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3 years ago

HELP ASAP PLEASEEE.

Mathematics

1 answer:

Troyanec [42]3 years ago

8 0

Please mark Brainliest. Plz.

Answer:

x^2 = 25 x = 5, -5

2x^2 = 98 x = 7, -7

x^2 + 64 = 0 x = 8i, -8i

9x^2 - 16 = 0 x = 4/3, -4/3

x^2 + 9 = 25 x = 4, -4

(x-2)^2 = 25 x = 7, -3

(x-2)^2 +9 = 25 x = 6, -2

4(x-2)^2 +9 = 25 x = 4, 0

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Work out the area of abcd.<br><br> please ensure you give workings out too.

ipn [44]

Answer:

$\displaystyle A_{\text{Total}}\approx45.0861\approx45.1$

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

$\displaystyle \cos(55)=\frac{AD}{10}$

Solve for AD:

$AD=10\cos(55)$

Now, we can use the formula. We have:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Substituting AD for a, 10 for b, and 55 for C, we get:

$\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)$

Simplify. Therefore, the area of the right triangle is:

$A=50\cos(55)\sin(55)$

We will not evaluate this, as we do not want inaccuracies in our final answer.

Scalene Triangle CDB:

We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

$\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}$

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

$\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}$

Where A and B are the angles opposite to its respective sides.

So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

$\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}$

Solve for CD. Cross-multiply:

$CD\sin(98)=10\sin(38)$

Divide both sides by sin(98). Hence:

$\displaystyle CD=\frac{10\sin(38)}{\sin(98)}$

Therefore, we can now use our area formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

We will substitute 10 for a, CD for b, and 44 for C. Hence:

$\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)$

Simplify. So, the area of the scalene triangle is:

$\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}$

Therefore, our total area will be given by:

$\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}$

Approximate. Use a calculator. Thus:

$\displaystyle A_{\text{Total}}\approx45.0861\approx45.1$

8 0

3 years ago

A football team charges $30 per ticket and averages 20,000 people per game. Each person spend an average of $8 on concessions.Fo

olya-2409 [2.1K]

The ticket price that would maximize the total revenue would be $ 23.

Given that a football team charges $ 30 per ticket and averages 20,000 people per game, and each person spend an average of $ 8 on concessions, and for every drop of $ 1 in price, the attendance rises by 800 people, to determine what ticket price should the team charge to maximize total revenue, the following calculation must be performed:

20,000 x 30 + 20,000 x 8 = 760,000
24,000 x 25 + 24,000 x 8 = 792,000
28,000 x 20 + 28,000 x 8 = 784,000
26,000 x 22.5 + 26,000 x 8 = 793,000
27,200 x 21 + 27,200 x 8 = 788,000
26,400 x 22 + 26,400 x 8 = 792,000
25,600 x 23 + 25,600 x 8 = 793,600
24,800 x 24 + 24,600 x 8 = 792,000

Therefore, the ticket price that would maximize the total revenue would be $ 23.

Learn more in brainly.com/question/7271015

4 0

3 years ago

A national military bureau for a certain country collects data on active members in the military. Results are published in a nat

Artemon [7]

Answer:

9.193259%

Step-by-step explanation:

In order to obtain the percentage of military members in the reserves who are Black, we will have to multiply the percentage of Black military members in the reserve by the percentage of military members in the reserve. This is calculated as follows:

Military members in the reserves who are Black (%) = 77.1771% × 11.9119%

= 9.193259%

Therefore, he percentage of military members in the reserves who are Black is 9.193259% .

Example

For example, let assume the total number of active members in the military is 100.

To obtain the number of military members who are in the reserves, we multiply 77.1771% by 100. This gives us 78 approximately.

To obtain the number of military members in the reserves who are Black, we multiply 11.9119% by 78 we got above who are active military members in the reserves. This gives us 9 members approximately.

I wish you the best.

3 0

3 years ago

Read 2 more answers

Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right

Agata [3.3K]

Answer:

6 StartRoot 3 EndRoot units

Step-by-step explanation:

7 0

2 years ago

Order 3/6 2/5 1/4 in descending order

sveta [45]

It is in the right order
3/6, 2/5, 1/4

3 0

3 years ago

HELP ASAP PLEASEEE.​

HELP ASAP PLEASEEE.