Answer
h(x) = 6 * (2/3)^x
Steps:
The graph specifically highlights two points that might interest us in obtaining the equation. They are x=0 and x=1.
For x=0,
h(x) = 6 {obtained from the graph}
h(x) = 6 = a*b^0
Implies, a=6, since anything to the power 0 is 1, therefore b^0 is 1.
For x=1,
h(x) = 4 {obtained from the graph}
h(x) = 4 = 6*b^1 {a substituted by 6}
Implies, 4=6*b, since anything to the power 1 is itself, therefore b^1 is b.
b then is given by 4/6, simplified to 2/3.
Therefore the equation then becomes,
h(x) = 6 * (2/3)^x
9514 1404 393
Answer:
6·x^6·y^12
Step-by-step explanation:
(3x^6)(2y^12) = (3)(2)x^6·y^12 = 6·x^6·y^12
Answer:
Yes, the right angle is angle B
Step-by-step explanation:
we have
![A(-2, 3), B(-3,-6),C(2,-1)](https://tex.z-dn.net/?f=A%28-2%2C%203%29%2C%20B%28-3%2C-6%29%2CC%282%2C-1%29)
Plot the vertices
see the attached figure
we know that
If triangle ABC is a right triangle
then
Applying the Pythagoras Theorem
![AB^{2} =AC^{2}+BC^{2}](https://tex.z-dn.net/?f=AB%5E%7B2%7D%20%3DAC%5E%7B2%7D%2BBC%5E%7B2%7D)
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
<em>Find the distance AB</em>
![A(-2, 3), B(-3,-6)](https://tex.z-dn.net/?f=A%28-2%2C%203%29%2C%20B%28-3%2C-6%29)
substitute in the formula
![d=\sqrt{(-6-3)^{2}+(-3+2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-6-3%29%5E%7B2%7D%2B%28-3%2B2%29%5E%7B2%7D%7D)
![d=\sqrt{(-9)^{2}+(-1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-9%29%5E%7B2%7D%2B%28-1%29%5E%7B2%7D%7D)
![AB=\sqrt{82}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B82%7D%5C%20units)
<em>Find the distance BC</em>
![B(-3,-6),C(2,-1)](https://tex.z-dn.net/?f=B%28-3%2C-6%29%2CC%282%2C-1%29)
substitute in the formula
![d=\sqrt{(-1+6)^{2}+(2+3)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-1%2B6%29%5E%7B2%7D%2B%282%2B3%29%5E%7B2%7D%7D)
![d=\sqrt{(5)^{2}+(5)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285%29%5E%7B2%7D%2B%285%29%5E%7B2%7D%7D)
![BC=\sqrt{50}\ units](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B50%7D%5C%20units)
<em>Find the distance AC</em>
![A(-2, 3),C(2,-1)](https://tex.z-dn.net/?f=A%28-2%2C%203%29%2CC%282%2C-1%29)
substitute in the formula
![d=\sqrt{(-1-3)^{2}+(2+2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-1-3%29%5E%7B2%7D%2B%282%2B2%29%5E%7B2%7D%7D)
![d=\sqrt{(-4)^{2}+(4)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-4%29%5E%7B2%7D%2B%284%29%5E%7B2%7D%7D)
![AC=\sqrt{32}\ units](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B32%7D%5C%20units)
Verify the Pythagoras theorem
![(\sqrt{82})^{2} =(\sqrt{32})^{2}+(\sqrt{50})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7B82%7D%29%5E%7B2%7D%20%3D%28%5Csqrt%7B32%7D%29%5E%7B2%7D%2B%28%5Csqrt%7B50%7D%29%5E%7B2%7D)
---> is true
therefore
Is a right triangle and the right angle is B
Hi there
The formula is
A=P(1+r/n)^(nt)
A future value?
p Present value 2000
R interest rate 0.05
N compounded quarterly 4
T time 8 years
So
A=2,000×(1+0.05÷4)^(4×8)
A=2,976.26
Hope it helps
80% of $300 is $240; 300-240 is $60