MATHEMATICS COLLEGE

A bill for dinner at a restaurant is $91.42.Lucy wants to leave a 15% tip. Which is a
good estimate for the tip?

Answers

Answer 1
Answer:

Answer:

f

Step-by-step explanation:

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What is the value of x? *
4x + 32
172°
Your answer

Answers

Answer:

x=35

Step-by-step explanation:

Because the 2 lines are parallel u kno 172=4x+32

from there: 172-32=4x or 140=4x, and then 140/4=x

Final answer:

To solve for 'x' in the equation 4x + 32 = 172, we isolate 'x' by first subtracting 32 from both sides of the equation. This gives us 4x = 140. Then, solving for 'x', we divide both sides by 4, resulting in 'x' equal to 35.

Explanation:

To find the value of x, we need to use the process of algebraic simplification. In the equation provided, isolate x by subtracting 32 from both sides of the equation:

4x + 32 = 172

4x = 172 - 32

4x = 140

Next, solve for x by dividing both sides of the equation by 4:

x = 140 / 4

x = 35

Therefore, the value of x in the equation is 35.

Learn more about Algebra here:

brainly.com/question/32436021

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For the characteristic polynomialp(s) =s5+ 2s4+ 24s3+ 48s2−25s−50(a) Use the Routh-Hurwitz Criterion to determine the number of roots ofp(s) in the right-half plane, in the left-half plane, and on thejω-axis.(b) Use Matlab to determine the roots ofp(s), and verify your results in part 2a.

Answers

Answer:

  • 1 root in the right half-plane
  • 1 conjugate pair on the imaginary axis
  • 2 roots in the left half-plane

Step-by-step explanation:

Without using the Routh-Hurwitz criterion at all, you know there is one positive real root. Descartes' rule of signs tells you the number of positive real roots is equal to the number of sign changes in the coefficients (perhaps less a multiple of 2). There is one sign change in + + + + - - , so there is one positive real root.

_____

(a) The Routh array starts as two rows of the polynomial's coefficients, alternate coefficients on each row. For this odd-degree polynomial, the number of coefficients is even, so no zero-padding is necessary at the right end of the second row. That is, we start with ...

  \begin{array}{cccc}s^5&1&24&-25\ns^4&2&48&-50\end{array}

The next row is formed from combinations of coefficients in the two rows above. The computation is similar to that of a determinant. By matching the numbers to those in the array, you can see the pattern of the computation.

The next row values are ...

  \begin{array}{ccc}s^3&((2)(24)-(1)(48))/(2)&((2)(-25)-(1)(-50))/(2)\end{array}

Simplifying, we find this row to be ...

  \begin{array}{ccc}s^3&0&0\end{array}

The zero row is a special case that requires we proceed as follows. The row above (identified with s⁴) represents an "auxiliary polynomial":

  2s^4 +48s^2 -50

To continue the process, we replace the zero row by the coefficients of the derivative of this auxiliary polynomial. Proceeding as before, the array now becomes ...

  \begin{array}{cccc}s^5&1&24&-25\ns^4&2&48&-50\ns^3&8&96\ns^2&24&-50\ns^1&112(2)/(3)&0\ns^0&-50\end{array}

The number of sign changes in the first column (1) tells the number of roots in the right half-plane. The auxiliary polynomial will give us the remaining two pairs of roots:

  2s^4+48s^2-50=0\n\n2(s^2+25)(s^2-1)=0\n\ns=\pm 5i,\ s=\pm 1

So, we have determined there to be ...

  • 1 root in the right half-plane
  • 2 roots on the jω axis
  • 2 roots in the left half-plane

__

(b) The original polynomial can be factored as ...

  p(s) = (s +2)(s² +25)(s +1)(s -1)

  p(s) = (s +2)(s +1)(s -5i)(s +5i)(s -1)

This verifies our result from part (a).

_____

Additional comments

Any row can be multiplied by a convenient factor to simplify the arithmetic. Here, it would be convenient to divide the second row by 2 and the third row by 8.

A zero element (not row) in the first column is replaced by "epsilon" (a small positive number) and the rest of the arithmetic is continued as normal. That row is not counted (it is ignored) when counting sign changes in the first column.

Someone help me on this.

Answers

Answer:

-57-39i

Step-by-step explanation:

So we have the expression:

(7+2i)(-9-3i)

FOIL:

=7(-9)+7(-3i)+2i(-9)+2i(-3i)

Simplify:

=-63-21i-18i-6i^2

Recall that i² is just -1. Thus:

=-63-21i-18i-6(-1)

Simplify:

=-63-21i-18i+6

Combine like terms:

=(-63+6)+(-21i-18i)

Add:

=-57-39i

And we're done!

Adrian shops for school clothes and spends a total of $93.42. If the local tax rate is 8%, how much was the cost without taxes?

Answers

Based on the amount that Adrian spent in total, the cost without taxes was $86.50.

The cost of the clothes was $93.42 including tax.

Assuming the original cost is x, the equation is:

Total cost = Original cost x ( 1 + tax)

Solving would give:

93.42 = x × (1 + 8%)

93.42 = 1.08x

x = 93.42 / 1.08

= $86.50

In conclusion, the cost without taxes was $86.50.

Find out more at brainly.com/question/17836987.

Answer:

85.95

Step-by-step explanation:

If the local tax was 8% and we want to know what is was without the tax then we need to do 93.42 times .92

93.42*.92=85.9464

Since money only goes to the hundredths place we need to round there

85.95

A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket? 35 dollars (0.08) 35 dollars (8) 35 dollars (0.08) + 35 dollars 35 dollars (8) + 35 dollars

Answers

Answer:

35 dollars (0.08)

Step-by-step explanation:

35 + 8%, taxes are most likely in cents

Answer:

35 dollars (0.08)

Step-by-step explanation:

A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket?

A.35 dollars (0.08)

B.35 dollars (8)

C.35 dollars (0.08) + 35 dollars

D.35 dollars (8) + 35 dollars

because i just took the test and i got 94.3 and this question is right.

Hopefully this helps.

Write an equation for the line through the points (7, 2) and (10,6) in point-slope form.

Answers

Answer:

Your answer is y-2=4/3(x-7)

Step-by-step explanation:

Answer:

y-2=4/3(x-7)

Step-by-step explanation:
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