Find the area of the region bounded by the given curves (a) using integration with respect to x and (b) using integration with respect to y.

y = 2, y = 5x + 6, x = 0


a. 14 b. 14

Mathematics

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Provide an appropriate response.The length of a screw is 4.275 in. Represent this length as a mixed number.

A.
B.
C.
D.

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Find the number of terms in the sequence or the sum of the sequence as requested.Find the sum of the following arithmetic sequence.1 + 2 + 3 + . . . + 500

A. 62,500 B. 251,001 C. 125,000 D. 125,250

Mathematics

Solve the problem.After receiving a discount of 13.5% on its bulk order of typewriter ribbons, John's Office Supply pays $3460. What was the price of the order before the discount?

A. $4000 B. $3927 C. $3166 D. $2993

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Provide an appropriate response.It can be shown that a hyperbola with center at the origin, foci at F'(-c, 0) and F(c, 0), and equation  has equation . Use this result to find an equation of a hyperbola with center at the origin, foci at (-4, 0) and (4, 0), and absolute value of the distances from any point of the hyperbola to the two foci equal to 4.

A.  -  = 1
B. x2 - y2 = 4
C.  -  = 1
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Mathematics