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andreev551 [17]

3 years ago

7

What is the mean of this data set? If necessy, round your answer to the nearest tenth. 12,16,22,23,34,44,46,47,48,64,67,73,83,88

,89

1 answer:

Dmitry_Shevchenko [17]3 years ago

8 0

The mean for the data set is 50.4

Rounded to the nearest 10th is 50

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If m∠a=47°, what is m∠b, m∠c, and m∠d? Explain how you know the measures are correct.

avanturin [10]

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°.

<h3>Further explanation</h3>

Follow the attached picture. I sincerely hope that's precisely a correct illustration.

We will use a graph of two intersecting straight lines.

Note that m ∠a and m ∠c are vertical angles. Since vertical angles share the same measures, in other words always congruent, we see $\boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}$

We continue to determine m ∠b and m ∠d.

Note that m ∠b and m ∠d represent supplementary angles. Recall that supplementary angles add up to 180°.

Let us see the following steps.

$\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }$

$\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }$

Both sides subtracted by 47°.

$\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }$

Thus $\boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}$

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, $\boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}$

<u>Conclusion:</u>

m ∠a = 47°
m ∠b = 133°
m ∠c = 47°
m ∠d = 133°

<u>Notes:</u>

Supplementary angles are two angles when they add up to 180°. $\boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }$
Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. $\boxed{ \ example: \angle{a} = \angle{c} \ }$

<h3>Learn more</h3>

About the measure of the central angle brainly.com/question/2115496
Undefined terms needed to define angles brainly.com/question/3717797
Find out the measures of the two angles in a right triangle brainly.com/question/4302397

Keywords: m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent

7 0

4 years ago

Read 2 more answers

What is the area of the composite figure shown

Greeley [361]

So, We Know That The Figure Shown Is A Square. So, We Need To Find The Area:
70*70 = 4900.

So, We Have:
490 - (Area Of The Triangle) = A

So, Lets Find The Area Of The Triangle.

(35*70)/2
Well, 35*70 = 2450.
So:
2450/2 = 1225.

Now, Do:

4900 - 1225 = A

4900 - 1225 = 3675

So:
3675cm² = A

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

2 years ago

Please answer this simple question!!!

vladimir1956 [14]

Just substitute the value of x from equation 2 in equation 1,
6y = x - 12
6y = 22 - 12
y= 10/6
y = 5/3

In short, Your Answer would be Option Option B) (22, 5/3)

Hope this helps!

6 0

3 years ago

Alvin is 13 years older than Elga the sum of their age is 55 what is elgas age

Makovka662 [10]

Answer:

Elga is 42 years old

Step-by-step explanation:

55-13=42

5 0

4 years ago