Answer:
r=-3
Step-by-step explanation:
-----(A)
Here we are given that
![(x_1,y_1) = (2,r)](https://tex.z-dn.net/?f=%20%28x_1%2Cy_1%29%20%3D%20%282%2Cr%29%20)
![(x_2,y_2) = (-5,11)](https://tex.z-dn.net/?f=%20%28x_2%2Cy_2%29%20%3D%20%28-5%2C11%29%20)
And the value of m is -2
Replacing them in (A)
![-2=\frac{11-r}{-5-2}](https://tex.z-dn.net/?f=%20-2%3D%5Cfrac%7B11-r%7D%7B-5-2%7D)
![-2=\frac{11-r}{-7}](https://tex.z-dn.net/?f=%20-2%3D%5Cfrac%7B11-r%7D%7B-7%7D)
![-7 \times -2=11-r](https://tex.z-dn.net/?f=%20-7%20%5Ctimes%20-2%3D11-r)
![14=11-r](https://tex.z-dn.net/?f=%2014%3D11-r)
![r=11-14](https://tex.z-dn.net/?f=%20r%3D11-14)
![r=-3](https://tex.z-dn.net/?f=%20r%3D-3)
Hence the value of r is -3 and the coordinate is(2,-3)
The volume of any prism is equal to its base times its height. V = Bh
A figure such as a pyramid or cone has 1/3 of the volume of the prism which contains it. V = Bh/3
In the case of our pyramid here...
B = 15√3 cm²
h = 4 cm
Plug these into our formula...
V = Bh/3 = (15√3)(4)/3 = (60√3)/3 = 20√3 cm³
Answer:
Option J 13
Step-by-step explanation:
we know that
If applying the Pythagoras Theorem
----> is an obtuse triangle
----> is an acute triangle
----> is a right triangle
where
c is the greater side
<em><u>Verify each case</u></em>
case F) we have
![c=10, a=6, b=8](https://tex.z-dn.net/?f=c%3D10%2C%20a%3D6%2C%20b%3D8)
substitute
![10^{2}> 6^{2} +8^{2}](https://tex.z-dn.net/?f=10%5E%7B2%7D%3E%206%5E%7B2%7D%20%2B8%5E%7B2%7D)
-----> is not true
Is a right triangle
case G) we have
![c=10, a=9, b=8](https://tex.z-dn.net/?f=c%3D10%2C%20a%3D9%2C%20b%3D8)
substitute
![10^{2}> 9^{2} +8^{2}](https://tex.z-dn.net/?f=10%5E%7B2%7D%3E%209%5E%7B2%7D%20%2B8%5E%7B2%7D)
-----> is not true
Is an acute triangle
case H) we have
![c=12, a=8, b=10](https://tex.z-dn.net/?f=c%3D12%2C%20a%3D8%2C%20b%3D10)
substitute
![12^{2}> 8^{2} +10^{2}](https://tex.z-dn.net/?f=12%5E%7B2%7D%3E%208%5E%7B2%7D%20%2B10%5E%7B2%7D)
-----> is not true
Is an acute triangle
case J) we have
![c=13, a=8, b=10](https://tex.z-dn.net/?f=c%3D13%2C%20a%3D8%2C%20b%3D10)
substitute
![13^{2}> 8^{2} +10^{2}](https://tex.z-dn.net/?f=13%5E%7B2%7D%3E%208%5E%7B2%7D%20%2B10%5E%7B2%7D)
-----> is true
Is an obtuse triangle
ANSWER
65
EXPLANATION
This will form a sequence with first term:
![a_{1} = 102](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%20102)
with constant difference d=6 and last term
![l = 486](https://tex.z-dn.net/?f=l%20%3D%20486)
The last term is a term in the sequence, therefore;
![l=a_1+d(n-1)](https://tex.z-dn.net/?f=l%3Da_1%2Bd%28n-1%29)
![486=102+6(n-1)](https://tex.z-dn.net/?f=486%3D102%2B6%28n-1%29)
![486 - 102 = 6(n-1)](https://tex.z-dn.net/?f=486%20-%20102%20%3D%206%28n-1%29)
Simplify the LHS
![384= 6(n-1)](https://tex.z-dn.net/?f=384%3D%206%28n-1%29)
Divide both sides by 6.
![64=n-1](https://tex.z-dn.net/?f=64%3Dn-1)
![64 + 1 = n](https://tex.z-dn.net/?f=64%20%2B%201%20%3D%20n)
Therefore
![n = 65](https://tex.z-dn.net/?f=n%20%3D%2065)
Hence there are 65 multiples of 6.
9514 1404 393
Answer:
420
Step-by-step explanation:
The prime factors of each denominator are ...
12 = 2²×3
14 = 2×7
5 = 5
10 = 2×5
The unique factors are 2²×3×5×7 = 420.
The least common denominator of these fractions is 420.
_____
<em>Additional comment</em>
- 5/12 = 175/420
- 9/14 = 270/420
- 2/5 = 168/420
- 1/10 = 42/420