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2 years ago

2. Write an expression that can be used to

Mathematics

1 answer:

kozerog [31]2 years ago

5 0

The expression to find the length of JH is $JH = 9\cdot \sin 35^{\circ}$ .

The expression to find the length of GJ is $GJ = 9\cdot \cos 35^{\circ}$ .

<h3 /><h3>Resolution - Determination of expression for the side lengths of a right triangle</h3>

<h3>Some facts on right triangles</h3>

A <em>right</em> triangle has two legs and a hypotenuse, the two legs are <em>adjacent</em> to a <em>right</em> angle and the hypotenuse is the side opposite to that angle. Besides, the hypotenuse is the longest side of the right triangle.

<h3>Determination of trigonometric expression for needed lengths</h3>

We can determine the value of each leg by means of trigonometric relations in terms of the hypotenuse and an angle <em>adjacent</em> to it, which are described below:

$JH = GH\cdot \sin \theta$ (1)

$GJ = GH\cdot \cos \theta$ (2)

If we know that $GH = 9$ and $\theta = 35^{\circ}$ , then the expressions are:

<h3>Length of JH</h3><h3 />

$JH = 9\cdot \sin 35^{\circ}$

<h3>Length of GJ</h3>

$GJ = 9\cdot \cos 35^{\circ}$

<h3>Conclusions</h3><h3 />

The expression to find the length of JH is $JH = 9\cdot \sin 35^{\circ}$ . $\blacksquare$

The expression to find the length of GJ is $GJ = 9\cdot \cos 35^{\circ}$ . $\blacksquare$

To learn more on right triangles, we kindly invite to check this verified question: brainly.com/question/7894175

<h3>Remark</h3>

The statement is incomplete and full of mistakes. In addition, there is an image missing. The complete and corrected expression is presented:

<em>Write an expression that can be used to find the length of </em> $JH$ <em> and an expression that can be used to find the length of </em> $GJ$ <em>.</em>

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4 years ago

Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets.

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Answer:

she should charge $7.395 per ticket in order to make the most money.

Step-by-step explanation:

From the given information:

If Rosalie charges $5 then 1175 people will attend the circus performance

If Rosalie charges $7 then 935 people will attend the circus performance

Let x be the cost and y to be the number of people that will attend the performance . Then, we will have two points which are;

(5, 1175) and (7, 935)

The slope(m) of this points = $\dfrac{\Delta y}{\Delta x}$

= $\dfrac{y_2-y_1}{x_2-x_1}$

$=\dfrac{935-1175}{7-5}$

Slope (m) = $\dfrac{-240}{2}$

Slope (m) = -120

However; we can now have the linear equation:

$y-y_1 = m(x-x_1)$

$y-1175= -120(x-5)$

$y-1175= -120x+600$

$y= -120x+600+1175$

$y= -120x+1775$

The linear function is : y = -120x + 1775

Now; the total amount of money she can now earn is:

f(x) = xy

f(x) = x(-120x + 1775)

f(x) = -120x² + 1775x

The above expression is a quadratic equation; Using the quadratic formula; we have:

$=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

where; a = -120 ; b = +1775 and c = 0

$=\dfrac{-(1775) \pm \sqrt{(1775)^2-4(-120)(0)}}{2(-120)}$

$=\dfrac{-(1775) + \sqrt{(1775)^2-4(-120)(0)}}{2(-120)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) -\sqrt{(1775)^2-4(-120)(0)}}{2(-120)}$

$=\dfrac{-(1775) + \sqrt{(1775)^2}}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) -\sqrt{(1775)^2}}{(-240)}$

$=\dfrac{-(1775) + (1775)}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) - (1775)}{(-240)}$

$=\dfrac{0}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-3550}{(-240)}$

= 0 OR 14.79

Since; we are considering the value greater than zero

x = 14.79

maximum value of x = 14.79/2 = 7.395

Thus ; she should charge $7.395 per ticket in order to make the most money.

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Answer:

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We have 38+24-16 = 46 people who either prefer plan A, are aged 40-49, or fit both descriptions. I subtracted off 16 because those 16 people were counted twice when adding 38 and 24.

An alternative way to get this value of 46 is to add up everything that is in column1 or row 3 (or both). So that would get 10+12+16+8 = 46.

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