Answers
Given:
[tex]\ln x+\ln (x+14)=3[/tex]Use the formula:
[tex]\ln ab=\ln a+\ln b[/tex][tex]\begin{gathered} \ln x+\ln (x+14)=3 \\ \ln x(x+14)=3 \\ x(x+14)=e^3 \\ x^2+14x=20.085 \end{gathered}[/tex]solve the equation :
[tex]\begin{gathered} x^2+14x=20.085 \\ x^2+14x-20.085=0 \\ x=\frac{-14\pm\sqrt[]{14^2-4(1)(-20.085)}}{2} \\ x=\frac{-14\pm\sqrt[]{276.34}}{2} \\ x=\frac{-14\pm16.623}{2} \\ x=-7\pm8.312 \\ x=-7+8.312;x=-7-8.312 \\ x=1.312;x=-15.312 \end{gathered}[/tex]Answer:
[tex]\textsf{Exact form}: \quad x=-7 +\sqrt{49+e^3}[/tex]
[tex]\textsf{Decimal form}: \quad x=1.312\; \sf (3\:d.p.)[/tex]
Step-by-step explanation:
Given equation:
[tex]\ln x + \ln (x+14)=3[/tex]
[tex]\textsf{Apply the product law} \quad \ln x + \ln y=\ln xy:[/tex]
[tex]\implies \ln (x(x+14))=3[/tex]
[tex]\implies \ln (x^2+14x)=3[/tex]
[tex]\textsf{Apply the log law} \quad e^{\ln x}=x:[/tex]
[tex]\implies e^{\ln (x^2+14x)}=e^3[/tex]
[tex]\implies x^2+14x=e^3[/tex]
Subtract e³ from both sides to form a quadratic equation:
[tex]\implies x^2+14x-e^3=e^3-e^3[/tex]
[tex]\implies x^2+14x-e^3=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
a = 1b = 14c = -e³Substitute these values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-14 \pm \sqrt{14^2-4(1)(-e^3)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{196+4e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4(49+e^3)} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4}\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm 2\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=-7 \pm \sqrt{49+e^3}[/tex]
Solutions:
[tex]x=-7 +\sqrt{49+e^3}, \quad x=-7 -\sqrt{49+e^3}[/tex]
Decimal form:
[tex]x= 1.312, \quad x=-15.312[/tex]
As logs of negative numbers cannot be taken, the only solution is:
[tex]x=-7 +\sqrt{49+e^3}\\\\x=1.312\;\sf (3\;d.p.)[/tex]
Related Questions
A local restaurant serves breakfast. They use 124 cups of pancake mix every hour. It takes 114 cups of mix to make one pancake. The pancakes are all equal in size.
About how many pancakes can the restaurant make in two hours?
A:99 pancakes
B:198 pancakes
C:251 pancakes
D:310 pancakes
Answers
Answer: B
Step-by-step explanation: I just did this on my test like 30 seconds ago
Answer:b
Step-by-step explanation:
I looked it up SPEED GANG FOR LIFE
The linear parent function, f(x) = x, transformed to g(x) = x+ 7. Whichstatement correctly compares the graphs of the functions?A. The graph of g(x) is less steep than the graph of f(x) and theyintercept has been shifted down.B. The graph of g(x) is steeper than the graph of f(x) and theyintercept has been shifted up.C. The graph of g(x) is less steep than the graph of f(x) and theyintercept has been shifted up.D. The graph of g(x) is steeper than the graph of f(x) and theyintercept has been shifted down.
