Answer:
696 students.
Step-by-step explanation:
From the sample of students 58/125 of them like milk.
So we can predict that 1500 * 58/125 of the 1500 students like milk.
This comes to (1500/125) * 58
= 12 * 58
= 696.
There is a little-known theorem to solve this problem.
The theorem says that
In a triangle, the angle bisector cuts the opposite side into two segments in the ratio of the respective sides lengths.
See the attached triangles for cases 1 and 2. Let x be the length of the third side.
Case 1:
Segment 5cm is adjacent to the 7.6cm side, then
x/7.6=3/5 => x=7.6*3/5=
4.56 cm
Case 2:
Segment 3cm is adjacent to the 7.6 cm side, then
x/7.6=5/3 => x=7.6*5/3=
12.67 cmThe theorem can be proved by considering the sine rule on the adjacent triangles ADC and BDC with the common side CD and equal angles ACD and DCB.
Answer:
Step-by-step explanation:
2x+5y=12
3x+4y=11
---------------
3(2x+5y)=3(12)
-2(3x+4y)=-2(11)
-----------------------
6x+15y=36
-6x-8y=-22
-----------------
7y=14
y=14/7=2
2x+5(2)=12
2x+10=12
2x=12-10=2
x=2/2=1
x=1, y=2. (1, 2)
---------------------
I just provided you an example of a system of equations and I already solved it for you.
la neta lo a mirado pero se me olvido if I'm right I think it' c
General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as
.
Comparing the function f(x)=ax^{2} +bx+c with the given function
, we get
,
and
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds
The maximum height is found by substituting
in the function as below:

Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts.