Answer:
x = 3, x = 9
Step-by-step explanation:
When solving this problem, keep the general format of a logarithm in mind:
[tex]b^x=y\\log_b(y)=x[/tex]
Where, (b) represents the base, (x) is the exponent, and (y) is the evalutaor. Please note that others might use slightly different terminotoly than what is used in this answer.
One is given the following expression, and is asked to solve for the parameter (x);
[tex]log_5(x-4)=1-log_5(x-8)[/tex]
First, manipulate the exquestion such that all of the logarithmic expressions are on one side. Use inverse operations to do this.
[tex](log_5(x-4))+(log_5(x-8))=1[/tex]
Now use the Logarithmic Base Change rule to simplify. The Logarithmic Base Change rule states the following;
[tex]log_b(x)=\frac{log(x)}{log(b)}[/tex]
Remember, if no base is indicated in a logarithm, then the logarithm's base is (10). Apply the Logarithmic Base Change rule to this problem;
[tex]\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1[/tex]
Now remove the denominator. Multiply all terms in the equation by the least common denominator; ([tex]log(5)[/tex]) to remove it from the denominator on the left side.
[tex](\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1)*(log(5))[/tex]
[tex]log(x-4)+log(x-8)=log(5)[/tex]
All logarithms have the same base, the left side of the equation has the addition of logarithms. This means that one can apply the Logarithm product rule. The logarithm product rules the following;
[tex]log_b(x*y)=(log_b(x))+(log_b(y))[/tex]
This rule can be applied in reverse to simplify the left side of the equation. Rather than rewriting the product of logarithms as two separate logarithms being added, one can rewrite it as one logarithm getting multiplied.
[tex]log(x-4)+log(x-8)=log(5)[/tex]
[tex]log((x-4)(x-8))=log(5)[/tex]
Now used inverse operations to bring all of the terms onto one side of the equation:
[tex]log((x-4)(x-8))=log(5)[/tex]
[tex]log((x-4)(x-8))-log(5)=0[/tex]
Similar to the Logarithm product rule, the Logarithm quotient rule states the following;
[tex]log_b(x/y)=(log_b(x))-(log_b(y))[/tex]
One can apply this rule in reverse here to simplify the logarithms on the left side:
[tex]log((x-4)(x-8))-log(5)=0[/tex]
[tex]log(\frac{(x-4)(x-8)}{5})=0[/tex]
The final step in solving this equation is to use the Logarithm of (1) property. This property states the following:
[tex]log_b(1)=0[/tex]
When applying this property here, one can conclude that the evaluator must be equal to (1), therefore, the following statements can be made.
[tex]log(\frac{(x-4)(x-8)}{5})=0[/tex]
[tex]\frac{(x-4)(x-8)}{5}=1[/tex]
Inverse operations,
[tex]\frac{(x-4)(x-8)}{5}=1[/tex]
[tex](x-4)(x-8)=5[/tex]
[tex](x-4)(x-8)-5=0[/tex]
Simplify,
[tex](x-4)(x-8)-5=0[/tex]
[tex]x^2-12x+32-5=0[/tex]
[tex]x^2-12x+27=0[/tex]
Factor, rewrite the quadratic expression as the product of two linear expressions, such that when the linear expressions are multiplied, the result is the quadratic expression:
[tex]x^2-12x+27=0[/tex]
[tex](x-3)(x-9)=0[/tex]
Now use the zero product property to solve. The zero product property states that any number times (0) equals (0).
[tex]x=3,x=9[/tex]
Hello,
I suppose the question is solve for x.
[tex]\displaystyle log_5\ (a)=\dfrac{ln (a)}{ln (5)} \\\\log_5(x-4)=1-log_5(x-8)\\\\\dfrac{ln(x-4)}{ln(5)} =1- \dfrac{ln(x-8)}{ln(5)}\\\\ln(x-4)=ln(5)-ln(x-8)\\\\ln(x-4)+ln(x+8)=ln(5)\\\\ln((x-4)*(x-8))=ln(5)\\\\(x-4)*(x-8)=5\\\\x^2-12x+27=0\\\\\Delta=12^2-4*27=36=6^2\\\\x=9\ or\ x=3\\\\Sol=\{3,9\}\\[/tex]
For Moderators,
this is a mathematical resolution without any bla-bla sentences that you will easily find. (I can not do it sorry)
Dora travels between the two mile markers shown and then finds her average speed in miles per hour. Select the three equations that represent this situation.