Answers
The parent function given is
[tex]\begin{gathered} f(x)=x \\ \text{its has a slope of 1} \end{gathered}[/tex]The transformed function given is
[tex]\begin{gathered} g(x)=\frac{1}{2}x+7 \\ \text{which has a slope of 1/2} \end{gathered}[/tex]There is a reduction in the slope of the functions which makes the transformed function become less steep
The slope reduced from
[tex]1\text{ to 1/2}[/tex]There is also a change in the intercept from
[tex]0\text{ to +7}[/tex]And this indicates that the transformed function has been shifted up by 7 units
With the explanation above, we can therefore conclude that the statement which compares the two graphs of the function is
The graph of g(x) is less steep than the graph of f(x) and the intercept has been shifted up
Hence, The correct answer is OPTION C
ANSWER FAST PLS
Write and solve an equation that represents the following math sentence. Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5. 24 = 10.5 + 4.5m; m = 60.75 24 = 10.5 + 4.5m; m = 3 24 equals 10.5 plus m over 4.5; m = 3 24 equals 10.5 plus m over 4.5; m = 60.75
Answers
24 = 10.5 + 4.5m; m = 3
24 equals 10.5 plus m over 4.5; m = 3
24 equals 10.5 plus m over 4.5; m = 60.75
Answer: I believe the answer is C
Step-by-step explanation: forgive me if im wrong im not completely sure
Hello I need help please
Answers
To graph the function using a table of values. The function is:
[tex]f(x)=\sqrt[]{x}[/tex]Since the root is even, because it is a square root, there is no Real values for
[tex]x<0[/tex]This already indicates that the probable correct alternative is C, however let's make the table to make sure.
The best way is to get x values that will easily get was f(x) values. Let's pick x = 0, x = 1 and x = 4:
[tex]\begin{gathered} f(0)=\sqrt[]{0}=0 \\ f(1)=\sqrt[]{1}=1 \\ f(4)=\sqrt[]{4}=2 \end{gathered}[/tex]So, the points (0,0), (1,1) and (4,2) should be in the line. This exclude alternatives A, B and D. In C we can see these points:
So, the graph of the given function is the one showed in option C
Solve this please !!!!
Answers
Given
[tex]1.5(x+4)-3=4.5(x-2)[/tex]To find: The value of x.
Explanation:
It is given that,
[tex]1.5(x+4)-3=4.5(x-2)[/tex]That implies,
[tex]\begin{gathered} 1.5(x+4)-3=4.5(x-2) \\ 1.5x+6-3=4.5x-9 \\ 1.5x+3=4.5x-9 \\ 4.5x-1.5x=9+3 \\ 3x=12 \\ x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Hence, the value of x is 4.
Please answer ASAP for 100 points and brainliest if possible and if its correct
PLEASE!!!!!!!!!!!!!!!!
Answers
Answer:
59.40
Step-by-step explanation:
the squares for each quadratic, list the center and rais, labeling its translated center: (a) x2 + 2x + y2 - 4y = 4 (c) 2x2 + 2y2 + 3x - 5y = 2 (e) x2 + y2 + 3x = 4 (g) x2 + y2 + 4x = 0 (i) x2 + y2 + 2mx - 2ny = 0 (b) 32-95.0 (d) * - 25.- (1) Akh + 47 - 165 (h) 2 + y - 7y=0 (j) 32 + y2 - 203. 2. Determine which of the following equations represents a circle with (a) x2 + y2 + 10x = -30 (b) 3x2 + 3y2 (c) 4x2 + 4y2 + 18x - 8y = -85 (d) 36x2 + 36
Answers
Determine which of the following equations represents a circle with a real non-zero radius:
a) First equation:
[tex]x^2+y^2+10x=-30[/tex]We need to complete squares, i.e., make the equation look like a sum of squared binomials. Separating x's and y's:
5. What is the slope that runs through the points (-4, 10) and (-4, 3)?
Answers
To find the slope, we will use the formula;
slope = y₂ - y₁ / x₂- x₁
From the points give,
x₁ = -4 y₁= 10
x₂ = -4 y₂=3
slope = 3 - 10 / -4+ 4
slope = -7/0
slope = ∞
The slope is undefined.
isabella bought tickets for 84 people. each ticket cost $16.22. how much did isabella spend on tickets
Answers
The total money Isabella spent on tickets will be $1362.48
In the given question, it is stated that Isabella bought a total of 84 Tickets. Each of the tickets she bought cost $16.22. We have to find out the total amount that she spent on buying tickets for everyone. From this given situation we know:
The cost of one ticket: $16.22
Total number of tickets: 84
From this formula, we can calculate the total amount spent
Total Amount = Total ticket * cost of one ticket
Putting values in this formula, we get:
=> Amount = cost*number
=> Amount = 16.22*84
=> Amount = 1362.48
Hence, the Total amount that she spent on Tickets will be $1362.48
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in a sale normal prices are reduced by 10% Nathaniel bought a pair of shoes in the sale for £54
what was the original price of the shoes?
Answers
Answer:
$59.40
Step-by-step explanation:
54*0.10 (10%) = 5.4
5.4+54= 59.4
therefore, the price of the shoes without the discount is $59.40
Answer:
[tex]x=540[/tex]
What are Percentages?Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they always have the same denominator, 100.
[tex]{\text}To find this.[/tex]
[tex]{\text}Right the formula:[/tex]
10% of x = £54
[tex]{\text}Indicating 10 percent of something is the sale given for the pair of shoes 54.[/tex]
[tex]{\text}Then calculate:[/tex]
[tex]\frac{10x}{100} =54[/tex]
[tex]{\text}Using crisscross multiplication:[/tex]
[tex]x=540[/tex]
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what is the y-intercept of the graph of y= 4.4 (0.34) x?
Answers
The y-intercept of the given graph would be (0, 0).
________________________________________
Hope this helps!
Find the volume of a cone with a base diameter of 6 yd and a height of 8 yd.Use the value 3.14 for 1, and do not do any rounding.Be sure to include the correct unit in your answer.
Answers
ANSWER
[tex]\begin{equation*} 75.36\text{ }yd^3 \end{equation*}[/tex]EXPLANATION
The volume of a cone is given by:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where r = radius of the base of the cone
h = height of the cone
The diameter of the base of the cone is twice the radius. This implies that the radius of the cone is:
[tex]\begin{gathered} D=2r \\ r=\frac{D}{2} \\ r=\frac{6}{2} \\ r=3\text{ }yd \end{gathered}[/tex]Hence, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}*3.14*3^2*8 \\ V=75.36\text{ }yd^3 \end{gathered}[/tex]That is the answer.
What are some similarities between sales tax and hotel tax? Select all that apply. Multiple select question. cross out A) Both are an additional amount one must pay. cross out B) Both must be paid in advance when you make a hotel reservation. cross out C) Both are based on a percentage of the original cost. cross out D) Both the sales tax and the hotel tax are equal when you stay in a hotel. cross out E) Both represent a guest fee that hotels charge their customers.
Answers
Some of the similarities between sales tax and hotel tax include the following:
B) Both must be paid in advance when you make a hotel reservation.
C) Both are based on a percentage of the original cost.
What is taxation?Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.
The types of tax.In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:
Hotel taxSales taxProperty taxIncome taxIn conclusion, we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.
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GIVING BRAINLIEST + 60 POINTS!
Solve for x: 1 < x + 3 < 4
A. 4 > x > 7
B. 4 < x < 7
C. −2 > x > 1
D. −2 < x < 1
Please explain why you have gotten the right answer!
Answers
Answer:
it's greater than one so it's value is not negative
and 3+4 is 7
so x is greater then 4 but less than 7
so it's b the correct option
Answer:
D. -2 < x < 1
Step-by-step explanation:
1 < x + 3 < 4
=
{1 < x + 3
{x + 3 < 4
=
{ 1 + ( -3 ) < ( x + 3 ) + ( -3 )
{ ( x + 3 ) + ( -3 ) < 4 + ( -3 )
=
{ 1 - 3 < x + 3 - 3
{ x + 3 - 3 < 4 - 3
=
{ -2 < x
{ x < 1
=
{ x > - 2
{ x < 1
Hence, the answer would be : -2 < x < 1
Hopes this helps!
