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garri49 [273]
3 years ago
7

1/6(x-5)=1/2(x+6) what is the solution to this equation

Mathematics
2 answers:
Alisiya [41]3 years ago
5 0

Step-by-step explanation:

1/6×-5/6=1/2×+3

cross multiply

6(×+3)=2(×-5)

6x+18=2×-10

group like terms

6x-2×=-10-18

4×=-28

×=7

Alexandra [31]3 years ago
3 0

Answer:

Exact Form:

x= -23/2

Decimal:

x= -11.5

Mixed Number:

x= -11/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

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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
Explain why the cubed root of -8/27 is -2/3
Len [333]
Help me and I’ll help you
4 0
2 years ago
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The automaker of your new car recommended an oil change following the 5,000 miles and then every 3,000 miles thereafter.if you p
Rus_ich [418]

Answer:

3 oil changes

Step-by-step explanation:

1. Find an equation that represents this word problem: 3000x + 5000 = y

Where y = the # of miles total. y = 250 miles/week * 52 weeks/year = 13000 miles.

2. Solve for x: 3000x + 5000 = 13000   3000x=8000

3. x = 8/3 integer round down x = 2 oil changes, but plus the one after 5000 miles is a total of 3 oil changes that year

3 0
3 years ago
Mariana wants to bring some friends on a ferry ride at the long beach port for her birthday. she has $200 total to spend on her
SSSSS [86.1K]

Answer:

200< 15p +35 (it's less than or equal to, but i can't put the bar under the sign)

Step-by-step explanation:

3 0
3 years ago
What is a third-degree binomial?
ankoles [38]

Answer:

  • B and D

Step-by-step explanation:

  • <em>Binomial = 2 terms in the expression</em>
  • <em>Third degree = highest added degree of variables in one term</em>

(A) It has 3 terms and highest degree of 4. It is trinomial of degree 4.

  • No

(B) It has 2 terms and highest degree of 3. It is binomial of degree 3.

  • Yes

(C) It has 2 terms and highest degree of 7. It is binomial of degree 7.

  • No

(D) It has 2 terms and highest degree of 3. It is binomial of degree 3.

  • Yes
8 0
3 years ago
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