The image of the 2 mile markers is missing as well as the options and so i have attached them.
Answer:
> 1.5 hours = 105 miles/speed
> Speed = 105 miles/1.5 hours
> 105 miles = 1.5 hours × speed
Step-by-step explanation:
From the image attached, the distance of the first mile marker is given as 50 miles while the distance of the second mile marker is given as 155 miles.
Thus, difference in distance between the two markers; d = 155 - 50 = 105 miles
Also, we see that the time of first marker is 3 pm while the second marker is 4:30 pm.
Thus, difference in time = 4:30 - 3 = 1 hour 30 minutes or 1.5 hours.
We know that;
Speed = distance/time
Thus;
Speed = 105/1.5
Speed = 70 mph
Thus, the 3 equations that represent this situation from the options are;
> 1.5 hours = 105 miles/speed
> Speed = 105 miles/1.5 hours
> 105 miles = 1.5 hours × speed
Answer:
1.5 hours = 105 miles/speed
Speed = 105 miles/1.5 hours
105 miles = 1.5 hours × speed
Step-by-step explanation:
Three text messages cost 5 cents to send. how much do 150 cost?
Answer:
30 ,,,,,,,, I hope it's helpful for you
3 text messages = 5 cents
So,
1 text messages
= 5 cents/3
= 5/3 cents
So,
150 text messages
= 150 × (5/3 cents)
= 50 × 5 cents
= 250 cents
HELP PLEASE! THIS IS MY LAST QUESTION ILL GIVE BRAINLIEST, NO LINKS. <3
Which of the following sets shows all the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20?
A) {1, 2, 3}
B) {2, 3, 4,}
C) {3, 4}
D) {4}
Answer: C {3, 4}
Step-by-step explanation:
Solve the inequality:
7x + 6 > 20
7x > 20 - 6
7x > 14
x > 2
Only 3 and 4 are greater than 2.
Which of the following is a radical equation
Answer:
7[tex]\sqrt{x}[/tex] = 14, D
Step-by-step explanation:
A radical equation is defined by having a variable under a radical sign. This is the only option with a variable (x) under the radical sign. Hence, 7[tex]\sqrt{x}[/tex] = 14 is the correct option.
The measures of the exterior angles of a pentagon are x', 38°, 45°,
5x", and 72. Solve for x.
Answer:
Step-by-step explanation:
sum of exterior angles of a polygon=360°
x+38+45+5x+72=360
6x=360-155=205
x=205/6=34 1/6
second question
x+3x+4x+5x+7x=360
20x=360
x=360/20=18
x=18
Which of these is the equation of the new function?
Answer:
B: g(x) = -4(x + 3)^2
Step-by-step explanation:
When we shift to the left by a units
we have the new equation become
( x + 3)^2
Stretching by a factor of 4, we have it that;
4(x + 3)^2
reflecting over the x-axis means the y-axis value becomes negative
So we have
g(x) = -4(x + 3)^2
help me solve the simultaneous linear inequalities
Answer:
The inequality form is -4<x<-2
The Interval Notation is (-4, -2]
I hope this helps!
Find RS.
A. 12
B. 5
C. 9
it may be 12...........
Answer:
B) RS=5
Step-by-step explanation:
(2x-6)+(1)+(x-4)=18
2x-6+1+x-4=18
3x-9=18
3x=18+9
3x=27
x=9
Find RS
x-4
9-4
=5
The force "F" applied on a spring and its extension "x" is given by the relation F = - k*x where "k" is the constant of proportionality.
Find "k" if a force of 10 Newtons produces an extension of 5 cm.
A. - 50 N/cm
B. 0.5 N/cm
C. - 20 N/cm
D. - 2 N/cm
HELP
Answer:
F = -k × X
10 Newtons = -k × 5 cm -k = 10 N/5 cm
-k = 2N/cm
k = -2N/cm
The value of spring constant "k" is -2 N/cm. Thus, the correct answer is option D.