Have a good day :)
? 60 Thanks for helping me Will give good feedback
Answers
Answer: F. $1.25
Explanation:
First, we need to find the probability of the coin landing faceup and facedown. We know that landing faceup is 3 times the probability of landing facedown. Since the highest probability is 1 (100%):
[tex]\begin{gathered} 3x+x=1 \\ 4x=1 \\ x=\frac{1}{4}=0.25 \end{gathered}[/tex]With this, we know that:
probability of the coin landing faceup = 3×0.25 = 0.75
probability of the coin landing facedown = 0.25
To find the expected value of each toss, we need to solve for the total of each value multiplied by its probability:
[tex]\begin{gathered} EV=\$1(0.75)+\$2(0.25) \\ EV=\$1.25 \end{gathered}[/tex]Therefore, the expected value of each toss of Coin C is $1.25
GH has a midpoint at M(-4.5, 5.5). Point G is at
(-10, 14). Find the coordinates of point H.
Answers
Answer:
(-1, 3)
Step-by-step explanation:
We could imagine the point G and H are points on a straight line.
We know that:
Point G is at (-10, 14)
Midpoint at M (-4.5, 5.5)
To calculate the x coordinate of the mid-point, we suppose to subtract x coordinate of H from coordinate x of G, divide by 2 to get the x coordinate of the midpoint m, which is -4.5
To calculate the y coordinate of the mid-point, we suppose to subtract y coordinate of H from y coordinate of G, divide by 2 to get the x coordinate of the midpoint m, which is 5.5
Therefore, x coordinate of H:
(- 10 - x) / 2 = -4.5
-10 - x = -9
- x = 1
x = - 1
And y coordinate of H:
(14 - y) / 2 = 5.5
14 - y = 11
- y = -3
y = 3
How many solutions does this equation have?
-8-10z = -4 - 10z
Answers
Step by step
-8-10z = -4-10z
Add 10z to both sides
-8 -10z + 10z = -4 -10z + 10z
-8 = -4
This is not true so no solution
If the value of a lies in between - 1 and 1 in the absolute value function y = a|x|, then the graph is farther from the ______________.y = -xy = xy-axisx-axis
Answers
SOLUTION:
If the value of a lies in between - 1 and 1 in the absolute value function y = a|x|, then the graph is farther from the y- axis. This is because the bounding lines of the function are the lines y = x and y = -x. Thus, when a varies from -1 to 1, the graph gets farther from the y-axis.
Final answer ;
Please help me solve this giving 20 points
Answers
Answer:
5005
Step-by-step explanation:
This seems to me like a permutations and combinations question.
Since the order doesn't matter, it's a combination.
15 c 6 = 5005
I hope this helps!
Peter enrolled $80,000 worth of debt with National Debt Relief. Peter’s fee for the service is 20% of the enrolled debt. How much is Peter’s fee?*
Answers
Answer:
16000
Step-by-step explanation:
{(-3,-4), (-1,2), (0, 0), (-3,5), (2,4)}
Determine whether the relation represents a function.
O Yes, It is a function.
No, it is NOT a function.
Answers
Answer:
No, it's not function
Step-by-step explanation:
Every function is a relation but every relation is not a function because:
Function: a special type of relation in which the first-order pairs are different.
In this case {(-3,-4), ......., (-3,5)} these two sets have the same first-order pair.
So, your answer will be 'It's not function.'.
Determine g(x−1) for the following function. g(x)=−4x−1
Answers
The function operation g( x - 1 ) of the function g( x ) = −4x − 1 is -4x + 3.
What is the function operation g( x - 1 ) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
g( x ) = −4x − 1g( x - 1 ) = ?To find g( x - 1 ), replace all the occurrence of x with ( x - 1 ) in the function and simplify.
g( x ) = −4x − 1
g( x - 1 ) = −4( x - 1 ) − 1
Simplify by distributive property
g( x - 1 ) = −4( x - 1 ) − 1
g( x - 1 ) = x( -4 ) - 1( -4 ) - 1
g( x - 1 ) = -4x + 4 - 1
g( x - 1 ) = -4x + 4 - 1
Add 4 and -1
g( x - 1 ) = -4x + 3
Therefore, the function operation g( x - 1 ) is -4x + 3.
