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spayn [35]
2 years ago
10

a waiter earns $13.65 per hour and must give 10% of his tips to the kitchen staff. he worked 8 hours last Friday and made $213 i

n tips. What was his gross pay for the shift?
Mathematics
1 answer:
Nata [24]2 years ago
4 0

Answer:

10% of 213 is 21.30

213-21.3= 191.7

gross income: 191.7

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List all possible rational roots. Then use synthetic division to confirm which rational roots exist:
Kisachek [45]

Answer:

\boxed{(1) \, x = \, \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10; (2) \, x = -2}

Step-by-step explanation:

2x³+ 6x² - x - 10 = 0

(1) Possible roots

The Rational Roots Theorem states that, if a polynomial has any rational roots, they will have the form p/q, where p is a factor of the constant term  and q is a factor of the leading coefficient.

\text{Possible rational root} = \dfrac{ p }{ q } = \dfrac{\text{factor of constant term}}{\text{factor of leading coefficient}}

In your function, the constant term is -10 and the leading coefficient is 2, so

\text{Possible root} = \dfrac{\text{factor of 10}}{\text{factor of 2}}

Factors of 10 = ±1, ±2, ±5, ±10

Factors of 2 = ±1, ±2

\text{Possible roots are } \large \boxed{\mathbf{x = \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10}}

(2) Synthetic division

Rather than work through all 12 possibilities, I will do one that works.

\begin{array}{r|rrrr}-2 & 2 & 6 & -1 & -10\\& & -4& -4 & 10\\& 2 & 2& -5 & 0\\\end{array}

So, x = -2 is a root, and the quotient is 2x² + 2x - 5.

(3) Check for other rational roots

2x² + 2x - 5 = 0

D = b² - 4ac =2²- 4(2)(-5) = 4 + 40 = 44

√44 = 2√11, which is irrational.

Since irrational roots come in pairs, the cubic equation has two real, irrational roots and one rational root at x = -2.

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Step-by-step explanation:

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20 beacause 20 x 2 = 40 and twice as many means 2 x ....
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Consider the system of equations. y=32x+5 y = 3 2 x + 5 y=34x+12 y = 3 4 x + 1 2 What is the solution to the system?
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Answer:( -7/2 -107)

Step-by-step explanation:

Y=32x+5

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Right?

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