Step-by-step explanation:
Using the following property of logarithms,
[tex]\ln{\left(\dfrac{a}{b}\right)} = \ln{a} - \ln{b}[/tex]
we can write the given equation as
[tex]\ln{(x^2 + 1)} - \ln{(x^2 - 1)} = \ln{\left(\dfrac{x^2 + 1}{x^2 - 1}\right)}[/tex]
[tex]\:\:\:\:\:\:\:\:\:= \ln{\dfrac{x(x + 1)}{x(x - 1)}} = \ln{\left(\dfrac{x + 1}{x - 1}\right)}[/tex]
But recall that [tex]\ln{e} = 1[/tex] so we can write our original equation as
[tex]\ln{\left(\dfrac{x + 1}{x - 1}\right)} = \ln{e}[/tex]
or simply
[tex]\dfrac{x + 1}{x - 1} = e[/tex]
Multiplying both sides by [tex](x - 1),[/tex] we get
[tex]x + 1 = e(x - 1)[/tex]
Solving for x, we get
[tex]x = \dfrac{e + 1}{e - 1}[/tex]
Andre drew a line connected to opposite corners of a parallelogram select a true statement about trying to create by the line andre drew
What is the solution -3(y+1)+7y=4(y+1)-5
No solution
Y=
All real number are solutions
Solve the inequality and graph the solution on the line provided.
7 + 5x < 42
Answer:
x < 7
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
5x+7<42
Step 2: Subtract 7 from both sides.
5x+7−7<42−7
5x<35
Step 3: Divide both sides by 5.
x<7
For the graph, draw an open circle at 7 and an arrow pointing left.
Hope this helps! :D
Step-by-step explanation:
5x<42-7
5x<35
5x/5<35/5
x<7
Maggie's brother is 11 years younger than three times her age. The sum of their ages is 41.
How old is Maggie?
Maggie is_______ years old
Answer:
Maggie is 13 years old.
Step-by-step explanation:
The explanation is attached.
H.O.T. Problems Higher Order Thinking
11. GCSS Use Math Tools Find examples of grocery item prices in a
newspaper, on television, or on the Internet. Compare unit prices of two
different brands of the same item. Explain which item is the better buy.
Answer: you would save 26 dollars per tire if you got the special deal instead of the normal price.
Step-by-step explanation: a pair = 2 (this is what i did i dont know what you learn by but the special deal is still cheaper.)
380/2=190
216-190=26
Does the following represent a function?
f = [ (3, -1), (2, 5), (4, -6), (3, 4), (5, -8) ]
Answer:
Not a function
Since x= produces y- -1 and y=-4, the relation (3,-1),(2,5),(4,-6),(3,4),(5,-8) is not a function.
Select the choice that translates the following verbal phrase correctly to algebra:
the difference of m and 7 increased by 15
m − (7 + 15)
7m + 15
(m − 7) + 15
m − 7 ÷ 15
Answer:
(m − 7) + 15
Step-by-step explanation:
what is statistics ???
explain !!!
Answer:
what is statistics ???
explain !!!
Step-by-step explanation:
Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. ... Probability is a mathematical language used to discuss uncertain events and probability plays a key role in statistics.Please mark me as brainliest
7m-4-9m-35=0
Solving linear equation
please help me
Step-by-step explanation:
-2m-39=0
-2m=0+39
-m= 39/2
m= -19.5
Answer:
[tex]7m - 4 - 9m - 35 = 0 \\ 7m - 9m = 35 + 4 \\ - 2m = 39 \\ 2m = - 39 \\ m = \frac{( - 39)}{2} \\ \boxed{m = - 19.5}[/tex]
m = -19.5 is the right answer.Find the value of x
50
x
Which of the following is equal to the rational expression when x ≠ -1 or -7?
(X+1)(x-1)
——————
(X+7)(x+1)
A. x+1
——
x+7
B. x+7
———
x-1
C. x-1
——
x+7
9514 1404 393
Answer:
C. (x -1)/(x +7)
Step-by-step explanation:
The factor (x +1) in the numerator cancels the same factor in the denominator, leaving the ratio (x -1)/(x +7). This matches choice C.
