[Quick Answer Needed] Which of the following shows the extraneous solution to the logarithmic equation?
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![[Quick Answer Needed] Which Of The Following Shows The Extraneous Solution To The Logarithmic Equation?(Image](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/x9gvOALzxLyDK22MWenga1H0F7OMXAlw.png)
Answers
Answer:
C
Step-by-step explanation:
Given the logarithmic equation
[tex]\log_4x+\log_4(x-3)=\log_4(-7x+21)[/tex]
First, notice that
[tex]x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x<21\ x<3[/tex]
So, there is no possible solutions, all possible solutions will be extraneous.
Solve the equation:
[tex]\log_4x+\log_4(x-3)=\log_4x(x-3),[/tex]
then
[tex]\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3[/tex]
Hence, [tex]x=3[/tex] and [tex]x=-7[/tex] are extraneous solutions
Related Questions
In a different plan forarea codes the first digit is 1 through 6 the second digit is either 5 6 7 or 8 the third digit could be any number except 5 with this plan how many ways is area code possible
Answers
Answer:
216
Step-by-step explanation:
There are 6 options for the first digit.
There are 4 options for the second digit.
There are 9 options for the third digit.
The total number of combinations is 6 × 4 × 9 = 216.
-x + y = 8
1/2x - 1/2y = 3
Do these equations have one solution, no solution, or infinitely many solutions?
Answers
Answer:
No solution
Step-by-step explanation:
-x + y = 8..............(1)
1/2x - 1/2y = 3......(2)
Multiply (2) by 2
x - y = 6 ............(3)
Adding (1) and (3)
-x + x + y - y = 8 + 3
x and y are both eliminated so no solution
Miriam is driving to Austin. This is what her gas gauge looks like when she stops for lunch. What fraction of her gas tank is filled?
A 1/4
B 1/5
C 1/3
D 3/4
PLEASE ME ANSWER!
Answers
Answer:
A. 1/4
Step-by-step explanation:
The attached picture is the complete question:
As you can see in the picture, the guage is divided into 4. The indicator is pointed at the at the first notch, from the empty area. This means that when it was full, it was at 4/4, as it goes towards empty, the notches decrease by 1/4. It is now on the 1st notch, that means that it is filled 1/4 or there is 1/4 left.
Find the x-component of this vector:
Answers
Answer: -13.9
This value is approximate.
==================================================
Explanation:
This angle is in quadrant Q2, which is where x is negative and y is positive.
The angle shown of 65 degrees is added to the 90 degree angle to the right resulting in 65+90 = 155 degrees overall. See diagram below.
The x component of the vector is found by the formula
x = r*cos(theta)
we will plug in r = 15.3 as the magnitude of the vector and theta = 155 as the angle
x = 15.3*cos(155)
x = -13.8665 approximately
x = -13.9 rounding to one decimal place (as 15.3 and 65.0 are both rounded to one decimal place)
Simplify:
11 - 3x - 2 + 18x
what is the answer
Answers
Step-by-step explanation:
11-2 = 9
18x-3x = 15x
so, 15x+9 or 3(5x+3)
The simplified expression is 15x + 9.
To simplify the given expression, we combine like terms. The expression given is:
[tex]\[ 11 - 3x - 2 + 18x \][/tex]
First, we combine the constant terms (11 and -2):
[tex]\[ 11 - 2 = 9 \][/tex]
Next, we combine the terms with the variable x (which are -3x and 18x):
[tex]\[ -3x + 18x = 15x \][/tex]
Now, we combine the constant term with the x term:
[tex]\[ 9 + 15x \][/tex]
So, the simplified form of the expression is:
[tex]\[ 15x + 9 \][/tex]
Solve the system. 23x - 12y = 1 - 43x +y =-3
Answers
Answer:
The values are [tex]x=\frac{35}{493}[/tex] and
[tex]y=\frac{26}{493}[/tex]
The solution is ([tex]\frac{35}{493},\frac{26}{493}[/tex])
Step-by-step explanation:
Given equations are [tex]23x-12y=1\hfill (1)[/tex]
[tex]-43x+y=-3\hfill (2)[/tex]
To solve the given equations :
Multiply the equation (2) into 12 we get
[tex]-516x+12y=-36\hfill (3)[/tex]Now adding equations (1) and (3) we get
23x-12y=1
-516x+12y=-36
____________
-493x=-35
[tex]x=\frac{35}{493}[/tex]
Substitute the value of [tex]x=\frac{35}{493}[/tex] in equation (1) we get
[tex]23\times (\frac{35}{493})-12y=1[/tex]
[tex]\frac{805}{493}-12y=1[/tex]
[tex]-12y=1-\frac{805}{493}[/tex]
[tex]-12y=\frac{-312}{493}[/tex]
[tex]y=\frac{26}{493}[/tex]
Therefore the values are [tex]x=\frac{35}{493}[/tex] and
[tex]y=\frac{26}{493}[/tex]
The solution is ([tex]\frac{35}{493},\frac{26}{493}[/tex])
Given the below sequence:
-1, -3, -5, -7, . . .
(a) What are the next 3 terms
(b) Is this an arithmetic or geometric sequence?
(c) Why?
(d) How would you find the 27th term? Find the 27th term. (show your work)
Answers
Answer:
a) The next three terms are -1,-3,-5,-7,-9,-11,-13
b) This is arithmetic sequence
C) The difference of second term and first term is -2 in given sequence so the given sequence is an arithmetic sequence.
d) The 27 th term is -53
Step-by-step explanation:
a) the given sequence is arithmetic sequence
the difference of second term and first term is -2
given sequence is -1,-3,-5,-7.....
the nth term in arithmetic sequence
[tex]t_{n} = a+(n-1)d[/tex]
First term is a = -1 and difference is d = -2
finding fifth term is
[tex]t_{5} = -1 +(5-1)(-2)[/tex]
[tex]t_{5} = -1-8 =-9[/tex]
finding sixth term is
[tex]t_{6} = -1 +(6-1)(-2)[/tex]
[tex]t_{6} = -1-10 =-11[/tex]
finding seventh term is
[tex]t_{7} = -1 + (7-1)(-2)[/tex]
[tex]t_{7} = -1 -12 =-13[/tex]
The next three terms are -9,-11,-13
The given sequence is -1,-3,-5,-7,-9,-11,-13
b) This is arithmetic sequence.
C) because the difference of second term and first term is -2 so the given sequence is arithmetic sequence.
d) by using nth term formula in arithmetic sequence
[tex]t_{n} = a+(n-1)d[/tex]
a= -1 and d =-2
find 27 t h term :-
[tex]t_{27} = -1 + (27-1)(-2) = -1-52=-53[/tex]
On a weather map,an isobar connects places with the same
Answers
Answer:
pressure
Step-by-step explanation:
the root words for isobar are
iso - same or equal
bar - pressure (from greek "baros")
Answer:
Pressure
Step-by-step explanation:
distributive property to match equivalent expression -7(4-+x)
Answers
For what value of the variable the value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x)?
Fastest answer and right answer will be awarded Brainliest!
Answers
For x=2, the value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x)
Step-by-step explanation:
We have to convert the given statement in mathematical or algebraic form to get the value of x for which the given condition is true.
So,
The problem can be written as:
[tex]4(5x-8) = 2(4-x)+4[/tex]
Applying distributive property
[tex]20x-32 = 8-2x+4\\20x-32 = 12-2x\\[/tex]
Adding 32 on both sides
[tex]20x-32+32 = 12-2x+32\\20x = 44-2x[/tex]
Adding 2x on both sides
[tex]20x+2x = 44-2x+2x\\22x=44[/tex]
Dividing both sides by 22
[tex]\frac{22x}{22} = \frac{44}{22}\\x = 2[/tex]
Hence,
For x=2, the value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x)
Keywords: Linear equation, variables
Learn more about linear equation at:
brainly.com/question/10364988brainly.com/question/10435816#LearnwithBrainly
Statement:5>4
Which is greater 5x or 4x
Answers
Answer:
5x
Step-by-step explanation:
Because the inequality sign means it greater and if it turned around than it means it less than and the = sign means it equal to
If x is positive, 5x is greater than 4x and if x is negative, 5x is less than 4x.
To determine whether 5x is greater than 4x, we need to consider the value of "x." The comparison between 5x and 4x depends on the value of "x."
If x is a positive number, then 5x will be greater than 4x because 5 is larger than 4, and multiplying by a positive number increases the value.
For example:
If x = 1, then 5x = 5, and 4x = 4. Since 5 is greater than 4, 5x is greater than 4x.
If x is a negative number, then 5x will be less than 4x because multiplying by a negative number changes the inequality sign.
For example:
If x = -1, then 5x = -5, and 4x = -4. Since -5 is less than -4, 5x is less than 4x.
Thus, it can be concluded that
If x is positive, 5x is greater than 4x. If x is negative, 5x is less than 4x.
Learn more about positive integers here:
https://brainly.com/question/31414162
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Enter the numerator and the denominator of the fraction in simplest form that is equal to the decimal shown.
0.63
Answers
To convert the decimal 0.63 to a fraction, write it as 63/100, and simplify if possible. Since 63 and 100 do not have a common divisor larger than 1, the fraction is already in its simplest form, which is 63/100.
Explanation:The question involves converting a decimal to a fraction in simplest form. To convert the decimal 0.63 into a fraction, you can write it as 63/100 because there are two digits after the decimal point, which equates to the hundredth place. To simplify the fraction, you look for the greatest common divisor (GCD) of both the numerator and the denominator. In this case, both 63 and 100 can be divided by the GCD which is 1. Thus, the fraction is already in its simplest form and the answer is 63/100.
The decimal 0.63 written as a fraction in simplest form is 63/100, which cannot be reduced further since 63 and 100 share no common factors other than 1.
Explanation:The numerator and denominator of the fraction in simplest form that is equal to the decimal 0.63 can be found by moving the decimal point two places to the right. This gives us the fraction 63/100 which can be simplified to 9/15 by dividing both the numerator and denominator by the greatest common factor, which is 9. To convert the decimal 0.63 into a fraction in simplest form, you can start by writing it as ⅓ over 100, since the last digit is in the hundredths place. This gives you the fraction 63/100. However, the question asks for the simplest form, so you should reduce the fraction by finding the greatest common factor of the numerator and denominator.
The greatest common factor of 63 and 100 is 1, so 63/100 cannot be reduced any further - it is already in its simplest form. Thus, the answer is simply ⅓ over 100 or 63/100.
determine whether each pair of functions are inverse functions. 1) f(x)=10x+9/8, g(x)=25x-9/10 2) f(x)=x-9, g(x)=x+9
a. both 1 and 2 are inverse functions.
b. only 2 is an inverse function
c. brother 1 nor 2 is an inverse function.
d. only 1 is an inverse function
Answers
Final answer:
After analyzing both pairs, it is evident that only the second pair, f(x) = x - 9 and g(x) = x + 9, meet the requirements for inverse functions, as both compositions f(g(x)) and g(f(x)) return the original input x. Hence, option b: only 2 is an inverse function, is correct.
Explanation:
To determine whether each pair of functions are inverse functions, we must check if applying one function following the other returns the original input value. For two functions, f(x) and g(x), to be inverses of each other, the following must hold true:
f(g(x)) = x
g(f(x)) = x
Pair 1: f(x) = 10x + 9/8, g(x) = 25x - 9/10
Applying g to f:
g(f(x)) = g(10x + 9/8) = 25(10x + 9/8) - 9/10
After simplifying, this does not equal x, so f and g are not inverse functions.
Pair 2: f(x) = x - 9, g(x) = x + 9
Applying g to f:
g(f(x)) = g(x - 9) = (x - 9) + 9 = x
Applying f to g:
f(g(x)) = f(x + 9) = (x + 9) - 9 = x
In the second pair, both compositions return the input x, so f and g are inverse functions of each other. Therefore, the answer is option b: only 2 is an inverse function.
70.5 - 6.81 =
63.69
63.71
64.69
77.31
Answers
Answer:
63.69
Step-by-step explanation:
Open Response 2
A glass containing water is in the shape of a right circular cylinder with a radius
of 3 centimeters. The height of the water in the glass is 10 centimeters.
a) What is the volume of the water in the glass? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
b) Five spherical marbles of equal size are dropped into the glass. The water in
the glass rises to a height of 11 centimeters. What is the increase in the
volume of the contents of the glass? Be sure to include units of measure in
your answer. Show or explain how you obtained your answer.
c) What is the volume of one of the marbles? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
d) What is the radius of one of the marbles? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
Answers
Answer:
b
Step-by-step explanation:
which of the binomials below is a factor of this trinomial? x^2+12x+35
Answers
Answer:
(x+5) (x+7)
Step-by-step explanation:
1. Which equation represents a linear function?
a. 3y + x2 + x = 0
b. 4x + 2(y – 1) = 0
c. y = 12vx – 5
d. 2x3 + y = 9
Answers
Answer:
b.
Step-by-step explanation:
4x + 2(y – 1) = 0
The variables are all of unit degree so it is linear.
in the problem 19.28 - 1.546, first round each number to the nearest tenth. Then subtract.
Answers
Answer:
17.8
Step-by-step explanation:
First, round the two. umbers to the nearest the th, or the first number past the decimal. 19.28 rounds to 19.3 (round up because 8 is bigger than 5) and 1.546 rounds to 1.5 (round down because 4 is smaller than 5). Then subtract. 19.3 - 1.5 = 17.8
what is the value of s+t-u if s= 12,t=8,and u=20
Answers
Answer:
0
Step-by-step explanation:
12 + 8 = 20
If we then take 20 from 20, you get 0.
Answer:
Answer is 0
Step-by-step explanation:
[tex]s + t - u \\ 12 + 8 - 20 \\ 20 - 20 = 0[/tex]
What does 18A +16B mean
Answers
Answer:
It is an Algebraic Expression
Explanation:
An algebraic expression is a mathematical expression that consists of variables, numbers and operations.
Will mark as BRAINLIEST!!
Answers
Answer:
a= 2s-b-c
Step-by-step explanation:
s=a+b+c/2
1) Multiply everything by 2, to get rid of the /2.
2s=a+b+c
2s-b=a+c
2s-b-c=a
Answer:
Its D TRUST ME IT IS
Step-by-step explanation:
He messed up but i got it right
the left and right page numbers of an open book are two consecutive integers whose sum is 169. find the numbers.
Answers
Answer:
84 and 85
Step-by-step explanation:
84+85=169
Please help!!
What is the location of the point on the number line that is 4/9 of the way from
A= -8 to B = 10?
Ο Α. 0
OB. 2
O c. -2
O D. -1
Answers
Answer:
Α. 0
Step-by-step explanation:
Given A = -8 and B = 10
The distance between A and B
= B - A
= 10 - (-8)
= 10 + 8
= 18 units
4/9 of the way between A and B
= 4/9 of the distance between A and B
= 4/9 x 18 units
= 8 units.
Hence the location of the point that is 4/9 of the way from A to B
= value at point A + 8 units
= -8 + 8
= 0 (answer)
A. 0
Step-by-step explanation:
The answer is 0 (zero)
Find the slope of the line that passes through (2,11) and (7,9).
Answers
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{11}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{2}}}\implies \cfrac{-2}{5}[/tex]
Answer:
it should be -2/5 if you're looking for the slope
find the slope of -1 / 3 + 3 / -2
Answers
Answer:
-1.83 (repeating decimal)
Step-by-step explanation:
A pound of chocolate costs 7 dollars. Keiko buys p pounds. Write an equation to represent the total cost c that keiko pays.
Answers
You need to multiply the cost per pound by the pounds to find the total cost
Answer:
7xp=c
Step-by-step explanation:
since you have to multiply p by 7. to get the answer is c. Take for example
7 x 3 =21
p=3
c=21
es -
Two linear functions of x are shown.
Which statement about the functions is true?
Function 2 can be described by the equation y= 25x - 100.
Function 2 can be described by the equation y = 13x - 11.
The y-intercept of function 1 is less than the y-intercept of function 2.
Rate of change of function 2 is less than the rate of change of function 1.
Answers
Answer:
The answer is D
Step-by-step explanation:
Answer:
THE ANSWER D ON USATESTPREP
plz help i will mark brainliest
Answers
Answer:
x = 9.
Step-by-step explanation:
42 - 15 = 27
27 ÷ 3 = 9
Which inequality is represented by the graph?
A. y>−32x−2
B. y≤−32x−2
C. y≥−32x−2
D. y<−32x−2
Answers
Inequality that represents the graph
[tex]y>\:-\frac{3}{2}x-2[/tex]
Option A
Explanation :
Given the graph of a linear inequality
Lets frame the linear equation of the dotted line first
Slope intercept form of linear equation is y=mx+b
where m is the slope and b is the y intercept
In the graph y intercept is -2. So value of b=-2
Now find out slope m using any two point on the dotted line
Lets pick (0,-2) and (-2,1)
slope formula
[tex]\frac{y_2-y_2}{x_2-x_1}[/tex]
Substitute the values of two points and find out slope
[tex]slope =\frac{y_2-y_2}{x_2-x_1}=\frac{1+2}{-2-0}=-\frac{3}{2}[/tex]
Now replace the values in equation y=mx+b
[tex]y=-\frac{3}{2} x-2[/tex]
In the graph we have dotted line so we use < or >
Lets use test point (0,0) origin.
x=0 and y=0
[tex]y=-\frac{3}{2} x-2\\0=-\frac{3}{2} (0)-2\\0=-2\\0>-2\\[/tex]
So the inequality becomes
[tex]y>-\frac{3}{2} x-2[/tex]
Learn more : brainly.com/question/5529505
5x−7=−10x+8
x = ___
(type your answer as a number)
Answers
Answer:
x=1
Step-by-step explanation:
5x-7=-10x+8
5x=−10x+8+7
5x=−10x+15
5x+10x=15
15x=15
Answer: x=1
Answer:
x = 1
Step-by-step explanation:
Put the like terms to same side of equation
5x -7 = -10x +8 ➡ 5x + 10x = 8 + 7
15x = 15
x = 1