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horrorfan [7]
3 years ago
9

Solve for x.

Mathematics
2 answers:
Nonamiya [84]3 years ago
7 0

-\dfrac{2}{3}(3x-4)+3x=\dfrac{5}{6}\ \ \ \ |\text{use distributive property}\\\\-\dfrac{2}{\not3_1}\cdot\not3^1x+\dfrac{8}{3}+3x=\dfrac{5}{6}\\\\-2x+3x+\dfrac{8}{3}=\dfrac{5}{6}\ \ \ \ |-\dfrac{8}{3}\\\\x=\dfrac{5}{6}-\dfrac{8}{3}\\\\x=\dfrac{5}{6}-\dfrac{8\cdot2}{3\cdot2}\\\\x=\dfrac{5}{6}-\dfrac{16}{6}\\\\\boxed{x=-\dfrac{11}{6}}

Other method:

-\dfrac{2}{3}(3x-4)+3x=\dfrac{5}{6}\ \ \ \ |\cdot6\\\\2(-2)(3x-4)+18x=5\\\\-4(3x-4)+18x=5\ \ \ \ |\text{use distributive property}\\\\-12x+16+18x=5\ \ \ \ |-16\\\\6x=-11\ \ \ \ |:6\\\\\boxed{x=-\dfrac{11}{6}}

Vikentia [17]3 years ago
5 0

Answer:

x=  -11/6

Step-by-step explanation:

I took the test!

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Factor the expression completely <br> 8y-36
Shtirlitz [24]

Answer:

4(2y - 9)

Step-by-step explanation:

8y - 36 \\  = 4(2y - 9) \\

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3 years ago
According to one cosmological theory, there were equal amounts of the two uranium isotopes 235U and 238U at the creation of the
FromTheMoon [43]

Answer:

6 billion years.

Step-by-step explanation:

According to the decay law, the amount of the radioactive substance that decays is proportional to each instant to the amount of substance present. Let P(t) be the amount of ^{235}U and Q(t) be the amount of ^{238}U after t years.

Then, we obtain two differential equations

                               \frac{dP}{dt} = -k_1P \quad \frac{dQ}{dt} = -k_2Q

where k_1 and k_2 are proportionality constants and the minus signs denotes decay.

Rearranging terms in the equations gives

                             \frac{dP}{P} = -k_1dt \quad \frac{dQ}{Q} = -k_2dt

Now, the variables are separated, P and Q appear only on the left, and t appears only on the right, so that we can integrate both sides.

                         \int \frac{dP}{P} = -k_1 \int dt \quad \int \frac{dQ}{Q} = -k_2\int dt

which yields

                      \ln |P| = -k_1t + c_1 \quad \ln |Q| = -k_2t + c_2,

where c_1 and c_2 are constants of integration.

By taking exponents, we obtain

                     e^{\ln |P|} = e^{-k_1t + c_1}  \quad e^{\ln |Q|} = e^{-k_12t + c_2}

Hence,

                            P  = C_1e^{-k_1t} \quad Q  = C_2e^{-k_2t},

where C_1 := \pm e^{c_1} and C_2 := \pm e^{c_2}.

Since the amounts of the uranium isotopes were the same initially, we obtain the initial condition

                                 P(0) = Q(0) = C

Substituting 0 for P in the general solution gives

                         C = P(0) = C_1 e^0 \implies C= C_1

Similarly, we obtain C = C_2 and

                                P  = Ce^{-k_1t} \quad Q  = Ce^{-k_2t}

The relation between the decay constant k and the half-life is given by

                                            \tau = \frac{\ln 2}{k}

We can use this fact to determine the numeric values of the decay constants k_1 and k_2. Thus,

                     4.51 \times 10^9 = \frac{\ln 2}{k_1} \implies k_1 = \frac{\ln 2}{4.51 \times 10^9}

and

                     7.10 \times 10^8 = \frac{\ln 2}{k_2} \implies k_2 = \frac{\ln 2}{7.10 \times 10^8}

Therefore,

                              P  = Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} \quad Q  = Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}

We have that

                                          \frac{P(t)}{Q(t)} = 137.7

Hence,

                                   \frac{Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} }{Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}} = 137.7

Solving for t yields t \approx 6 \times 10^9, which means that the age of the  universe is about 6 billion years.

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Gabby is 2 kg heavier than her sister who weighs 3.4 kg. what is their combined weight?​
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Answer:

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Step-by-step explanation:

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WILL GIVE BRAINLIEST
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256.
EXPLANATION:

When you are using exponents, you are basically just doing repeated multiplication.

Whatever the exponent (smaller number is) is how many times you multiply the base number by itself.

So 4 ^4 is 4 x 4 x 4 x 4. (4 fours.)

So 4 x 4 x 4 x 4 is 256.
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