All categories

3 years ago

2. Complete the proof of the exterior angle theorem

Mathematics

1 answer:

Sonbull [250]3 years ago

7 0

Answer:

The correct answer is:

1. Because of collinearity and supplementarity-

2. They remain along the same line.

3. The sum of them is 180 degrees.

4. Supplementarity.

5. The sum of the internal angles of a triangle is 180ª

6. Supplementarity and external angle theorem sum up the same.

7. Nothing.

Step-by-step explanation:

1. The reason why the exterior angle of 3 is 4, its because the last one is supplementary and collinear to the other.

2. Angle 3 and 4, form a collinear pair since they remain along the same line.

3. Angle 3 is supplementary to 4 because the sum of them is 180 degrees.

4. The sum of the angles are 3 and 4 is 180 because they are supplementary.

5. The sum of the angles mentioned is: 180 because of internal angle theorem.

6. It's like that because supplementarity and external angle theorem sum up the same. i.e, angle 1 + angle 2 + angle 3 = angle 3 + angle 4 =180

7. Nothing.

You might be interested in

Which expression is equivalent to 4√6/3

Nookie1986 [14]

Answer:

$\frac{4}{3}{\sqrt3}$

Step-by-step explanation:

The question seem incomplete;

The full question is

<em>Which expression is equivalent to 4√6/3√2 </em>

Given

4√6/3√2

Required

Find equivalent

$4\sqrt6/3\sqrt2$

Rewrite Expression

$\frac{4\sqrt6}{3\sqrt2}$

Expand the above expression

$\frac{4\ *\ \sqrt6}{3\ * \ \sqrt2}$

Further split the fraction

$\frac{4}{3}\ *\ \frac{\sqrt6}{\sqrt2}$

Using rule of surds;

$\frac{\sqrt a}{\sqrt b} = \sqrt{\frac{a}{b}}$

So, the above expression becomes

$\frac{4}{3}\ *\ \sqrt{\frac{6}{2}}$

$\frac{4}{3}\ *\ {\sqrt3}$

$\frac{4}{3}{\sqrt3}$

At this stage, the expression cannot be further simplified;

Hence, 4√6/3√2 = $\frac{4}{3}{\sqrt3}$

4 0

3 years ago

Evaluate each expression.

Airida [17]

1) 8 + 10 = 18
2) f / d
3) 8 + 7
4) 2 x 5

I hope this helps! Sorry if I did it incorrectly! ❤️ Have a nice day!

3 0

3 years ago

Let f(x)=100 / −10+e^−0.1x .

Montano1993 [528]

Answer:

-14.29422

Step-by-step explanation:

rounded to the nearest tenth = <em>-14.3</em>

3 0

3 years ago

Write the place value of each underlined digit in the numbers below:

sladkih [1.3K]

<h3>♫ :::::::::::::::::::::::::::::: // Hello There ! // :::::::::::::::::::::::::::::: ♫</h3>

➷ I believe saying the number out loud will help

'three hundred and forty nine'

The '4' represents 40

In place value, 40 would hold the 'tens' place

Thus, the place value is 'tens'

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

8 0

4 years ago

A marketing research firm believes that more than half of adults drink mostly either regular or diet soda. To test this claim, G

Korolek [52]

Answer:

The test statistic is z = -2.82.

Step-by-step explanation:

A marketing research firm believes that more than half of adults drink mostly either regular or diet soda.

This means that the null hypothesis is: $H_{0} = 0.5$

The alternate hypothesis is: $H_{a} > 0.5$

The test statistic is:

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

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.5 tested at the null hypothesis:

This means that:

$\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5$

Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. The survey shows that 950 of those surveyed drink mostly either regular or diet soda.

This means that $n = 2027, X = \frac{950}{2027} = 0.4687$

Test statistic:

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

$z = \frac{0.4687 - 0.5}{\frac{0.5}{\sqrt{2027}}}$

$z = -2.82$

The test statistic is z = -2.82.

5 0

3 years ago