Answer:
x=-2
Step-by-step explanation:
2(3x – 1) = 4x - 6
Distribute
6x-2=4x-6
Moving like terms (4x)
2x-2=-6
Moving like terms (-2)
2x=-4
Divide both sides by 2 to isolate x
x=-2
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We get the value of h and k as 9 and -8
The quadratic function g(x) = a(x - h)^2 + k, if a is not equal to 0,which means that equation has a quadratic value then it is said to be in standard quadratic form.
If a is positive, then the graph opens upwards,
If a is negative, then it opens downwards.
The line of symmetry of the quadratic equation is the vertical line x = h, and the co-ordinate of the point of vertex is (h,k).
We are given the co-ordinate of the vertex point in the question and hence all that is required is to equate it.
Therefore, the values of h and k are 9 and -8 in the given equation in vertex form
You can learn more about quadratic equation in standard form here:
brainly.com/question/25025116?referrer=searchResults
Disclaimer: the question may be incomplete and hence has been answered accordingly
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(x-6)(x+6) this is the answer my student thought of in class
Answer:
Q(t) = Q_o*e^(-0.000120968*t)
Step-by-step explanation:
Given:
- The ODE of the life of Carbon-14:
Q' = -r*Q
- The initial conditions Q(0) = Q_o
- Carbon isotope reaches its half life in t = 5730 yrs
Find:
The expression for Q(t).
Solution:
- Assuming Q(t) satisfies:
Q' = -r*Q
- Separate variables:
dQ / Q = -r .dt
- Integrate both sides:
Ln(Q) = -r*t + C
- Make the relation for Q:
Q = C*e^(-r*t)
- Using initial conditions given:
Q(0) = Q_o
Q_o = C*e^(-r*0)
C = Q_o
- The relation is:
Q(t) = Q_o*e^(-r*t)
- We are also given that the half life of carbon is t = 5730 years:
Q_o / 2 = Q_o*e^(-5730*r)
-Ln(0.5) = 5730*r
r = -Ln(0.5)/5730
r = 0.000120968
- Hence, our expression for Q(t) would be:
Q(t) = Q_o*e^(-0.000120968*t)
Answer: 
; 
Step-by-step explanation:
You can write two expressions that are in terms of 'x' and 'y'. This is a right triangle, so Pythagorean's theorem can be used. We can also use the angle to find the sine of 30 degrees.
<u>Pythagorean's Theorem:</u>
The values 'a' and 'b' are the two shorter sides of the triangle, while the value 'c' is the longest side of the triangle; the hypotenuse.
<u>Sine of the Angle:</u>
Sine is defined to be the opposite side divided by the hypotenuse. Let's take the sine of 30 degrees:
Plug this value of 'y' into the first expression derived from Pythagorean's theorem:
Use this value of 'x' to solve for 'y' in the expression from Pythagorean's theorem:
