The solution to the logarithmic equation [tex]\mathbf{log_2(x-6) = 4}[/tex] is x =24
The logarithmic equation is given as:
[tex]\mathbf{log_2(x-6) = 4}[/tex]
Apply exponential law of logarithm
[tex]\mathbf{(x-6) = 2^4}[/tex]
Remove the brackets
[tex]\mathbf{x-6 = 2^4}[/tex]
Add 6 to both sides
[tex]\mathbf{x-6 +6= 6+ 2^4}[/tex]
Express 2^4 as 16
[tex]\mathbf{x-6 +6= 6+ 16}[/tex]
Add -6 and 6
[tex]\mathbf{x= 6+ 16}[/tex]
Add 6 and 16
[tex]\mathbf{x= 24}[/tex]
Hence, the solution to the logarithmic equation [tex]\mathbf{log_2(x-6) = 4}[/tex] is x =24
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Write the prime factorization of 315.
315 =
(TRY TO ANSWER THIS WHILE UR AT IT PLS?
Answer:
315 = 3^2 × 5^1 × 7^1
Step-by-step explanation:
1/243 as an expression using a negative exponent other than -1
Answer: To get the expression with negative exponent, we need to convert the number 1024 in exponential form
Replace the denominator by 2^10
Now we apply exponential property
negative exponent other than -1 is
Graph the equation on the coordinate plane using the slope and y-intercept.
y=−2x
Answer:
Step-by-step explanation:
Halppppppppppppp..............
Answer:
1 2/3, and -1 2/3
Step-by-step explanation:
Im wondering how old you are, and since you seem young just based off the math you're asked to do, please listen to the explanation and teach yourself this. This skill in particular is SOOO important to the rest of the math world. So since your number line is already divided into thirds, there are two ways you could find your answer. One, you can count 5 thirds away from zero, or two, you could simplify 5/3 from an improper fraction to a mixed number (1 2/3) and find your spot from there. "and the opposite" means not only the point 5/3 Away from zero on the Right, but also 5/3 away from zero on the Left. start from zero again and count the same amount away but in the opposite direction. With negatives it can help to think of how all numbers are just descriptions of how far left or right a number is from zero. i hope this helped lol, negatives are a confusing batch, but they're so so important to math as a whole.
help ? yes ? no ? maybe ?
Answer:
They are proportional
Step-by-step explanation:
Proportionality:
They are proportional because the cost is going up by 10 the entire time and the hours rented is going up by 2 the entire time.
Graphing:
Go to the 2 on the x-axis (horizontal line)
Go up to the 20 on the y-axis (vertical line)
The points to graph are:
(2,20)
(4,30)
(6,40)
(8,50)
I put a pic of what your graph should look like below!
Answer:
To plot the graph put the hours along the x axis and the cost on the y axis. Its a positive realationship because when the hours go up the cost goes up to, it isn't proportional because both values don't go up at the same rate.
Step-by-step explanation:
answer the three questions pls
I need help with question 5
Answer:Hi!
where is the question?
Step-by-step explanation:
Solve.
−5x+6=−4(2x−1)
x=−14/3
x=−10/13
x=−2/3
Answer:
x=-2/3
Step-by-step explanation:
Please helppppp
Reagan solved 5.25 = 5 and got 105. What did Reagan do wrong?
Answer:
He did not simplify correctly and forgot to place the decimal point correctly.
Step-by-step explanation:
To simplify the equation, one needs to divide both sides of the equal sign by 5.
i.e 5.25/5=5/5
Here we find 1.05=1
Note the placement of the decimal point.
Please help me with this
Step-by-step explanation:
such an equation is a simple linear function :
y = ax + b
b is in this case the flat fee, and a (the slope) drives the incline of the function for various numbers of students x.
our job is now to find the correct a and b values.
we do this by using the informative we have and create 2 equations for a and b, and then we solve this system.
132.5 = a×25 + b
145 = a×30 + b
now, we can use a little trick and simply subtract the whole first equation from the second equation.
145 = a×30 + b
- 132.5 = a×25 + b
------------------------------
12.5 = a×5 + 0
5a = 12.5
a = 2.5
with this we go into one of the original equations, e.g. the second one :
145 = 2.5×30 + b = 75 + b
70 = b
so, it full equation is
y = 2.5x + 70
the costs for 85 students are
y = 2.5×85 + 70 = 212.5 + 70 = $282.50
right now michael earns an annual salary of $46,023 he is Considering a job offer with an annual salary of $51,145 what is the difference in the monthly pay for these two jobs rounded to the nearest cent
Answer: The job pays $32,400 per year, and the agency fee is equal to 45% of one month's pay.
What is the slope for this table?
Give an explanation.
Answer:
the shape of the graph is a vertical straight line. So the angle is 90°
So tan 90° = infinite
Answer: The slope is undefined.
Step-by-step explanation:
The slope is undefined because it is based on the Rise (y) over the Run (x) of the data points. X is not changing even as y goes from -2 to 8. If we took the first and last points, (-1,-2) and (-1,8) and go from left to right, y increases by (8-(-2)) = 10 while x is unchanged, or o. Rise/Run therefore becomes 10/0. Division by 0 is undefined in math, so the slope is undefined.
This is a straight vertical line going through x = -1. All y's are on this line. Undefined slope.
Which graph is right?
Answer:The first option is correct
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
3rd option because m is bigger than or equal -2 which means that it is going to be from [-2,infinity[
Give one example of an urban area and one example of a rural area.
Answer:
An urban area would be New York City, a rural area would be a small town in western Kansas.
Step-by-step explanation:
What is 2 and 2/3 x 5
Answer:
13 and 1/3
Step-by-step explanation:
2×5=10
2/3 ×5 =10/3
10/3 simplifies to 3 and 1/3
Add them together to get 13 and 1/13
Chase has a $42,500 line of credit which charges an annual percentage rate of prime rate plus 5%. His starting balance on June 1 was $2,550. On June 4, he borrowed $5,300. On June 9, Chris made a payment of $800, and on June 17, he borrowed $5,600. If the current prime rate is 10%, what is his new balance?
The best interest rate which banks can charge a customer is the prime rate.
His new balance is $12,735.291[tex]\overline 6[/tex]Reasons:
The Annual Percentage Rate, APR = Prime + 5%
∴ APR = 10% + 5% = 15%
[tex]\displaystyle The \ periodic \ rate = \frac{15}{12} = 1.25 \%[/tex]
The balance on June 1 = $2,550
Daily balance, June 1 — 3 = $2,550 × 3 = $7,650
June 4 borrowed $5,300
The new unpaid balance = $2,550 + $5,300 = $7,850
Daily balance from June 5 — 8 = $7,850 × 3 = $23,550
Chris made payment on June 9
Unpaid balance = $7,850 - $800 = $7,050
Daily balance from June 9 — 16= $7,050 × 8 = $56,400
June 17 borrowed $5,600
Unpaid balance = $7,050 + $5,600 = $12,650
Daily balance June 17 — 30 = $12,650 × 14 = $177,100
Sum of daily balance = 7,650 + 23,550 + 56,400 + 117,100 = 204,700
[tex]\displaystyle Average \ daily \ balance = \frac{204,700}{30} = 6,823.\overline 3[/tex]
Finance charge = Average daily balance × Periodic rate
∴ Finance charge = $6,823.[tex]\overline 3[/tex] × 0.0125 = $85.291[tex]\overline 6[/tex]
New balance = Cash advance + Credits and payment + Previous balance + Finance charge
New balance = $2,550 + $5,300 - $800 + $5,600 + $85.291[tex]\overline 6[/tex]
= $12,735.291[tex]\overline 6[/tex]
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A binomial experiment consists of 14 trials. The probability of success on trial 7 is 0. 55. What is the probability of success on trial 11?.
Answer: Using the conditions required for a binomial experiment, the probability of success is the same for each trial in the experiment, Hence, the probability of failure on trial 11 will be 0.16 . The probability of success, p = 0.84; the probability of failure can be expressed as; p(failure) = 1 - p(success) = 1 - 0.84 = 0.16 . The probability of success or failure in each and every trial of a binomial experiment is the same and hence, does not change from trial to trial. Therefore, the probability of failure in the 11th trial is 0.16.
Step-by-step explanation: Generally, one the attributes of a binomial experiment is that the probability of success and failure is constant every trial so given from the question that the probability of success is 0.84 for trial 7, then the probability of failure of trial 7 will be evaluated as => q=1-0.84. q=0.16. And from the attribute stated above the probability of failure of trial 11 is q=0.16
r(2)=120 and r(4)=378 divide the difference in the r(x) values by the difference in the x-value
Answer:
im not sure ask siri
Step-by-step explanation:
she knows everything
There are mangoes and oranges in a basket in the ratio 7: 11. If the total number of fruits is 720, then how many mangoes are there in the basket?
Answer:
280 mangoes
Step-by-step explanation:
sum the parts of the ratio, 7 + 11 = 18 parts
Divide the total by 18 to find the value of one part of the ratio.
720 ÷ 18 = 40 ← value of 1 part of the ratio , then
7 × 40 = 280 ← number of mangoes
Answer:293
Step-by-step explanation:
720-719= 1
1+292= 293
The perimeter of a rectangle is 30 inches. If the length of the rectangle is 10 inches, which equation could be used to find the width of the rectangle "w" in inches
Answer:
30=2(10 x w)
Step-by-step explanation:
P=2(l x w)
Perimeter(P) equals two times length(l) times width(w)
Hope this helps
Me podrian ayudar con estas equaciones de 2º grado pliss?
