Answer:
[tex]x = \displaystyle \frac{5 + \sqrt{17}}{2}[/tex].
Step-by-step explanation:
Because [tex]3\, x[/tex] is found in the input to a logarithm function in the original equation, it must be true that [tex]3\, x > 0[/tex]. Therefore, [tex]x > 0[/tex].
Similarly, because [tex](x - 4)[/tex] and [tex](2\, x - 1)[/tex] are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, [tex]x > 4[/tex].
Let [tex]a[/tex] and [tex]b[/tex] represent two positive numbers (that is: [tex]a > 0[/tex] and [tex]b > 0[/tex].) The following are two properties of logarithm:
[tex]\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)[/tex].
[tex]\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)[/tex].
Apply these two properties to rewrite the original equation.
Left-hand side of this equation:
[tex]\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}[/tex]
Right-hand side of this equation:
[tex]\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)[/tex].
Equate these two expressions:
[tex]\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}[/tex].
The natural logarithm function [tex]\ln[/tex] is one-to-one for all positive inputs. Therefore, for the equality [tex]\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}[/tex] to hold, the two inputs to the logarithm function have to be equal and positive. That is:
[tex]\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)[/tex].
Simplify and solve this equation for [tex]x[/tex]:
[tex]x^2 - 5\, x + 2 = 0[/tex].
There are two real (but not rational) solutions to this quadratic equation: [tex]\displaystyle \frac{5 + \sqrt{17}}{2}[/tex] and [tex]\displaystyle \frac{5 - \sqrt{17}}{2}[/tex].
However, the second solution, [tex]\displaystyle \frac{5 - \sqrt{17}}{2}[/tex], is not suitable. The reason is that if [tex]x = \displaystyle \frac{5 - \sqrt{17}}{2}[/tex], then [tex](x - 4)[/tex], one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.
The only solution that satisfies the requirements would be [tex]\displaystyle \frac{5 + \sqrt{17}}{2}[/tex].
Therefore, [tex]x = \displaystyle \frac{5 + \sqrt{17}}{2}[/tex].
What is the inverse operation that will isolate the variable X-4=-2
A)division
B)multiplication
C)subtraction
D) addition
Answer ASAP will give brainliest, thanks.
Answer:
B
Step-by-step explanation:
4x+2y=6
6x-4y=-12
2y=6-4x
y=3-2x
6x-4(3-2x)=-12
6x-12+8x=-12
2x-12=-12
2x=0
x=0
4(0)+2y=6
2y=6
y=3
(0,3)
Use these abbreviations for the properties of real numbers, and complete the flow diagram.
C. for the commutative property of addition
Cx for the commutative property of multiplication
2
Suggest e
A. for the associative property of addition
A. for the associative property of multiplication
Answer:
c and a
Step-by-step explanation:
can someone help me please i don't understand the process
Answer:
Yes, because a triangle can have any lengths.
which value if x makes this proportional true? 14/20=56/x A.x=62 B.x=70 C.x=80 D.x=100
==================================================
Work Shown:
Let's cross multiply to get the following
14/20 = 56/x
14*x = 20*56
14x = 1120
x = 1120/14
x = 80
-------------------
As a way to check the answer, we can type 14/20 - 56/80 into the calculator and we should get 0. I'm taking advantage of the rule that if A = B, then A-B = 0. This trick is handy to check if two sides of any equation are equal to one another.
your answer will be 80 pretty sure
2. Sandra has earned 284 out of 300 points in Math class. What grade did Sandra
make in her math class? (Round your answer to the nearest whole percent)
Answer:
95%
Step-by-step explanation:
300/284 = 0.946666... rounded the the whole percent is 95%
300 * 95% = 285
the height of an object after t seconds is given by f(t)=-5t^2+20t (a) find the height of the object after 2 seconds, and include the correct units with your answer. (b) find the average (vertical) velocity of the object on the time interval [0,2]. show your work, include the correct units, and. circle your final answer. (c) find the instantaneous velocity at t=2
Answer:
t=20 4=5 =6 =8 =9 10
Step-by-step explanation:
And that is iy
What is 31/26 simplified?
