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Allisa [31]
2 years ago
5

PLEASE ANSWER THIS ITS URGENT

Mathematics
2 answers:
kirza4 [7]2 years ago
4 0

Answer:

  • Graph C

Step-by-step explanation:

We can solve it without actually plotting the inequalities.

<u>Observations:</u>

  • Both lines have positive slopes and both have same inequality symbol ⇒ ≤
  • It means both shaded regions are below the lines and the lines are solid.
  • The y-intercepts, the steeper line has b = - 3 and the other line has b = 2

All the above observations are reflected on the graph C only.

Oksi-84 [34.3K]2 years ago
3 0

Answer:

  • Option C

Explanation:

First, I plotted both the lines on the graph, then I graphed the inequality.<u> </u><em>Please check out image.</em> Looking at the image, we can tell that the graph matches with Graph-C. Hence, Option C is correct.

Hoped this helped!

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Answer:

<h2>Q1. y = 3</h2><h2>Q2. m∠B = 125°</h2><h2>Q3. m∠SPQ = 110°</h2><h2>Q4. x = 55</h2><h2>Q5. x = 123</h2>

Step-by-step explanation:

<h3>Q1.</h3>

If ABCD is a rectangle, then diagonals are congruent: AC = BD.

We have

AC = 5y - 2

BD = 4y + 1

Substitute:

5y - 2 = 4y + 1           <em>add 2 to both sides</em>

5y - 2 + 2 = 4y + 1 + 2

5y = 4y + 3            <em>subtract 4y from both sides</em>

5y - 4y = 4y - 4y + 3

y = 3

<h3>Q2.</h3>

In a parallelogram opposite angles are congruent. Therefore m∠D = m∠B.

We have m∠D = 125° → m∠B = 125°

<h3>Q3.</h3>

In the rhombus, the diagonals are bisectors of the rhombus angles.

Therefore ∠SPR and ∠QPR are congruent.

We have

m∠SPR = (2x +15)°

m∠QPR = (3x - 5)°

The equation:

2x + 15 = 3x - 5           <em>subtract 15 from both sides</em>

2x + 15 - 15 = 3x - 5 - 15

2x = 3x - 20         <em>subtract 3x from both sides</em>

2x - 3x = 3x - 3x - 20

-x = -20           <em>change the signs</em>

x = 20

Substitute it to the expression m∠SPR = (2x + 15)°:

m∠SPR = (2(20) + 15)° = (40 + 15)° = 55°

m∠SPR = m∠QPR → m∠QPR = 55°

∠SPQ = ∠SPR + ∠QPR → m∠SPQ = 2(55°) = 110°

<h3>Q4.</h3>

In the parallelogram, the sum of the angle measures on one side is 180°.

Therefore we have the equation:

(2x + 15) + x = 180      <em>combine like terms</em>

(2x + x) + 15 = 180           <em>subtract 15 from both sides</em>

3x + 15 - 15 = 180 - 15

3x = 165            <em>divide both sides by 3</em>

3x/3 = 165/3

x = 55

<h3>Q5.</h3>

In a parallelogram opposite angles are congruent.

Therefore z = y and x = 2z + 9 → x = 2y + 9    (*)

In the parallelogram, the sum of the angle measures on one side is 180°.

Therefore x + y = 180     (**)

Substitute (*) to (**)

(2y + 9) + y = 180          <em>combine like terms</em>

(2y + y) + 9 = 180             <em>subtract 9 from both sides</em>

3y + 9 - 9 = 180 - 9

3y = 171          <em>divide both sides by 3</em>

y = 57

Put it to (*):

x = 2(57) + 9

x = 114 + 9

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next we need t set up a function for Time in terms of x.
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T = \frac{dR}{5} + \frac{dW}{10} = \frac{4 \sqrt{2}}{5} \sqrt{1-cos(180-2x)}+\frac{4}{5} x
Finally, take derivative and set equal to 0
Once you solve for x, plug it back into Time function to obtain final answer.

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