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Missed the class now lost
Answers
substitute the given values in the formula of (BAC) we have
[tex]48\cdot3.2\colon160-3\cdot0.015[/tex]Remember
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
so
step 1
solve the multiplication
48*3.2=153.6
substitute
[tex]153.6\colon160-3\cdot0.015[/tex]step 2
Solve the division
153.6/160=0.96
substitute
[tex]0.96-3\cdot0.015[/tex]step 3
solve the multiplication
3*0.015=0.045
substitute
[tex]0.96-0.045[/tex]step 4
solve the subtraction
0.96-0.045=0.915
What is the Area of 8 and 3 1/2
Answers
The area of the rectangle with 8 and 3 1/2 units is 28 sq. units.
How to estimate the area of the rectangle?The region occupied by a rectangle within its four sides or boundaries is known as its area. The area of a rectangle is determined by its sides. Essentially, the formula for area is equal to the product of the rectangle's length and breadth.
It is given that the length of the rectangle is 8 units and the breadth 3 1/2 units.
the area of the rectangle = length x breadth = 8 x 3 1/2 = 8 x 7/2 = 28 sq. units
So, the area of the rectangle is 28 sq. units.
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Compare. Select >, <, or = to make the sentence true.
8 meters 6,000 millimeters
Answers
Answer: 8,0000 meters
Step-by-step explanation: if im wrong let me know and i will fix it
Answer: your answer is the alligator facing the left/8 meters is more
Step-by-step explanation:
the reason for this is because 1 meter is 1,000 millimeters so if you have 8 meters, then you obviously 8,000 millimeters
hope this helps :)
please give brainliest if possible
The first half of this problem is complete, but I dont understand how to do the second part.
Answers
Okay, here we have this:
According with the provided info we obtain the following equation:
[tex]v=30\cdot(\frac{1}{2})^{\frac{t}{36}}[/tex]Let's calculate first the 20% of the initial leval:
[tex]30\cdot\frac{20}{100}=\frac{600}{100}=6mg[/tex]Now, let's replace in the equation "v" with 6 to find the estimated time:
[tex]\begin{gathered} v=30\cdot(\frac{1}{2})^{\frac{t}{36}} \\ 6=30\cdot(\frac{1}{2})^{\frac{t}{36}} \end{gathered}[/tex]And, finally let's clear t:
[tex]\begin{gathered} 6=30\cdot(\frac{1}{2})^{\frac{t}{36}} \\ \frac{6}{30}=(\frac{1}{2})^{\frac{t}{36}} \\ \frac{1}{5}=(\frac{1}{2})^{\frac{t}{36}} \\ \frac{t}{36}\ln (\frac{1}{2})=\ln (\frac{1}{5}) \\ t=\frac{36\ln\left(5\right)}{\ln\left(2\right)} \\ t=83.589 \\ t\approx84 \end{gathered}[/tex]Finally we obtain that after approximately 84 hours the valium concentration will reach 20% of it's initial level.
Factor-2x² + 10x.
O-2x(x + 5)
O 2x(-x + 5)
O2(-x² + 10x)
Ox(2x + 10)
Answers
Answer:
I believe it is B.
Step-by-step explanation:
When you solve B, you get the expression that you are supposed to factor.
What in cardinality?
Answers
Have a good day!
Find (f◦g)(x) and (g◦f)(x) for the pair of functions and give the domains. f(x)= 16 x2,
Answers
Need more information to solve, but the standard rule is:
(f◦g)(x) = f(g(x))
(g◦f)(x) = g(f(x))
7 Describe the error in solving the equation
(1) 3 (X + 4) = 13
(2) 3x + 4 =13
(3) 3 x = 9
(14)X = 3
Answers
Answer:
(2) The 3 was not distributed correctly.
3(x + 4) is the same as 3(x) + 3(4) Which is 3x + 12 not 3x + 4
Step-by-step explanation:
Answer: The error was at the first step since 4 was never multiplied by 3, therefore the final answer would be incorrect.
Step-by-step explanation: 3(x + 4) = 13
multiply 3 by everything in the parenthesis, so
3x + 12 = 13
subtract 12 from each side.
3x = 1
divide both sides by 3
x = 1/3 = 0.33