Answer:
it cant be simplified
Step-by-step explanation:
Answer:
1 5/26 i used a calculator
I need help with this :(
♀️♀️♀️♀️♀️♀️♀️♀️
Answer:
The sum of the areas of square N and square L is equal to the area of square K
How to write the slope intercept form of
y - 4 = 3 (x-2)
Answer:
y=3x-2
Step-by-step explanation:
y-4=3(x-2)
y-4=3x-6
y=3x-2
X + 7/8 = 23/8
They are fractions
Please help
Answer:
X=2
Step-by-step explanation:
Please mark brainliest.
Answer:
x=2
subtract 7/8 from both of the sides
x= 23/8-7/8
Simplify 23/8 - 7/8 to 2
x=2
A certain CD has a mass of 10 grams. How many of these CDs would you need to equal a total mass of 2 kg?
write the number of CDs needed in the box.
Answer:
200 CDs
Step-by-step explanation:
1000 g = 1 kg
2 kg = 2000 g
2000 / 10 = 200 CDs :D
What is 820 milliliters equal to in liters?
Answer:
0.82 L
Step-by-step explanation:
Answer: 0.82 liters
Step-by-step explanation:
what is the value of tan(arccos(-sqrt2/2)
Answer:
i think is -1 because the value is -1
Answer:
D. -1
Step-by-step explanation:
ed2021
a map has a scale of 1.5 inches = 9 miles. On the map, two towns are 4 inches apart. What is the distance, in miles between the two towns?
Answer:
36
Step-by-step explanation:
i multpliy 9x4=36
PLZ HELP!! ITS ALMOST DUE!! ILL MARK BRAINLIEST!!
Answer: $32.74
Is your answer
Glad I could help!
Step-by-step explanation:
Pentru sala de mese a scolii s-au adus 12 scaune si 7 mese, plătindu-se 320lei.Știind că 4 scaune costă cât trei mese, află prețul unui scaun și prețul unei mese.
Răspuns:
Costul scaunului = 15
Costul mesei = 20
Explicație pas cu pas:
Dat fiind:
Să prețul scaunelor = c; pretul mesei = t
12c + 7t = 320 - - - (1)
4c = 3t; c = 3/4 t - - - (2)
Introducerea c = 3 / 4t în (1)
12 (3 / 4t) + 7t = 320
9t + 7t = 320
16t = 320
t = 320/16
t = 20
c = 3 / 4t
c = 3/4 (20)
c = 15
Costul scaunului = 15
Costul mesei = 20
what is 13,931 rounding by 10
Answer:
13,930
Habe ein gut tag.
Find the line's slope and a point on the line. y-2=1/3(x+4)
slope:
point on the line:
If one term of a proportion is not known, what can be used to find the value of that term?
A: Substitution
B: Graphing
C: Cross-multiplication
D: Adding all the numbers together
Please select the best answer from the choices provided.
Answer:
cross multification is correct answer
answer this question plzzzzz
Answer:
This is my best solution for your question
Step-by-step explanation:
radius=10cm
<A0B=90°
Length of arc AB,
[tex] 10 \times \frac{\pi}{2 } = 5 \times 3.14 = 15.4cm[/tex]
[tex]perimeter \: of \: quadrant = \: 10 + 10 + 15.4 = 35.4cm[/tex]
Area of quadrant=
[tex] \frac{90}{360 } \times 3.14 \times {10 }^{2} = 78.5cm ^{2} [/tex]
The diagram below shows the start and finish diagrams of a construction using a compass and straightedge. Which of the following statements are true about this construction? Select all that apply.
Answer: 1st and 4th
Step-by-step explanation:
Answer: The answers are the first and fourth one.
Step-by-step explanation: Because of the rules of linear measures
On a horizontal number line, -45 is located to the left of -35
Answer:
true
Step-by-step explanation:
<________________________>
-45 -35 0
pls help me and really fast
Please help with all pleaseeeee.