[tex]x^{2} +2x-15=0[/tex]
[tex]x^{2} -4x- 12=0[/tex]
Thankss
Step-by-step explanation:
Las ecuaciones dadas son ,
=> x² + 2x -15 = 0
Y necesitamos encontrar la solución de la Ecuación dada.
=> x² + 5x -3x -15 = 0
=> x(x+5) -3(x+15) = 0
=> (x+5)(x-3) = 0
=> x = 3,-5
La segunda ecuación es,
=> x² -4x -12 = 0
=> x² -6x+2x-12=0
=> x(x-6)+2(x-6) = 0
=> (x+2)(x-6) = 0
=> x = 6,-2
Espero eso ayude :)
The density of glass in a bottle is 2.4gcm^3. The volume of glass used to make the bottle is 13.4cm^3. Calculate the mass of the glass bottle.
Answer:
Density is g/cm^3, not gcm^3
Mass = 32.16 grams [32.2 grams for 3 sig figs)
Step-by-step explanation:
Density = Mass/Volume
Density = 2.4g/cm^3
Volume = 13.4cm^3
---
2.4g/cm^3 = Mass/13.4cm^3
Mass = (2.4g/cm^3)*(13.4cm^3)
Mass = 32.16 grams [32.2 grams for 3 sig figs)
The mass of the glass-bottle is 32.16 grams.
What is volume?Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.
Given:
The density of glass in a bottle is 2.4 grams per cubic centimeters.
The volume of glass used to make the bottle is 13.4 grams per cubic centimeters.
Density = Mass/Volume
Density = 2.4 grams per cubic centimeters.
Volume = 13.4 cubic centimeters.
Substituting all the values,
2.4 = Mass / 13.4
Mass = 13.4 x 2.4
Mass = 32.16
Therefore, mass = 322.16 grams.
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find the length of segment AB
Answer:
E. 214
Step-by-step explanation:
Since the other angles of the triangle are congruent, and separated creates 2 right triangles, this means that segment (because i cant put the actual names for some reason) A to F and segment F to B are equal
8x - 37 = 5x + 17
3x = 54
x = 18
Now substitute to check
8(18) - 37 = 5(18) + 17
107 = 107
So if this is true, to find the segment A to B, just add segments A to F and F to B together
107 + 107 = 214
The length of segment AB is 214
[tex]\sf 6-2x+5+4x[/tex]
Last one! bye!
Thanks!
[tex]\sf 6-2x+5+4x[/tex]
[tex]\sf \longmapsto - 2x + 4x + 6 + 5[/tex]
[tex]\sf \longmapsto - 2x + 4x + 11[/tex]
[tex]\sf \longmapsto2x + 11[/tex]
The arithmetic sequence 1, 3, 5, 7, 9,. . . Represents the set of odd natural numbers. What is the explicit rule for the sequence? ak = (k - 1).
The explicit rule for the sequence is Tn = 2n - 1
Given the sequence 1, 3, 5, 7, 9...
The explicit formula for the nth term is expressed as:
[tex]T_n=a+(n-1)d[/tex]
a is the first term = 1
d is the common difference = 3 - 1 = 5 - 3 = 2
n is the number of terms
Substitute the given parameters into the formula to have;
[tex]T_n = 1+(n-1)(2)\\T_n=1+2n-2\\T_n=2n-1[/tex]
Hence the explicit rule for the sequence is Tn = 2n - 1
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Answer:
1st: 1+(k-1)2
2nd: 399
3rd: C
4th: 40,000
4.
Which of the following is the minimum value of the equation y= 1/3x^2 + 2x + 5?
A. 1/3
B. -3
C. 2
D. 5
Answer:
C. 2
Step-by-step explanation:
Use the formula
x = − b /2 a
to find the maximum and minimum.
( − 3 , 2 )
i need this answer answered for me asap
Answer: i think it's A or D
Step-by-step explanation:
Answer:
A) x > -6
Step-by-step explanation:
X is bigger than negative 6 since the arrow of the number line is pointing to the positive numbers then that means x is one of the positive numbers.
Find the slope of the line that passes through (7,1) and (6,8)
Answer:
-7
Step-by-step explanation:
[tex]\frac{(8-1)}{(6-7)}[/tex] = [tex]\frac{7}{-1}[/tex] = -7
14. Which of the following relations has an inverse that is not a function?
(1,1),(1,2).(3,4)
(1,2).(1,3),(4,3)
(1,4),(4,5),(5,6)
(0,0),(1,1),(2, 2)
Answer:
(1,2).(1,3),(4,3)
Step-by-step explanation:
The inverse of (1,2).(1,3),(4,3) is (2, 1), (3, 1), (3, 4) and this is not a function as a function is a set X to a set Y, not multiple to one.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
a rule in a relation in which each input is paired with, or assigned to, exactly one output.
Answer:
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Step-by-step explanation: