Given:
In a right angle triangle ABC, altitude BD drawn to hypotenuse AC.
AD=3 and, AC=27.
To find:
The length of AB.
Solution:
Draw a figure by using the given information as shown below.
In triangle ABC and ADB,
(Right angles)
(Common angle)
(AA similarity postulate)
We know that the corresponding parts of congruent triangles are proportional. So,
![\dfrac{AC}{AB}=\dfrac{AB}{AD}](https://tex.z-dn.net/?f=%5Cdfrac%7BAC%7D%7BAB%7D%3D%5Cdfrac%7BAB%7D%7BAD%7D)
After substituting the given values, we get
![\dfrac{27}{AB}=\dfrac{AB}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B27%7D%7BAB%7D%3D%5Cdfrac%7BAB%7D%7B3%7D)
![27\times 3=AB\times AB](https://tex.z-dn.net/?f=27%5Ctimes%203%3DAB%5Ctimes%20AB)
![81=AB^2](https://tex.z-dn.net/?f=81%3DAB%5E2)
Taking square root on both sides, we get
![\sqrt{81}=AB](https://tex.z-dn.net/?f=%5Csqrt%7B81%7D%3DAB)
![9=AB](https://tex.z-dn.net/?f=9%3DAB)
Therefore, the length of AB is 9 units.
A)
![\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccll} y = &{{ -1}}x^2&{{ +28}}x&{{ -192}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7B%20vertex%20of%20a%20vertical%20parabola%2C%20using%20coefficients%7D%5C%5C%5C%5C%0A%0A%5Cbegin%7Barray%7D%7Bllccll%7D%0Ay%20%3D%20%26%7B%7B%20-1%7D%7Dx%5E2%26%7B%7B%20%2B28%7D%7Dx%26%7B%7B%20-192%7D%7D%5C%5C%0A%26%5Cuparrow%20%26%5Cuparrow%20%26%5Cuparrow%20%5C%5C%0A%26a%26b%26c%0A%5Cend%7Barray%7D%5Cqquad%20%0A%5Cleft%28-%5Ccfrac%7B%7B%7B%20b%7D%7D%7D%7B2%7B%7B%20a%7D%7D%7D%5Cquad%20%2C%5Cquad%20%20%7B%7B%20c%7D%7D-%5Ccfrac%7B%7B%7B%20b%7D%7D%5E2%7D%7B4%7B%7B%20a%7D%7D%7D%5Cright%29)
check the picture below.
b)
![\bf f(x)=-x^2+28x-192\implies 0=-x^2+28x-192 \\\\\\ x^2-28x+192=0\implies (x-16)(x-12)=0\implies x= \begin{cases} 16\\ 12 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D-x%5E2%2B28x-192%5Cimplies%200%3D-x%5E2%2B28x-192%0A%5C%5C%5C%5C%5C%5C%0Ax%5E2-28x%2B192%3D0%5Cimplies%20%28x-16%29%28x-12%29%3D0%5Cimplies%20x%3D%0A%5Cbegin%7Bcases%7D%0A16%5C%5C%0A12%0A%5Cend%7Bcases%7D)
what does this mean? check the picture below, notice the x-intercepts points.
Answer:
Distance = Square Root [(x2 -x1)^2 + (Y2 -Y1)^2]
Distance = Square Root [(8 --6)^2 + (10 -2)^2]
Distance = Square Root [14^2 + 8^2]
Distance = Square Root [196 +64]
Distance = Square Root [260]
Distance = 16.1245154966
Source: https://www.1728.org/distance.htm
Step-by-step explanation:
f(g(x))=10x+105
Option C is correct.
Step-by-step explanation:
We are given:
f(x)=10x+25
and g(x)=x+8
We need to find f(g(x)).
Finding f(g(x))
Putting value of g(x), in the f(x)
![f(g(x))=f(x+8)\\f(x+8)=10(x+8)+25\\f(x+8)=10x+80+25\\f(x+8)=10x+105](https://tex.z-dn.net/?f=f%28g%28x%29%29%3Df%28x%2B8%29%5C%5Cf%28x%2B8%29%3D10%28x%2B8%29%2B25%5C%5Cf%28x%2B8%29%3D10x%2B80%2B25%5C%5Cf%28x%2B8%29%3D10x%2B105)
So, f(g(x))=10x+105
Option C is correct.
Keywords: Composite Functions
Learn more about Composite Functions at:
#learnwithBrainly
Answer:
9 red shirts
Step-by-step explanation:
30 x 0.30 = 9 red shirts