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Nina [5.8K]
3 years ago
13

A salesperson's weekly paycheck is 10% more than a second salesperson's paycheck. The two paychecks total $1525. Find the amount

of each paycheck. (Round your answers to the nearest cent.)
Mathematics
1 answer:
Kaylis [27]3 years ago
6 0
1525 ➗ 2 = 762.5
762.50 x 10% is 76.25
762.50 - 76.25 = 686.25
one paycheck is 762.50
the other is 686.25

I hope this helps.
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Step-by-step explanation:

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Five less than twice what negative number squared is 157?
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Five less than twice what negative number squared is 157 <- put into an expression
-5 + 2(-x^2) = 157
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Write the equation of a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2(sqrt5)
Xelga [282]

Answer:

\frac{x^2}{16}-\frac{b^2}{4}=1

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4

The foci c is at +/-2√5, using c² = a² + b²:

c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2

Substituting the value of a and b to get the equation of the hyperbola:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1

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3 years ago
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