_____
Additional comment
Even though (x+1)/(x+1) = 1 and can be removed from the expression, the fact that it is undefined at x=-1 means the reduced ratio (x-1)/(x+7) is only a valid representation of the original ratio when x≠-1. The factor (x+1) may be gone, but the domain restriction associated with it remains.
Explain how you know that the sums of 12.6,3.1 and 5.4 is greater than 20
Answer:
2.6+3.1+5.4 =21.1
if you have 20
subtract 21.1-20
then you have 1.1
since the difference is 1.1 then we say
21.1>20
8. Evaluate 5-3 with no negative exponents.
A. 125 B. -125
c. 1 D.
D. - 1
Answer:
5 - 3 = 2?
Explanation:
It's 2?
please help me solve it
Answer:
below
Step-by-step explanation:
1 corn equals 700-800 the yellow tiny thing.
so, lets just assume it has 700,
therefore, 700 - 6 = 694
694 + 1 = 695.
or 700 + 1 = 701.
or perhaps
800 - 6 = 794
794 + 1 = 795
or 800 + 1 = 801
but then again it depends on how much the yellow tiny thing is on the corn. bc, it could be 705, 807, or even 900, who knows.
What is the area of the shaded rectangle?
Answer:
Step-by-step explanation:
The yellow face has a height of 2 inches and a length of 7 inches.
The area = 2 * 7 = 14.
Find the 2 and 7 on the left diagram.
Two angles are supplementary. One angle measures 52 degrees more than the other angle. Find the measure of the LARGER angle.
[tex]\begin{array}{l}\text{We\ have\ } \alpha +\beta =180\ \text{and} \ \beta =\alpha +52\text{\ then}\\\\\alpha +\alpha +52=180\\\\\Longrightarrow 2\alpha =180-52\\\\\Longrightarrow \alpha =\frac{128}{2} =64\\\\\therefore \beta =64+52=116\\\\\therefore \boxed{\text{The\ larger\ angle\ is\ 116\ degrees}}\end{array}[/tex]
I need help with number 3 plzzz fast
Step-by-step explanation:
the domain is the interval of the x (input) values.
in other words, is g(x) invalid for certain x ?
it does not look like it. it looks like g(x) is valid for every possible value of x from -infinite to +infinite.
the range is the interval of possible y (functional) values.
and that is clearly valid for every y between -1 and +infinity.
please help me answer this question.. am giving brainliest
Step-by-step explanation:
We are going to use the following properties of logarithms to solve this problem:
[tex]\log{\dfrac{a}{b}} = \log{a} - \log{b}[/tex]
and
[tex]\log{ab} = \log{a} + \log{b}[/tex]
So we can rewrite the given equation as
[tex]\log{2x^3} - \log{x} = \log{\left(\dfrac{2x^3}{x}\right)} = \log{2x^2}[/tex]
Also,
[tex]\log{16} + \log{x} = \log{(16x)}[/tex]
So we can write
[tex]\log{2x^2} = \log{(16x)}[/tex]
or eliminating the log symbols, we get
[tex]2x^2 = 16x[/tex]
The solutions for the equation above are
[tex]x = 8\:\text{and}\: 0[/tex]
The volume of a crate with length of x feet, width of 8 - x feet, and a height of x - 3 feet is given by V(x)=x(8−x)(x−3) find the maximum volume of the crate and the dimensions for this volume
Find cos(x) if [tex]\frac{sin^2x-1}{cosx} =-1[/tex].
A -1
B 2
C 1
D 0
(sin²(x) - 1)/cos(x) = -1
-cos²(x)/cos(x) = -1
-cos²(x) = -cos(x)
cos²(x) - cos(x) = 0
cos(x) (cos(x) - 1) = 0
Then it follows that cos(x) = 0 or cos(x) = 1. But if cos(x) = 0, then the original expression on the left side of the equation would be undefined. Then C is the only valid solution.
A calculator which was bought for Rs.450,was sold at Rs.495.What was the gain percent?
Answer:
10%
Step-by-step explanation:
495-450=45
45x100/450=10
Answer:
Profit made by reselling = 495 - 450 = ₹45
So, percentage =
[tex] \frac{45}{450} \times 100 = 10\%[/tex]
So, gain percentage is 10%
PLEASE MARK ME BRAINLIEST.The _____ measures the variation in the dependent variable that is explained by variables other than the independent variable in simple regression analysis .
a. total sum of squares
b. sum of squares error
c. sum of squares within
d. sum of squares regression
plz help!!!!!!!!!!!!!!!!!!!
