Answer:
mABD=24
mDBC=24
Step-by-step explanation:
First, set up x+15 and 4x-12 as equivalent equations
Subtract x from both sides to get 3x-12=15
Add 12 to get 3x=27
x=9
Plug 9 into the original equations representing the measurements of angles
You should get 24 for both because bisected means both are congruent
Answer:
![\large\boxed{f(1-x)=x^2-4x+5}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bf%281-x%29%3Dx%5E2-4x%2B5%7D)
Step-by-step explanation:
![f(x-3)=x^2-4x+5\\\\f((x-3)+3)\to\text{put x + 3 to the equation of the function:}\\\\f(x-3+3)=(x+3)^2-4(x+3)+5\\\text{use the distributive property and}\ (a+b)^2=a^2+2ab+b^2\\f(x)=x^2+2(x)(3)+3^2+(-4)(x)+(-4)(3)+5\\f(x)=x^2+6x+9-4x-12+5\qquad\text{combine like terms}\\f(x)=x^2+(6x-4x)+(9-12+5)\\f(x)=x^2+2x+2\\\\f(1-x)\to\text{put 1 - x to the equation of the funtion f(x):}\\\\f(1-x)=(1-x)^2+2(1-x)+2\\\text{use the distributive property and}\ (a-b)^2=a^2-2ab+b^2](https://tex.z-dn.net/?f=f%28x-3%29%3Dx%5E2-4x%2B5%5C%5C%5C%5Cf%28%28x-3%29%2B3%29%5Cto%5Ctext%7Bput%20x%20%2B%203%20to%20the%20equation%20of%20the%20function%3A%7D%5C%5C%5C%5Cf%28x-3%2B3%29%3D%28x%2B3%29%5E2-4%28x%2B3%29%2B5%5C%5C%5Ctext%7Buse%20the%20distributive%20property%20and%7D%5C%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5C%5Cf%28x%29%3Dx%5E2%2B2%28x%29%283%29%2B3%5E2%2B%28-4%29%28x%29%2B%28-4%29%283%29%2B5%5C%5Cf%28x%29%3Dx%5E2%2B6x%2B9-4x-12%2B5%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5Cf%28x%29%3Dx%5E2%2B%286x-4x%29%2B%289-12%2B5%29%5C%5Cf%28x%29%3Dx%5E2%2B2x%2B2%5C%5C%5C%5Cf%281-x%29%5Cto%5Ctext%7Bput%201%20-%20x%20to%20the%20equation%20of%20the%20funtion%20f%28x%29%3A%7D%5C%5C%5C%5Cf%281-x%29%3D%281-x%29%5E2%2B2%281-x%29%2B2%5C%5C%5Ctext%7Buse%20the%20distributive%20property%20and%7D%5C%20%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2)
![f(1-x)=1^2-2(1)(x)+x^2+(2)(1)+(2)(-x)+2\\f(1-x)=1-2x+x^2+2-2x+2\qquad\text{combine like terms}\\f(1-x)=x^2+(-2x-2x)+(1+2+2)\\f(1-x)=x^2-4x+5](https://tex.z-dn.net/?f=f%281-x%29%3D1%5E2-2%281%29%28x%29%2Bx%5E2%2B%282%29%281%29%2B%282%29%28-x%29%2B2%5C%5Cf%281-x%29%3D1-2x%2Bx%5E2%2B2-2x%2B2%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5Cf%281-x%29%3Dx%5E2%2B%28-2x-2x%29%2B%281%2B2%2B2%29%5C%5Cf%281-x%29%3Dx%5E2-4x%2B5)
Answer:
Step-by-step explanation:
We can use the exponential growth formula:
y = a(1 + r)ˣ
where
y = amount after x time
a = initial amount
r = growth rate as a decimal fraction
x = years since 2013
Data:
y = 2300
r = 0.12
x = 2022 - 2013 = 9
Calculations:
x = 2022 - 2013 = 9
![\begin{array}{rcll}2300 &= &a(1.12)^{9} & & \\\ln 2300& = &\ln a+9 \ln1.12 & \text{Took the natural logarithm of each side}\\7.741 &= & \ln a + 9 \times 0.1133 & \text{Evaluated the logarithms}\\7.741 & = & \ln a + 1.020 & \text{Simplified}\\6.721 & = & \ln a & \text{Subtracted 1.020 from each side}\\\end{array}\\](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D2300%20%26%3D%20%26a%281.12%29%5E%7B9%7D%20%26%20%26%20%5C%5C%5Cln%202300%26%20%3D%20%26%5Cln%20a%2B9%20%5Cln1.12%20%26%20%5Ctext%7BTook%20the%20natural%20logarithm%20of%20each%20side%7D%5C%5C7.741%20%26%3D%20%26%20%5Cln%20a%20%2B%209%20%5Ctimes%200.1133%20%20%26%20%5Ctext%7BEvaluated%20the%20logarithms%7D%5C%5C7.741%20%26%20%3D%20%26%20%5Cln%20a%20%2B%201.020%20%26%20%5Ctext%7BSimplified%7D%5C%5C6.721%20%26%20%3D%20%26%20%5Cln%20a%20%26%20%5Ctext%7BSubtracted%201.020%20from%20each%20side%7D%5C%5C%5Cend%7Barray%7D%5C%5C)
![\begin{array}{rcll}e ^{6.721} & = & \ln a & \text{Took the anti ln of each side}\\a & = & \mathbf{829} & \text{Evaluated the function}\\\end{array}\\\text{The population affected by dengue in 2013 was $\large \boxed{\mathbf{829}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7De%20%5E%7B6.721%7D%20%26%20%3D%20%26%20%5Cln%20a%20%26%20%5Ctext%7BTook%20the%20anti%20ln%20of%20each%20side%7D%5C%5Ca%20%26%20%3D%20%26%20%5Cmathbf%7B829%7D%20%26%20%5Ctext%7BEvaluated%20the%20function%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20population%20affected%20by%20dengue%20in%202013%20was%20%24%5Clarge%20%5Cboxed%7B%5Cmathbf%7B829%7D%7D%24%7D)
The figure below shows the growth curve for dengue victims since 2013
The answer is 48 because you have to do is 21 x 4 which is 48