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3 years ago

Which is the solution for log(4x-1)=log(x+1)+log2?

Mathematics

2 answers:

JulsSmile [24]3 years ago

4 0

Answer:

It's x=3/2

Step-by-step explanation:

Took it just now

Thepotemich [5.8K]3 years ago

3 0

Answer:

x = 1.5

Step-by-step explanation:

Solution

log(4x - 1) - log(x+1) = log2 log(x + 1) was subtracted from both sides
log[(4x - 1)/log(x+1)] = log2 Subtaction of logs means division
(4x - 1) / (x + 1) = 2 Take the antilog of both sides
4x - 1 = 2(x + 1) Remove the brackets
4x - 1 = 2x + 2 Add 1 to both sides
4x = 2x + 3 Subtract 2x
4x - 2x = 3
2x = 3 Divide by 2
x = 3/2 Answer

Check

Left Hand Side

log(4*1.5 - 1)
log(6 - 1)
log(5)

Right Hand Side

log(1.5 + 1) + log(2)
log(2.5) + log(2)
log2*2.5
log 5

And they check

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Minimum point of the quadratic x^2+6x-2

WITCHER [35]

Answer:

(-3,-11)

Step-by-step explanation:

Compare the given quadratic equation with the general quadratic equation.

a=1, b=6 and c=-2

$x=-\dfrac{(6)}{2(1)}\\=-3$

Subsitute $-3$ for $x$ in given quadratic equation.

$y=(-3)^2+6(-3)-2\\=9-18-2\\=-11$

The minimum point is (-3,-11).

3 0

3 years ago

Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. Here are th

Vesnalui [34]

Answer:

Part a:

"The unit has 7 or more rooms" in terms of X is given by the unit which has 7, 8, 9 or 10 rooms.

P{ X≥7}= 0.424

Part b:

The event {X > 7} in words is that the unit has more than 7 rooms. .

Part C:

A continuous random variable is given by intervals of numbers

A discrete random variable is the variable that is obtained by counting.

Step-by-step explanation:

Part a:

"The unit has 7 or more rooms" in terms of X is given by

{ X≥7} = {x=7} + {x=8} + {x=9} + {x=10}

the unit which has 7, 8, 9 or 10 rooms.

The probability of this event is given by

P{ X≥7} =P {x=7} + P {x=8} + P {x=9} + P {x=10}

P{ X≥7} = 0.198 + 0.149+ 0.053 + 0.024

P{ X≥7}= 0.424

Part b:

The event {X > 7} in words is that the unit has more than 7 rooms. This does not include the unit having 7 rooms.

Part C:

A continuous random variable takes all the values in the given interval as in part a.The random variable X takes the values between 7 and 10 inclusive of 7.

A discrete random variable is the variable that is obtained by counting as in part b. The variable X takes the values of the units with 8 , 9 or 10 rooms.

8 0

3 years ago

Find the next five terms 512 256 128 64

Alborosie

The pattern is dividing by 2.

512, 256, 128, 64

512/2 = 256, 256/2 = 128, 128/2 = 64

64/2 = 32, 32/2 = 16, 16/2 = 8, 8/2 = 4, 4/2 = 2, ...

6 0

3 years ago

There are 320 students in a school. 16 come to school by car. 96 walk to school. Estimate the probability that a particular stud

lorasvet [3.4K]

Answer:

a. The probability that a particular student arrives by car is $\frac{1}{20}$ = 0.05, which equals 5%.

b. The probability that a particular student walks to school is $\frac{3}{10}$ = 0.3, which equals 30%.

c. The probability that a particular student does not walk to school is $\frac{7}{10}$ = 0.7, which equals 70%.

d. The probability that a particular student does not walk or come by car is $\frac{13}{20}$ = 0.65, which equals 65%.

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

In this case, the number of possible cases is always the same, which is equal to the total number of students. So the number of possible cases is 320 students. The number of favorable cases varies as follows:

a. Number of favorable cases= number of students that arrive by car= 16

So: $P(A)=\frac{16}{320}$

P(A)= $\frac{1}{20}$ = 0.05, which equals 5%

The probability that a particular student arrives by car is $\frac{1}{20}$ = 0.05, which equals 5%.

b. Number of favorable cases= number of students that walk to school= 96

So: $P(A)=\frac{96}{320}$

P(A)= $\frac{3}{10}$ = 0.3, which equals 30%

The probability that a particular student walks to school is $\frac{3}{10}$ = 0.3, which equals 30%.

c. Number of favorable cases= number of students that do not walk to school = 320 students - number of students that walk to school= 320 students - 96 students= 224 students

So: $P(A)=\frac{224}{320}$

P(A)= $\frac{7}{10}$ = 0.7, which equals 70%

The probability that a particular student does not walk to school is $\frac{7}{10}$ = 0.7, which equals 70%.

d. Number of favorable cases= number of students that do not walk or come by car= 320 students - number of students that walk to school - number of students that arrive by car= 320 students - 96 students - 16 students= 208 students

So: $P(A)=\frac{208}{320}$

P(A)= $\frac{13}{20}$ = 0.65, which equals 65%

The probability that a particular student does not walk or come by car is $\frac{13}{20}$ = 0.65, which equals 65%.

6 0

3 years ago

PLEASE HELP ME ILL GIVE FIRST PERSON BRAINLIEST!!!!!!!

Helga [31]

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3 years ago

Read 2 more answers