Step-by-step explanation:
5. da^2
7×4^2
=7×16
=112
6.g(b+e)
=10(8+3)
=10×11
=110
7.a+b(f+g)
=4+8(9+10)
=4+8×19
=4+152
=156
8.a+b/3
=4+8/3
=12/3
=4
This list shows the lengths in feet of the 25 longest bridges in the United States.
1010
1470
1600
2000
2800
1053
1495
1632
2150
3500
1200
1596
1750
2150
3800
1207
1600
1800
2300
4200
1380
1600
1850
2310
4260
Jamie made a frequency table of the bridge data.
U.S. Bridges
Length (ft)
Tally
Frequency
(first interval)
|||| ||
7
(last interval)
||
2
Based on the tallies and frequencies for the first and last intervals, how many intervals of what length did Jamie use?
a.
4 intervals of 1000 feet
c.
6 intervals of 500 feet
b.
5 intervals of 1000 feet
d.
7 intervals of 500 feet
Answer:
D. 7 intervals of 500 feet
Step-by-step explanation:
Got it right
Jamie used 5 intervals of 1000 feet as per the given data. The correct option is b.
What are tallies and frequencies?A tally chart is a straightforward method of recording and counting frequencies. Each occurrence is represented by a tally mark, and every fifth tally is drawn diagonally to form a five-pointed star.
The first interval has a frequency of 7, which corresponds to the first 7 data points in the list:
1010
1470
1600
2000
2800
1053
1495
The last interval has a frequency of 2, which corresponds to the last 2 data points in the list:
2310
4260
Since there are 25 data points in total, and the first 7 and last 2 have been accounted for, that leaves 16 data points for the remaining intervals.
If Jamie used 1000-foot intervals, each interval would cover a 1000-foot range. The remaining data points range from 1200 to 4200 feet, so they are divided into 1000-2000, 2000-3000, and 3000-4000 foot intervals.
If Jamie used 500-foot intervals, each interval would cover a 500-foot range.
Thus, because the remaining data points range from 1200 to 4200 feet, they are divided into 1000-1499, 1500-1999, 2000-2499, 2500-2999, 3000-3499, 3500-3999, and 4000-4499 foot intervals.
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Determine S44 of the arithmetic series 1 + 4 + 7 + 10 + ...
9514 1404 393
Answer:
2882
Step-by-step explanation:
The sum of an arithmetic series is given by ...
[tex]S_n=\dfrac{n(2a_1+d(n-1))}{2}[/tex]
For a1 = 1, d = 3, n = 44, we can fill in the values and do the arithmetic:
[tex]S_{44}=\dfrac{44(2(1)+3(44-1)}{2}=22(2+3\cdot43)\\\\\boxed{S_{44}=2882}[/tex]
what is 344.7234 to 1 decimal point
Answer: 344.7
Explanation:
344.7∣234
(Cut ^off point at the line)
The digit to the right of the cut of the point is less than 5. So the digit to its left (the 7) is not changed and all those to the right are changed to 0 gives you:
344.7000
Written as 344.7
Hope this helps and hope you have a wonderful day :)
A string is 5.8 meters long. What is it's length in centimeters
Answer:
a
Step-by-step explanation:
because I said it was jejwjwjeiejehxueh ed uejrhcu
Answer:
580
Step-by-step explanation:
If 100 centimeters are in a meter, then we have to multiply 5.8 by 100 to find out the length of the string in centimeters.
(hope this helped)
What is the volume of the following rectangular prism?
units
NI
1
16- units
4.
Answer:
60
Step-by-step explanation:
The volume of the rectangular prism is V = 64 units³
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
Let the volume of the rectangular prism be represented as V
Now , the height of the prism is H = 4 units
The length and width of the prism is 1 and 16 units respectively
So , the base area of the prism B = 16 units²
Now , Volume of Prism = B x h
On simplifying , we get
The volume of rectangular prism V = 16 x 4
The volume of rectangular prism V = 64 units³
Hence , the volume of the rectangular prism is 64 units³
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