeter that was given to us: 36=2(W+2) + 2W, and 36 = 2W + 4 + 2W; 36 = 4W + 4; 32 = 4W and W = 8. Now go back to where you said that the length is 2 feet longer than the width. If the width is 8, then 8+2 = 10 for the length.
Answer:
Step-by-step explanation:
Answer:
the correct answer is 1,272 bottles
Step-by-step explanation:
24x53=1,272
