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3 years ago

A triangle has sides of length 2 cm and 12 cm. What can you say about the length of the third side?

Mathematics

1 answer:

pishuonlain [190]3 years ago

3 0

Answer:

The third side must be between 10cm and 14 cm

Step-by-step explanation:

Let the third side be x

Triangle inequality theorem: sum of the length of any two sides must be greater than the third side length:

2 + 12 > x ⇒ x < 14
2 + x > 12 ⇒ x > 10
x + 12 > 2 ⇒ x > -10, we change it to x > 0 as it should be a positive number

Combined together we have:

10 < x < 14

The third side must be between 10cm and 14 cm

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Find the nth term of this quadratic sequence 4, 7, 12, 19, 28,...

Len [333]

Tn=n²+3

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therefore we constantly add 2 to the difference

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3 years ago

A model airplane is built on the scale of 0.5 inch for every 11 feet. The length of the

Tema [17]

Answer:

$9.59$ ft

Step-by-step explanation:

$\frac{211}{11}$

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2 years ago

Solve each proportion. show your work. 2x/7 = 12/14

dybincka [34]

2x/7 = 12/14
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3 years ago

SOS if anyone could help that would be appreciated!!!❤️

Anastaziya [24]

Answer:

See below

Step-by-step explanation:

$2e)15-4x=10x+45$

Solve:

$15-4x=10x+45\\-4x-10x=45-15\\-14x=30\\ \boxed {x=-\dfrac{15}{7}}$ $3(x+1)=21$

Check:

$15-4 \left(-\dfrac{15}{7} \right)=10\left(-\dfrac{15}{7} \right)+45$

$15+\dfrac{60}{7} \right)=-\dfrac{150}{7} +45$

$\dfrac{210}{7} =30$

$30=30$

$3a) 3(x+1)=21$

Solve:

$3(x+1)=21\\3x+3=21\\3x=18\\x=6$

$3b) 2+3(x+1)=6x$

$2+3x+3=6x\\5=3x\\$

$x=\dfrac{5}{3}$

$3c) -2(2x-3)=-2$

Solve:

$-2(2x-3)=-2\\-4x+6=-2\\-4x=-8\\x=2$

3 0

3 years ago

(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the

goblinko [34]

Given that the scale readings of the laboratory scale is normally distributed with an unknown mean and a standard deviation of 0.0002 grams.

Part A:

If the weight is weighted 5 times and the mean weight is 10.0023 grams, the 98% confidence interval for μ, the true mean of the scale readings is given by:

$98\% \ C. \ I.=\bar{x}\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right) \\ \\ =10.0023\pm2.33\left(\frac{0.0002}{\sqrt{5}}\right) \\ \\ =10.0023\pm2.33(0.000089) \\ \\ =10.0023\pm0.00021 \\ \\ =(10.0023-0.00021, \ 10.0023+0.00021) \\ \\ =(10.0021, \ 10.0025)$

Thus, we are 98% confidence that the true mean of the scale readings is between 10.0021 and 10.0025.

Part B:

To get a margin of error of +/- 0.0001 with a 98% confidence, then

$\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right)=\pm0.0001 \\ \\ \Rightarrow2.33\left(\frac{0.0002}{\sqrt{n}}\right)=0.0001 \\ \\ \Rightarrow\left(\frac{0.0002}{\sqrt{n}}\right)= \frac{0.0001}{2.33} =0.0000429 \\ \\ \Rightarrow\sqrt{n}= \frac{0.0002}{0.0000429} =4.66 \\ \\ \Rightarrow n=4.66^2=21.7156\approx22$

Therefore, the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence is 22.

8 0

3 years ago

A triangle has sides of length 2 cm and 12 cm. What can you say about the length of the third​ side?

A triangle has sides of length 2 cm and 12 cm. What can you say about the length of the third side?