Answer:
k=21
Step-by-step explanation:
Find the slope of MN which is 1/5 (use the slope formula)
Use the slope formula for AB using k as y_2
Substitute and you get k=21
21-2.25/-2.25-1.5=-5
The lines are perpendicular because the slopes are the negative reciprocal of one another.
Answer:
7 equal to 5
1 equal to 5/7
28 equal to 5/7*28=20
Step-by-step explanation:
Answer:
![x=-2\sqrt5\ and\ x=2\sqrt5](https://tex.z-dn.net/?f=x%3D-2%5Csqrt5%5C%20and%5C%20x%3D2%5Csqrt5)
Step-by-step explanation:
Given:
The given equation to solve is:
![x^2=20](https://tex.z-dn.net/?f=x%5E2%3D20)
In order to solve the above equation, we take square root on both the sides.
While taking square root on both sides, we must consider both positive and negative values. So, this gives:
![\sqrt{x^2}=\pm\sqrt{20}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%7D%3D%5Cpm%5Csqrt%7B20%7D)
From the definition of square root function, we have
![\sqrt{a^2}=a](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%7D%3Da)
Therefore,
![x=\pm\sqrt{20}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B20%7D)
Now, writing 20 into the product of its prime factors, we have
![20=2^2\times 5](https://tex.z-dn.net/?f=20%3D2%5E2%5Ctimes%205)
Therefore, ![x=\pm\sqrt{2^2\times 5}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B2%5E2%5Ctimes%205%7D)
We also know, ![\sqrt{a\times b}=\sqrt{a}\times\sqrt{b}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5Ctimes%20b%7D%3D%5Csqrt%7Ba%7D%5Ctimes%5Csqrt%7Bb%7D)
So, ![\sqrt{2^2\times 5}=\sqrt{2^2}\times \sqrt{5}=2\sqrt5](https://tex.z-dn.net/?f=%5Csqrt%7B2%5E2%5Ctimes%205%7D%3D%5Csqrt%7B2%5E2%7D%5Ctimes%20%5Csqrt%7B5%7D%3D2%5Csqrt5)
Therefore, ![x=\pm2\sqrt5](https://tex.z-dn.net/?f=x%3D%5Cpm2%5Csqrt5)
So, there are two values of 'x'. They are:
![x=-2\sqrt5\ and\ x=2\sqrt5](https://tex.z-dn.net/?f=x%3D-2%5Csqrt5%5C%20and%5C%20x%3D2%5Csqrt5)
Answer:
The answers to each question are:
a)![A=f(r=4cm)=50.26cm^2](https://tex.z-dn.net/?f=A%3Df%28r%3D4cm%29%3D50.26cm%5E2)
b)![\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2](https://tex.z-dn.net/?f=%5CDelta%20A%2810.91cm-10.9cm%29%3Df%2810.91cm%29-f%2810.9cm%29%3D0.6851cm%5E2)
c)![C=5\cdot f(r=12.7cm)=2533.54cm^2](https://tex.z-dn.net/?f=C%3D5%5Ccdot%20f%28r%3D12.7cm%29%3D2533.54cm%5E2)
d)![D=f(r=28cm)+59cm^2=2522.01cm^2](https://tex.z-dn.net/?f=D%3Df%28r%3D28cm%29%2B59cm%5E2%3D2522.01cm%5E2)
Step-by-step explanation:
The function f(r) that represents the area of a circle (in square cm) is:
![f(r)=\pi r^2](https://tex.z-dn.net/?f=f%28r%29%3D%5Cpi%20r%5E2)
a) To represent the area (in square cm) of a circle whose radius is 4 cm, you just have to evaluate the function with a radius of 4cm:
![A=f(r=4cm)=50.26cm^2](https://tex.z-dn.net/?f=A%3Df%28r%3D4cm%29%3D50.26cm%5E2)
b) To represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm, you have to represent the difference between the final area with a radius of 10.91cm and the initial area of a radius of 10.9cm:
![\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2](https://tex.z-dn.net/?f=%5CDelta%20A%2810.91cm-10.9cm%29%3Df%2810.91cm%29-f%2810.9cm%29%3D0.6851cm%5E2)
c) To represent the area of 5 circles that all have a radius of 12.7 cm, we can use the function f(r) to represent the area of a circle with a radius of 12.7cm and multiply it for 5:
![C=5\cdot f(r=12.7cm)=2533.54cm^2](https://tex.z-dn.net/?f=C%3D5%5Ccdot%20f%28r%3D12.7cm%29%3D2533.54cm%5E2)
d) To represent the area of the larger circle that is 59 square cm more than the first circle (with a radius of 28 cm), we can use the function f(r) to obtain the area of the first circle and addition 59 square cm:
![D=f(r=28cm)+59cm^2=2522.01cm^2](https://tex.z-dn.net/?f=D%3Df%28r%3D28cm%29%2B59cm%5E2%3D2522.01cm%5E2)
Answer:
The coordinates of the midpoint of M is (1,5/2)