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Alisiya [41]
3 years ago
5

what is the algebraic equation 3 times the sum of a number and 7 is 2 less than five times the number

Mathematics
1 answer:
stealth61 [152]3 years ago
7 0
Let n = number

"3 times the sum of a number and 7" translates to 3(n + 7)

"2 less than five times the number" translates to 5n - 2

The word "is" becomes the equals sign.

3(n + 7) = 5n - 2

I think you already asked this one. 
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The equation (x-6)^2/16 + (y+7)^2/4 = 1 represents an ellipse. What are the vertices of the ellipse?
topjm [15]

Answer:

The correct option is C.

Step-by-step explanation:

The given equation is

\frac{(x-6)^2}{16}+\frac{(y+7)^2}{4}= 1

It can be rewritten as

\frac{(x-6)^2}{4^2}+\frac{(y+7)^2}{2^2}= 1         .....(1)

The standard form of an ellipse is

\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1           ....(2)

Where (h,k) is center of the ellipse.

If a>b, then the vertices of the ellipse are (h\pm a, k).

From (1) and (2) we get

h=6,k=-7,a=4,b=2

Since a>b, therefore the vertices of the ellipse are

(h+a, k)=(6+4,-7)\Rightarrow (10,-7)

(h-a, k)=(6-4,-7)\Rightarrow (2,-7)

The vertices of the given ellipse are (10, –7) and (2, –7). Therefore the correct option is C.

5 0
2 years ago
Read 2 more answers
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