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3 years ago

Line a is parallel to line b, m 6=85, and m 3=2x. Find m 1.

Mathematics

2 answers:

Paladinen [302]3 years ago

3 0

Since a line =180 degrees you could set it up as (180-85) and you would get 95.
Hope this helps!!!

Sergeu [11.5K]3 years ago

3 0

Answer:

m ∠1 = 95.

Step-by-step explanation:

Given : Line a is parallel to line b, angle 6 = 85, and angle 3 =2x.

To find : Find m ∠1.

Solution : We have given that Line a is parallel to line b,

By the transversal angles property : m ∠3 and m ∠6 are the pair of interior angles on the same side of the transversal is supplementary.

m ∠3 + m ∠6 = 180

2x + 85 = 180 .

2x = 180 -85.

2x = 95

Then m ∠3 = 95.

m ∠3 and m ∠1 are vertically opposite angles are equal.

m ∠3 = m ∠1

m ∠1 = 95.

Therefore, m ∠1 = 95.

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Step-by-step explanation:

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3 years ago

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ValentinkaMS [17]

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3 years ago

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Answer:

Step-by-step explanation:

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4 years ago

Read 2 more answers

The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth

Art [367]

Answer:

a) $N_0=250\; k=0.15$

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies $t=0$ . And $N(0)=N_0$ . The process is:

$N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250$

b) After 2 days means $t=48$ . So, we just replace and operate:

$N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}$

c) $N(t_1)=4000; \;t_1=?$

$N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\ \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h$

d) $t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)$

$N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h$

6 0

3 years ago