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2 years ago

List 3 values that would make this inequality true 4n <_ 12

1 answer:

4 0

Divide both sides by 4 to get

$4n \le 12$

$\frac{4n}{4} \le \frac{12}{4}$

$n \le 3$

So we can pick n to be 3 or it can be less than 3

Three values we can pick are: n = 0, n = 1, n = 2

Or we could pick: n = 1, n = 2, n = 3

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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

2 years ago

Please someone answer my questions please

navik [9.2K]

Answer:

What is your question?

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Which functions have graphs that are less steep than the graph of f(x)= -4x^2

LiRa [457]

TTese are all parabolas whose axis of symmetry is the y axis. The negative coefficient means they open downwards and the positive mean they open upwards. The higher the absolute value of the coefficient is the greater the slope, so 2x^2 will be steeper than x^2 and -4x^2 will be steeper than - 2x^2.

So h(x) and j(x) are the answers.

8 0

2 years ago

A truck rental company rents a moving truck One Day by charging $39 + 0.09 per mile write a linear equation that relates the cos

Ivanshal [37]

Answer:

$(a)\ c(x) = 39 + 0.09 x$

$(b)\ \$53.4$

Step-by-step explanation:

Given

$Base\ Charge = \$39$

$Rate = 0.09$ per mile

Solving (a): Linear Equation

The total charges (c(x)) is: the base charge + the rate * number of miles (x).

So, we have:

$c(x)= 39 + 0.09 * x$

$c(x) = 39 + 0.09 x$

Solving (b): Cost of rent, if miles = 160

This implies that x = 160

So, we have:

$c(x) = 39 + 0.09 x$

$c(160) = 39 + 0.09 *160$

$c(160) = 39 + 14.4$

$c(160) = 53.4$

7 0

2 years ago

The ratio that describes how far an estimate is from the actual amount?

STatiana [176]

A ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Please mark as brainliest if this helped

6 0

2 years ago