Answer:
1) The slant height = 9.8 cm ⇒ (C)
2) The slant height = 11.4 cm ⇒ (D)
Step-by-step explanation:
1) ∵ The slant height of the cone = √[(radius)² + (height)²]
∵ Diameter = 8 cm
∴ Radius = 4 cm
∵ Height = 9 cm
∴ Slant height = √(4² + 9²) = √97 = 9.8 cm ⇒ (C)
2) ∵ The slant height of the cone = √[(radius)² + (height)²]
∵ Diameter = 18 cm
∴ Radius = 9 cm
∵ Height = 7 cm
∴ Slant height = √(9² + 7²) = √130 = 11.4 cm ⇒ (D)
Expanded Form:
3+0.4
2+0.50+0.01
Word Form:
three and four tenths
two and fifty-one hundredths
For this case we have:
To begin we must graph 
, for this:
We do 
, then:
So, we have the point 
We do 
, then:
So, we have the point
We place both points in a coordinate plane and graph the line. Now, we must find the shaded region that identifies the inequality 
We must replace any point located to the left or to the right of the line. If the inequality is met, then the shaded region will be on the respective side.
We substitute the point
The inequality is met, then the shaded region is to the right of the line.
Answer:
See attached image
well, the sequence goes, 1100, to 1135, to 1170.... notice, is simply adding 35 to get the next term, so the common difference is 35, and the first term is 1100 of course.
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1100\\ d=35\\ a_n=3725 \end{cases} \\\\\\ 3725=1100+(n-1)35\implies 3725=1100+35n-35 \\\\\\ 3725=1065+35n\implies 2660=35n\implies \cfrac{2660}{35}=n\implies 76=n](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%0A%5C%5C%5C%5C%0Aa_n%3Da_1%2B%28n-1%29d%5Cqquad%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ad%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%0A%5Chrulefill%5C%5C%0Aa_1%3D1100%5C%5C%0Ad%3D35%5C%5C%0Aa_n%3D3725%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A3725%3D1100%2B%28n-1%2935%5Cimplies%203725%3D1100%2B35n-35%0A%5C%5C%5C%5C%5C%5C%0A3725%3D1065%2B35n%5Cimplies%202660%3D35n%5Cimplies%20%5Ccfrac%7B2660%7D%7B35%7D%3Dn%5Cimplies%2076%3Dn)
Answer:
OPTION B: K = 15
Step-by-step explanation:
The given equation is: 21 + 3x = 3x + K
Substitute K = 3x
we get: 21 = 3x + 3x + 3x
⇒ 21 + 3x = 6x
⇒ 21 = 3x
This gives the value of x = 7. That means K = 3x gives us a solution. So, OPTION A is eliminated.
Now, K = 15
The equation becomes 21 + 3x = 3x + 15
Subtracting 3x on both the sides, we get:
⇒ 21 + 3x - 3x = 15 + 3x - 3x
⇒ 21 = 15 which can not be correct. So, K = 15 renders the equation meaningless and hence with no solution.
So, OPTION B is the answer.
Note that K = 21 will give the equation with infinitely many solutions.
