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2 years ago

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An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greate

st possible length of the longest side, rounded to the nearest tenth?
18.8 cm
24.2 cm
42.0 cm
72.7 cm

2 answers:

inna [77]2 years ago

4 0

Answer:

B. 24.2 cm

Step-by-step explanation:

We are given that,

Lengths of the sides of a triangle are 21 cm, x cm and 2x cm.

Using Triangle Inequality Theorem, which states that,

<em>'The sum of measure of any two sides must be greater than the measure of the third side'.</em>

Since, 21 cm is the shorter side. We have,

A) $21+x>2x$ i.e. $21>x$ or $x$ .

B) $x+2x>21$ i.e. $3x>21$ or $x>7$

So, $7$

That is, $14$

Thus, the length of the larger side has measure between 14 cm and 42 cm.

Hence, the possible length of the longest side is 24.2 cm.

Aliun [14]2 years ago

3 0

we know that

<u>The Triangle Inequality Theorem</u> states that the sum of any two sides of a triangle must be greater than the measure of the third side

so

<u>case a)</u> $21+x > 2x$

$21+x > 2x\\21> 2x-x\\21> x\\x < 21\ cm$

<u>case b)</u> $x+2x > 21$

$x+2x > 21\\3x> 21\\x> 7\ cm$

therefore

the longest side is $2x$

$x < 21\ cm\\2x < 42\ cm$

the longest side could be $41.99\ cm$

rounded to the nearest tenth is $42\ cm$

<u>the answer is the option</u>

$42\ cm$

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Answer:

Length A of the magazine garden is 28 feet is true.

Length B of the Magazine garden is 17.5 feet is true.

Length C of the Magazine garden is 35 feet is true.

Step-by-step explanation:

Please refer the attached figure.

Given:-

Magazine Scale is 1 inch = 3.5 feet.

Imogen's scale is 2 inches = 6 feet,

Therefore Imogen's scale is 1 inch = 3 feet.

In Triangle ABC,

side a = 8 inches, side b= 5 inches, side c= 10 inches.

To find:- The correct 3 options(actual size of sides of triangle ABC).

Solution:-

In triangle ABC,

Let,

AB=side a =8 inches

BC=side b =5 inches

AC=side c= 10 inches

Now, as per the given scale's of Magazine and Imogen's we can find the actual sizes.

Length A as per Magazine scale (1 inch = 3.5 feet) is,

$\therefore Length\ A=8\times 3.5$ -------------(as per scale)

$\therefore Length A=28\ feet$

and Length A as per Imogen's scale(1 inch =3 feet) is,

AB = side a

$\therefore Length\ A=8\times 3$ -------------(as per scale)

$\therefore Length A=24\ feet$

Therefore Length A of the magazine garden is 28 feet is true.

Now, Length B as per Magazine scale (1 inch = 3.5 feet) is,

BC = side b

$\therefore Length\ B=5\times 3.5$

$\therefore Length B=17.5\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

BC = side b

$\therefore Length\ B=5\times 3$

$\therefore Length B=15\ feet$

Therefore Length B of the Magazine garden is 17.5 feet is true.

Now, Length C as per Magazine scale (1 inch = 3.5 feet) is,

AC = side c

$\therefore Length\ C=10\times 3.5$

$\therefore Length C=35\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

AC = side c

$\therefore Length\ C=10\times 3$

$\therefore Length B=30\ feet$

Therefore Length C of the Magazine garden is 35 feet is true.

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2 years ago

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2 years ago

In constructing a 95 percent confidence interval, if you increase n to 4n, the width of your confidence interval will (assuming

Damm [24]

Answer:

about 50 percent of its former width.

Step-by-step explanation:

Let's assume that our parameter of interest is given by $\theta$ and in order to construct a confidence interval we can use the following formula:

$\hat \theta \pm ME(\hat \theta)$

Where $\hat \theta$ is an estimator for the parameter of interest and the margin of error is defined usually if the distribution for the parameter is normal as:

$ME = z_{\alpha} SE$

Where $z_{\alpha/2}$ is a quantile from the normal standard distribution that accumulates $\alpha/2$ of the area on each tail of the distribution. And $SE$ represent the standard error for the parameter.

If our parameter of interest is the population proportion the standard of error is given by:

$SE= \frac{\hat p (1-\hat p)}{n}$

And if our parameter of interest is the sample mean the standard error is given by:

$SE = \frac{s}{\sqrt{n}}$

As we can see the standard error for both cases assuming that the other things remain the same are function of n the sample size and we can write this as:

$SE = f(n)$

And since the margin of error is a multiple of the standard error we have that $ME = f(n)$

Now if we find the width for a confidence interval we got this:

$Width = \hat \theta + ME(\hat \theta) -[\hat \theta -ME(\hat \theta)]$

$Width = 2 ME (\hat \theta)$

And we can express this as:

$Width =2 f(n)$

And we can define the function $f(n) = \frac{1}{\sqrt{n}}$ since as we can see the margin of error and the standard error are function of the inverse square root of n. So then we have this:

$Width_i= 2 \frac{1}{\sqrt{n}}$

The subscript i is in order to say that is with the sample size n

If we increase the sample size from n to 4n now our width is:

$Width_f = 2 \frac{1}{\sqrt{4n}} =2 \frac{1}{\sqrt{4}\sqrt{n}} =\frac{2}{2} \frac{1}{\sqrt{n}} =\frac{1}{\sqrt{n}} =\frac{1}{2} Width_i$

The subscript f is in order to say that is the width for the sample size 4n.

So then as we can see the width for the sample size of 4n is the half of the wisth for the width obtained with the sample size of n. So then the best option for this case is:

about 50 percent of its former width.

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2 years ago

The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write and

notsponge [240]

Answer:

$4.65\leq x\leq 5.35$

Step-by-step explanation:

Let the actual width of belt be x

we are given that the ideal width of safety belt strap is 5 cm

So, Difference between actual and ideal = (x-5)cm

We are also given that An actual width can vary by at most 0.35 cm.

So, The difference between actual and ideal width should be less than or equal to 0.35 cm

So, $|x-5|\leq 0.35$

We know

$x-5\leq 0.35$ and $x-5\geq -0.35$

$x\leq 0.35+5$ and $x\geq -0.35+5$

$x\leq 5.35$ and $x\geq 4.65$

So, $4.65\leq x\leq 5.35$

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2 years ago

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Novay_Z [31]

Menjawab:

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Penjelasan langkah demi langkah:

Dari identitas trigonometri, pemuaiannya benar:

Cos (A + B) = cosAcosB-sinAsinB

Menerapkan ini dalam memperluas cos (x + 60).

cos (x + 60) = cosxcos60 - sinxsin60

Jika sinx = p = berlawanan / sisi miring

opp = p, hyp = 1

adj² = 1²-p²

adj = √1-p²

Cos (x) = adj / hyp = √1-p² / 1

Cos (x) = √1-p²

Cos60 = 1/2 dan sin60 = √3 / 2

Mengganti nilai-nilai ini ke dalam rumus

cos (x + 60) = cosxcos60 - sinxsin60

cos (x + 60) = √1-p² (1/2) - p (√3 / 2)

cos (x + 60) = (√1-p²) / 2 - √3p / 2

Temukan KPK tersebut

cos (x + 60) = [(√1-p²) -3√p] / 2

Oleh karena itu cos (x + 60) = [(√1-p²) -3√p] / 2

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2 years ago