Assuming that the two investments are X & Y
X + Y = 6300
X = 6300 - Y (1)
9/100X + 4/100 Y = 372 (2)
replacing X from (1) into (2)
9/100(6300-Y) + 4/100 Y = 372
567 - 9/100Y +4/100Y = 372
(-9+4)/100Y = 372 - 567
5/100Y = -195
Y = 100*195/5 = 3900
From (1) we can get X
X = 6300 - 3900 = 2400
I hope this is helpful
Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0
As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81
Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2
So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2
A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.
3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.
So 2k^2 = 9 + 3k have two rational solutions (Option B).
Hope this Helps! :)
Answer:
It takes 2.8 seconds for the ball to fall 215 ft.
Step-by-step explanation:
We are given a position function s(t) where s stands for the number of feet the ball has fallen, so we have to replace s with the given value of 215 ft and solve for the time t.
Setting up the equation.
The motion equation is given by
We can replace there s = 215 ft to get
Solving for the time t.
From the previous equation we can move all terms in one side to get
At this point we can solve for t using quadratic formula.
where a, b and c are the coefficients of the quadratic equation
So we get
Replacing on the quadratic formula we get
Using a calculator we get
Physically speaking the only result that makes sense is to move forward in time that give us t = 2.8 seconds.
We can conclude that it takes 2.8 seconds for the ball to fall 215 ft.
Answer:
YES. (2, 7) is a solution of the system.
Step-by-step explanation:
System of linear inequalities has been given as,
y ≥ -x + 1 --------(1)
y < 4x + 2 ------(2)
If (2, 7) is a solution of the given system of inequalities, it will satisfy both the inequalities.
By substituting the coordinates of point (2, 7) in inequality (1),
7 ≥ -2 + 1
7 ≥ -1
True.
By substituting the coordinates of point (2, 7) in inequality (2),
7 < 4(2) + 1
7 < 9
True.
Therefore, point (2, 7) lie in the solution area of system of inequalities.
YES. (2, 7) is a solution of the system.
We can use the arc length formula to solve this.
Arc length = 
Given arc length is 7 and radius is 5, we can plug in the values and solve for q.
ANSWER:
We can use the equation 
to find the value of q. And, the value of q is 80.21°.
