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3 years ago

2.6 written as a reduced fraction?

Mathematics

2 answers:

beks73 [17]3 years ago

8 0

13/5 or 2 3/5 by the way nice profile picture

vfiekz [6]3 years ago

3 0

2 3/5 is one reduced fraction.
Hope this helps!!! i love your profile too!!

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Work out the area of abcd. 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 between 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

Find the sine ratio of angle Θ. Hint—Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no sp

Ainat [17]

Answer:

sinΘ = $\frac{12}{13}$

Step-by-step explanation:

sinΘ = $\frac{opposite}{hypotenuse}$ = $\frac{AB}{BC}$ = $\frac{12}{13}$

5 0

2 years ago

What is the value of the expression below when x 3 and y = 8? 6x + 10y

suter [353]

Answer:

Step-by-step explanation:

So we have the expression:

$6x+10y$

And we want to evaluate it when x is 3 and y is 8.

So, substitute:

$=6(3)+10(8)$

Multiply:

$=18+80$

Add:

$=98$

And we're done!

7 0

3 years ago

Read 2 more answers

1) The deer population in a national park is expected to decline over time. The park

Lorico [155]

Answer:

Here's what I find.

Step-by-step explanation:

You have 800 deer at the end of Year 1, and you expect the population to decrease each year thereafter.

a) i) The recursive formula

Let dₙ = the deer population n years after the initial measurement.

$d_{n} = d_{n - 1}r^{n}$

For this situation,

$d_{n} = d_{n - 1}(0.5)^{n}$

a) ii) Definitions

n = the number of years from first measurement

r = the common ratio, that is, the deer population at the end of one year divided by the population of the previous year.

a) iii) First term of sequence

The first term of the sequence is d₀, the population when first measured.

b) The function formula

The formula for the nth term of a geometric series is

$d_{n} =d_{0}r^{n - 1}$

c) Value of d₀

Let n = 2; then d₂ = 800

$\begin{array}{rcl}800 & = & d_{0}(0.5)^{2 - 1}\\800 & = & d_{0}(0.5)\\\\d_{0} & = & \dfrac{800}{0.5}\\\\& =&\mathbf{1600}\\\end{array}$

4 0

3 years ago

I NEED HELP!!! PLEASE!!!!!!!!!!!!!!!!!

ale4655 [162]

The awnser to ur question is A because take 2.3 time 3 and get 6.9 and then add the 108 and -3 and get 105

3 0

3 years ago