Ask question

Ask question

All categories

2 years ago

9

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>

$42\ cm$

You might be interested in

Millie has a box of 1 hundred cubes. She also has a bag of 70 cubes. How many trains of 10 cubes can she make?

Serga [27]

100 + 70 = 170

170 / 10 = 17

17, 10 cube trains

5 0

1 year ago

Read 2 more answers

PT=7x-24 and TQ=6x-2, Find PT.

Nastasia [14]

We can't find what PT exactly is because we don't know TQ or x. However, we can find PT in terms of TQ!

Multiply the second equation by seven sixths to get:

$\frac{7TQ}{6}=7x- \frac{7}{3}$

Subtract $\frac{65}{3}$ from both sides to get:

$\frac{7TQ}{6}- \frac{65}{3}=7x-24$

Substituting PT for 7x-24, we see that:

$PT= \frac{7TQ}{6} - \frac{65}{3}$ , which is our answer.

4 0

2 years ago

Determine which of (a)-(d) form a solution to the given system for any choice of the free parameter. (HINT: All parameters of a

Alecsey [184]

Answer:

Please see attachment

8 0

2 years ago

Read 2 more answers

Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?

dimaraw [331]

Answer:

D) n^6 - 6m^6 + 7mn^5 + 14m^2n^4 -5m^3 n^3

Step-by-step explanation:

The given polynomial is 8mn^5 -2m^6 +5m^2 n^4 - m^3 n^3 + n^6 - 4m^6 + 9m^2n^4 -mn^5 - 4m^3n^3

Now we have to identify the like terms and simplify.

Like terms are nothing but the terms which have the same variables with same powers.

= (8mn^5 - mn^5) -2m^6 - 4m^6 + 5m^2 n^4 + 9m^2 n^4 - m^3n^3 - 4m^3n^3 +n^6

Now combine the like terms

= 7mn^5 - 6m^6 +14m^2 n^4-5m^3n^3 + n^6

It can be written in standard form

= n^6 - 6m^6 + 7mn^5 + 14m^2n^4 -5m^3 n^3

The answer is D)

Hope this will helpful.

Thank you.

6 0

2 years ago

Read 2 more answers

A new curing process developed for a certain type of cement results in a mean compressive strength of 5000 kilograms per square

Sedbober [7]

Answer:

$\alpha =0.0668$

Step-by-step explanation:

Data given and notation

The info given by the problem is:

$n=25$ the random sample taken

$\mu =5000$ represent the population mean

$\sigma =100$ represent the population standard deviation

The critical region on this case is $\bar X$ so then if the value of $\bar X \geq 4970$ we fail to reject the null hypothesis. In other case we reject the null hypothesis

Null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the true mean is 5000, the system of hypothesis would be:

Null hypothesis: $\mu = 5000$

Alternative hypothesis: $\mu \neq 5000$

Let's define the random variable X ="The compressive strength".

We know from the Central Limit Theorem that the distribution for the sample mean is given by:

$\bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})$

Find the probability of committing a type I error when H0 is true.

The definition for type of error I is reject the null hypothesis when actually is true, and is defined as $\alpha$ the significance level.

So we can define $\alpha$ like this:

$\alpha= P(Error I)= P(\bar X$

And in order to find this probability we can use the Z score given by this formula:

$Z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And the value for the probability of error I is givn by:

$\alpha= P(\bar X$

4 0

1 year ago