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aleksandrvk [35]
3 years ago
5

Find the measures of all four angles if m∠2 − m∠1=30°

Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0

Answer:

m∠1 = m∠3 = 75°

m∠2 = m∠4 = 105°

Step-by-step explanation:

From the figure attached,

m∠1 + m∠2 = 180° [Supplementary angles]------(1)

Since, m∠2 - m∠1 = 30°

m∠2 = 30° + m∠1 -----(2)

By substituting the value of ∠2 from equation (2) to equation (1),

m∠1 + (m∠1 + 30°) = 180°

2(m∠1) + 30° = 180°

2(m∠1) = 150°

m∠1 = 75°

Therefore, m∠2 = 180°- m∠1 = 180° - 75°

                  m∠2 = 105°

Since, ∠ 2 ≅ ∠4 [Vertical angles]

m∠2 = m∠4 = 105°

Similarly, ∠1 ≅ ∠3 [Vertical angles]

m∠1 = m∠3 = 75°

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Which number is NOT in the solution set of x + 8 &gt; 15?<br> A)6<br> B)8<br> C)10 <br> D•12
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Answer:

A) 6

Step-by-step explanation:

Firstly, the solution set to the inequality is : x > 7

Because, x + 8 > 15 ⇌ x > 15 - 8 ⇌ x > 7

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The only number that is NOT in the solution set is 6

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The brain volumes ​(cm cubed​) of 20 brains have a mean of 1162.8 cm cubed and a standard deviation of 127.1 cm cubed. Use the g
Free_Kalibri [48]

Answer:

- The limits are  908.6 cm^3 and 1417cm^3

- 1337.0cm^3 is in between the limits

Step-by-step explanation:

To determine the limit by taking into account the range rule of thumb, you use the fact that the limits are given by the mean plus and minus twice the standard deviation, that is:

\overline{x}\pm 2\sigma        (1)

\overline{x}: mean of brain volume = 1162.8 cm^3

σ: standard deviation = 127.1 cm^3

You replace the values of the parameters in the equation (1):

1162.8cm^3+2(127.1cm^3)=1417cm^3\\\\1162.8cm^3-2(127.1cm^3)=908.6cm^3

Limits = (1417 , 908.6)

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5 0
3 years ago
John has two colored varieties of water bottles: white water bottles and black water bottles. The total number of water bottles
mixas84 [53]

Answer:

15 black water bottles

Step-by-step explanation:

let w represent white water bottles, and let b represent black water bottles.

set up a system of equations:

w+b=20

w+2b=35

(the top equation shows that the number of white water bottles he sold and the number of black water bottles he sold equals to 20, since it says that the total number of water bottles is 20. the bottom equation shows that white water bottles cost $1, and black water bottles cost $2, and that the total amount of money he got from selling them is $35).

in the top equation, isolate w:

w+b=20

w=20-b

now we do substitution. in the bottom equation, substitute 20-b for w:

w+2b=35

20-b+2b=35

then, solve:

b+20=35

b=15

this means that he sold 15 black water bottles.

4 0
3 years ago
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