Answer:
Exact Form: 9/14
Decimal Form: 0.6428571
Step-by-step explanation:
Simplify the expression
Hope this helps!
Answer:
Given statement: The number of gallons of water in the swimming pool x minutes after turning on the faucet is represented by :
.....[1]
The equation of straight line is represented by
.....[2]
where
m represents the slope of line
and
b is the y-intercepts.
On comparing the equation [1] with [2] we get;
slope(m) = 24 and
y-intercept(b) = 285.
x-intercept defined as the graph crosses the x-axis i.e,
substitute the value of y =0 in [1] to solve for x;
0= 24x + 285
Subtract 285 from both sides we get;
-285 = 24x
Divide both sides by 24 we get;
![x = -\frac{285}{24} = -11.875](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B285%7D%7B24%7D%20%3D%20-11.875)
x = -11.875
(a)
y= 24x + 285 where x is in minute.
You can see the graph of the equation as shown below.
(b)
Slope of the equation = 24
y-intercepts = 285
(c)
Since, x intercept is not applicable to this problem because value of x is negative as x represents the time(in minutes)
Answer:
<h2>x = -1</h2>
Step-by-step explanation:
![4(4^x-2^x)+1=0\\\\4\bigg((2^2)^x-2^x\bigg)+1=0\qquad\text{use}\ (a^n)^m=a^{nm}\\\\4(2^{2x}-2^x)+1=0\\\\4\bigg((2^x)^2-2^x\bigg)+1=0\qquad\text{substitute}\ 2^x=t>0\\\\4(t^2-t)+1=0\qquad\text{use the distributive property}\\\\4t^2-4t+1=0\\\\4t^2-2t-2t+1=0\\\\2t(2t-1)-1(2t-1)=0\\\\(2t-1)(2t-1)=0\\\\(2t-1)^2=0\iff2t-1=0\qquad\text{add 1 to both sides}\\\\2t=1\qquad\text{divide both sides by 2}\\\\t=\dfrac{1}{2}](https://tex.z-dn.net/?f=4%284%5Ex-2%5Ex%29%2B1%3D0%5C%5C%5C%5C4%5Cbigg%28%282%5E2%29%5Ex-2%5Ex%5Cbigg%29%2B1%3D0%5Cqquad%5Ctext%7Buse%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C4%282%5E%7B2x%7D-2%5Ex%29%2B1%3D0%5C%5C%5C%5C4%5Cbigg%28%282%5Ex%29%5E2-2%5Ex%5Cbigg%29%2B1%3D0%5Cqquad%5Ctext%7Bsubstitute%7D%5C%202%5Ex%3Dt%3E0%5C%5C%5C%5C4%28t%5E2-t%29%2B1%3D0%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5C%5C%5C4t%5E2-4t%2B1%3D0%5C%5C%5C%5C4t%5E2-2t-2t%2B1%3D0%5C%5C%5C%5C2t%282t-1%29-1%282t-1%29%3D0%5C%5C%5C%5C%282t-1%29%282t-1%29%3D0%5C%5C%5C%5C%282t-1%29%5E2%3D0%5Ciff2t-1%3D0%5Cqquad%5Ctext%7Badd%201%20to%20both%20sides%7D%5C%5C%5C%5C2t%3D1%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B1%7D%7B2%7D)
![\text{We're going back to substitution}\\\\t=\dfrac{1}{2}\Rightarrow2^x=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\2^x=2^{-1}\iff x=-1](https://tex.z-dn.net/?f=%5Ctext%7BWe%27re%20going%20back%20to%20substitution%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B1%7D%7B2%7D%5CRightarrow2%5Ex%3D%5Cdfrac%7B1%7D%7B2%7D%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7Ba%7D%5C%5C%5C%5C2%5Ex%3D2%5E%7B-1%7D%5Ciff%20x%3D-1)
Answer:
a
Step-by-step explanation:
i just took the test
Confused on the question could I have a picture?