Answer:
X= 30
y= 10
Step-by-step explanation:
(2x+90)=5x ( Opposite angles)
2x+90=5x
5x-2x= 90
3x=90
x=90/3
x= 30°
5x =5(30)=150
2x+90=2(30)+90=60+90=150
3y+150=180
3y=180-150
3y=30
y=30/3
y=10
I hope I helped you^_^
Answer:
Step-by-step explanation:
A cab company charges $3 per cab ride,
plus an additional $2 per mile driven. How
long is a cab ride that costs $11?
miles
Answer:
The answer is c = 2 + 3d .
Step-by-step explanation:
It is given that a cab ride cost $2 which is a fixed amount and charges additional $3 per mile. So you have to make an equation of c in terms of d :
Let c be the cost,
Let d be the distance,
c = 2 + 3d
WILL GIVE BRAINLEST!!!!
PLS HELP...
using the recursive definition for the following arithmetic sequence, find the second, third, and fourth terms of the sequence. then writes the explicit formula that represents the sequence.
Step-by-step explanation:
[tex]A(2)=A(2-1)+6=A(1)+6=12+6=18[/tex]
Really need help quick
Answer:
Total Number of times Spun = 1200
Key sentence: "Pr(Red) is same as Pr(Yellow).
Pr(Green)= 0.2
0.2 = x/1200
x= 0.2 x 1200
x = 240.
It landed on green 240 times
Pr(Brown) =0.54
0.54 = y/1200
y= 1200 x 0.54
y= 648.
Now
To get the Number of times it landed on Red and Yellow
You simply subtract that of Green and Brown from 1200 and divide this result by 2(Since Red and Yellow are have equal occurrence).
1200 – (648 + 240)
= 312.
312/2 = 156.
So It landed on Red and Yellow 156 times each.
Step-by-step explanation:
Red ----- 156times
Green -----240times
Brown ----- 648times
Yellow -----156times
for f(x) = 2x+1 and g(x)=x*2-7
find (f/g) (x).
An old principle of public landscaping says "build sidewalks last." In other words, let
the people find their chosen paths and then build the sidewalks on the paths. The
picture below shows a campus quadrangle that measures 40 meters by 30 meters.
The path between each building is an illustration of Pythagoras theorem.
The sidewalk between library and humanities is 21.21 metersThe sidewalk between chemistry and humanities is 29.15 metersThe sidewalk between chemistry and humanities is 36.06 metersSee attachment for a copy of the given image.
The sidewalk between library and humanities
This is represented with (a).
The value of (a) will be calculated using Pythagoras theorem.
So, we have:
[tex]a^2 = 15^2 + 15^2[/tex]
[tex]a^2 = 450[/tex]
Take square roots
[tex]a = 21.21[/tex]
Sidewalk between chemistry and library
This is represented with (d).
First calculate the value of (b) and (c)
[tex]c + 15 = 30[/tex]
So:
[tex]c = 15[/tex]
Also:
[tex]b + 15 = 40[/tex]
So:
[tex]b = 25[/tex]
The value of (d) will be calculated using Pythagoras theorem.
[tex]d^2 = b^2 + c^2[/tex]
[tex]d^2 = 25^2 + 15^2[/tex]
[tex]d^2 = 850[/tex]
Take square roots
[tex]d = 29.15[/tex]
The sidewalk between chemistry and humanities
This is represented with (e).
The value of (e) will be calculated using Pythagoras theorem.
[tex]e^2 = d^2 + a^2[/tex]
[tex]e^2 = 850 + 450[/tex]
[tex]e^2 = 1300[/tex]
Take square roots
[tex]e = 36.06[/tex]
Learn more about Pythagoras theorem at:
https://brainly.com/question/343682
Liliana has $2.10 in nickels and quarters in her backpack. She has 12 more nickels than quarters. How many coins of each type does she have?
Step-by-step explanation:
17 nickels and 5 quarters I just thought way to much for such a simple question