To find the constant of proportionality "k," we can rearrange the formula:
F = -k x x
Since we are given that a force of 10 Newtons produces an extension of 5 cm, we can substitute these values into the equation:
10 N = -k x 5 cm
To solve for "k," we divide both sides of the equation by 5 cm:
k = -10 N / 5 cm
Simplifying the expression:
k = -2 N/cm
Therefore, the value of "k" is -2 N/cm. Thus, the correct answer is option D.
To know more about an expression follow
https://brainly.com/question/28866664
#SPJ2
Look at the diagram. Which angle is supplementary to 1.) 2.) 3.) 4.)
Answer:
it's going to be EOC
Step-by-step explanation:
I used my brain
what’s the answer? how do I solve this?
Answer:
39.96 is what I think is the answer :)
What is the value of W?
5 units
7 units
14 units
15 units
Answer:
5 units!
Step-by-step explanation:
Because Rectangle Perimeter = 2(a+b)
a=2w-1, b=w
2(2w-1+w)=28
3w-1=14
3w=15
w=5
So the answer is 5! 5! 5! A!A!A!
Fighting!! o(≧o≦)o
A study of homeowners in the 5th congressional district in Maryland found that their annual household incomes are normally distributed with a mean of $41,182 and a standard deviation of $11,990 (based on data from Nielsen Media Research). If an advertising campaign is to be targeted at those whose household incomes are in the top 20%, find the minimum income level for this target group.
Answer:
The minimum income level for this target group is of $51,253.6.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of $41,182 and a standard deviation of $11,990
This means that [tex]\mu = 41182, \sigma = 11990[/tex]
Find the minimum income level for this target group.
The 100 - 20 = 80th percentile, which is X when Z has a p-value of 0.8, so X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 41182}{11990}[/tex]
[tex]X - 41182 = 0.84*11990[/tex]
[tex]X = 51253.6[/tex]
The minimum income level for this target group is of $51,253.6.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 10.7
Step-by-step explanation:
We have:
[tex]\frac{x}{sin 90}[/tex] = [tex]\frac{9.2}{sin59}[/tex]
=> x × sin59 = 9.2 × sin90
=> x × sin59 = 9.2
=> x = 9.2 ÷ sin59
=> x = 10.733027...
=> x = 10.7 (Round to the nearest tenth)
<3 Have a nice day!!
5^4x+3 ×100^-2x+1=50000
Answer:
5^4x+3 ×100^-2x+1=50000
5^4x×100^-2x=49996
isolate the variable by dividing each side by factors that don't contain the variable. Exact Form: x = 8 √ 12499 , Decimal Form: x = 894.39141319 …
Someone help me please?
Answer:
([tex]a^{2}[/tex] + 9 ) × (2[tex]a^{2}[/tex] + 1)
for the first one try two but im not sure
Use the elimination method to solve the system of equations
2x+3y=8
x-y=9
Answer:
Step-by-step explanation:
Answer: x = 7 and y = -2
Step-by-step explanation:
2x +3y = 8 ----------------(1)
x-y = 9 ----------------------(2)
multiply (2) by 2
2x-2y = 18--------------------(3)
subtract (2) from (3)
-5y = 10
Divide bothside by -5
y = -2
Similarly, multiply (2) by 3
3x-3y = 27-----------------------(4)
add (1) and (4) together
5x = 35
Divide bothside by 5
x= 7
Therefore, x =7 and y= -2
The diagram shows a prism …,
Answer:
See figure below.
Step-by-step explanation:
See the figure below.
Explain why |−3| + |9| represents the distance between the points (−3Explain why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5)., −5) and (9, −5).
Answer:
Here we need to use:
[tex]\sqrt{x^2} = |x|[/tex]
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Then the distance between:
(-3, -5) and (9, -5) is just:
[tex]D = \sqrt{(-3 - 9)^2 - (-5 - (-5))^2} \\\\D = \sqrt{(-3 - 9)^2} = |-3 - 9|[/tex]
because both numbers inside the absolute value, we can rewrite it as:
|-3 - 9| = |-3| + |-9| = |-3| + |9| = 12
So, by finding the distance between (−3, −5) and (9, −5), we got the given expression, in this way we prove that the given expression represents the distance between these points.
Answer:
under
Step-by-step explanation:
The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).
At the baseball stadium there are 548 seats that are divided into 14 rows how many seats are in each row
Answer:
There are 39 seats I think.
Step-by-step explanation:
548 divided by 14 is a decimal but rounded it to the nearest full number.
Calculate the exact value of number one
Answer:
1. a. (ii) 1/27
Step-by-step explanation:
1st one is already given, I will give you the answer to the second one,
³√27/9²
= 3/81
= 1/27
Answered by GAUTHMATH
Answer:
17/42 or in decimal 0.405
Step-by-step explanation:
Add: 1 4/7+2/3- 1 5/6= 47/21- 1 5/6
Subtract: 47 - 1 5/6 = 17/42
Simplify: 17/42
brainlest if correct !!!!!
Answer: C. x > 0
Step-by-step explanation:
It is an empty circle, meaning the value of 0 is not included in the inequality, so it's not ≤ or ≥.The arrow goes to the right, towards values greater than 0, therefore it is > and not <.The answer would be x > 0.
Answer:
C
Step-by-step explanation:
yall rockin w yung kayo
Answer:
YALLLLLLLLL
Step-by-step explanation:heheh okie thats funnie
The price of a laptop was first increased by 10% and then the new price was decreased by 20%. The final price was what percent of the initial price.
Answer:
88%
Step-by-step explanation:
to initial price (100%) was increased by 10% (resulting in 110% of the initial price).
then these 110% were decreased by 20%.
so, the final price is actually 80% of 110% of the initial price
20/100 = 1/5
80/100 = 4/5
so, the customer pays only 4/5 of the 110% price.
110 × 4/5 = 22 × 4 = 88%
so, the final price was 88% of the initial price
NO LINKS!!! JUST ANSWER PLS AND ILL GIVE BRAINLIEST
Helppppp and explain !!!!
Answer:
dat I don't know the answer sorry I could not answer u
given that O is the center of the circle, find the measure of angle BAC of arc DC = 120
Answer:
30 degrees.
Step-by-step explanation:
DC is given as 120, so start off by finding arc BC.
180-120= Semicircle-DC=60.
BC=60.
Inscribed angles are half of their arcs.
60/2=30.
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with
mass 7 kg, the acceleration of the object is 4 m/s?. If the same force acts upon another object whose mass is 2 kg, what is this object's acceleration?
Answer:
14 m/s²
Step-by-step explanation:
From the question
a ∝ F/m.............. Equation 1
Where a = aceleration, m = mass, F = force
make F the subject of the equation
F = ma............ equation 2
Given: m = 7 kg, a = 4 m/s²
Therefore,
F = 7(4)
F = 28 N
For another object whose mass is 2 kg,
Make a the subject of equation 2
a = F/m
a = 28/2
a = 14 m/s²
Convert the following 4.5 hours Into Second- ( Soin 24
Answer: 16,200 Seconds
Step-by-step explanation:
Data: 4.5 hours(h)=x seconds(s)
Step One, Convert Hours Into Minutes
4.5h=4h and 30 minutes(m)
1h=60mx4=240m+30=270m
Reason: Since to convert to seconds, minutes are needed, you have to convert everything to minutes. And with 60 minutes in an hour you have to multiply 60 by 4 to get 240 and add 30 minutes to it(since it's 4.5 hours) to find ourselves at 270 minutes.
Step two, Convert Minutes Into Seconds
1m=60s
270mx60=16,200s
Reason: Since we are ultimately trying to get 4.5 hours into seconds, we have to convert the minutes we have into seconds by multiplying 270 minutes by 60(since 60 seconds are in a minute) to get our final answer of 16,200 seconds.
I hope this helps!
I NEED ANSWER ASAP WILL GIVE BRAINLIEST(WORTH 30 POINTS)
Which function is represented by the graph?
A. f(x) = -2|x|+ 1
B. f(x) = -1/2|x|+1 C. f(x) = -2|x + 1|
D. f(x) =-1/2|x-1|
Answer: b
Step-by-step explanation:
