What are the roots of the function f(x) = (log(3x) − 2log(3)) · (x2 − 1) with x ∈ R?
Answer:
x = 1, x = 3
Step-by-step explanation:
Given function:
[tex]f(x)=\left(\log(3x)-2 \log(3)\right) \cdot \left(x^2-1\right)[/tex]
The roots of the function are when f(x) = 0:
[tex]\begin{aligned}f(x) & = 0\\ \implies \left(\log(3x)-2 \log(3)\right) \cdot \left(x^2-1\right) & = 0\\\\ \textsf{Therefore,} \:\:\:\log(3x)-2 \log(3) & = 0\\ \textsf{and }\:\:\:x^2-1 & = 0 \end{aligned}[/tex]
Case 1
[tex]\begin{aligned}\left(\log(3x)-2 \log(3)\right) & = 0\\\log(3x) & = 2 \log(3)\\ \log(3x) & = \log (3)^2\\ \log(3x) & = \log (9)\\ 3x & = 9\\ x & = 3\end{aligned}[/tex]
Case 2
[tex]\begin{aligned}\left x^2-1\right & = 0\\x^2 & = 1\\ x & = \pm 1\end{aligned}[/tex]
As logs of negative numbers cannot be taken, x = 1 only.
Therefore, the roots of the given function are: x = 1, x = 3
Alberto estuvo en el refugio con sus amigos durante cuatro días cuántos Ligias eran?
Answer:
Step-by-step explanation:
Alberto was in the shelter with his friends for four days how many Ligias were they?
Can 0.56214 be written as a fraction? It is a terminating or repeating or neither
Answer:
yes. we can write it as a fraction= 56214/100000
it is terminating because it has a stop and its not repeating
Trinity Brown
5 M1 TD Lesson 19
EUREKA N
3. A typical midsize car weighs 1.5 tons. It has a gas tank that holds 15 gallons of gas.
a. How many quarts does the gas tank hold?
The gas tank holds 60 quarts.
What is quarts?
The quart is an English volume unit equivalent to one-quarter gallon. There are now three types of quarts in use: the liquid quart and dry quart of the US customary system, as well as the imperial quart of the British imperial system. All of them are essentially equivalent to one liter. It is split into two pints or four cups (in the United States). The exact size of the quart has historically fluctuated with the varying values of gallons over time and in relation to different commodities.
1 US gallon = 4 US quarts
so, 15 US gallons = 15 x 4 = 60 quarts
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f(x) = √5x - 7+10
Graph
f(x) = √5x - 7+10 = ( 0, 3) ( -0.6 , 0 ) are graph value .
What does a graph's value represent?
Let (x, y) be a point on a function f's graph. The function's value for the specified value of x is then y. 5 is the value of f(x) at x = 2 if (2, 5) is on the graph of the function.What are the names of the values on a graph?
One of a group of numbers called coordinates is used to specify a point's location on a graph. Both an x-coordinate and a y-coordinate are used to identify each point. A point's x-coordinate is a number that indicates how far away from the origin it is on the horizontal, or x-axis.On f(x) = √5x - 7+10 = ( 0, 3) ( -0.6 , 0 )
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find z
-6x-7y-7z=-68
Pls help
11% of 57 =
39% of 28 =
8% of 97 =
6% of 24.4 =
77% of 9.2 =
Calculate surface area of square diameter 25 in
sharon's organizaion hopes to raise more than $10,000 at their 5k race. what is the inequalities with the variables on both sides
Answer:
x>10000
Step-by-step explanation:
The length of a rectangle is 4 meters longer than the width. If the area is 40 square meters, find the rectangles dimentions. Round to the nearest tenth of a meter
Answer:
L = 32
W = 8
Step-by-step explanation:
Set it up algebraically:
A = L x W
A = 40 m^2
L = 4w
40 = 4w x w
40 = 5w
40/5 = 5w/5
W = 8
L = 4(8)
L = 32
Bennett created the table below. Which
operation did he perform on the numbers
in the left column to find the numbers in the
right column?
F Add 8.
G Add 9.
X
1
2
3
4
5
6
y
9
10
11
12
13
14
H
Multiply by 8.
J Multiply by 9.
Step-by-step explanation:
He added 8 to each number on the left column to get the number on the right column
So that
X 1, 2, 3, 4, 5, 6,
Y 1+8 = 9
Y 2 + 8 = 10
Y 3+8 = 11
Y 4 + 8 = 12
Y 5 + 8 = 13
Y 6 + 8 = 14
Please answer the question quick i’mma mark brainlist
Step-by-step explanation:
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
You didn't show her answer so I don't know her mistake, but you round to the nearest hundredth by looking at the ten's value, if it's a 5 or greater, add one to the hundredths digit. If its lesser than five, leave the hundredth place.
Ex. Rounding 1,567. Because the tens digit is a 6, you round the 5 up to a 6 and get rid of the tens and one digit. 1,567 rounds to 1,600
Ex. Rounding 1,445. Because the tens digit is a 4, you leave the hundredths digit and get rid of the rest. 1,445 rounds to 1,400.
Hope this helps!
can someone help me with this
Answer:
b) -8
c) 11
d) {x is a member of all real numbers | except for 2}
Answer:
(a) Choice C is correct
(b) f(x) = -8 Point is (1, -8)
(c) x =11 Point is at (11,2)
(d) Domain of f is x is [tex]\:x < 2\quad \mathrm{or}\quad \:x > 2\:[/tex]
In interval notation [tex]\:\left(-\infty \:,\:2\right)\cup \left(2,\:\infty \:\right)[/tex]
(e) x intercept is at x = -7
(f) y-intercept is at [tex]-\frac{7}{2} = -3.5[/tex]
Step-by-step explanation:
(b) Plug in x = 1 into the equation [tex]\:\:\frac{x+7}{x-2} = \frac{1+7}{1-2} = \frac{8}{-1} = -8[/tex]
(c) If f(x) = 2 then we get [tex]2 = \:\:\frac{x+7}{x-2}[/tex]
==> 2(x-2) = x + 7
==> 2x - 4 = x + 7
==> 2x - x = 7 +4 =11
==> x = 11
(d) Domain of f is all values of x -∞ < x < ∞ except at x = 2 since at x = 2 the denominator is 0 and division by zero is undefined; So we can say the domain is x < 2 or x >2
(e) To get the x-intercept set y = 0 and solve for x
We get (x+7)/(x-2) = 0
x+7 = (x-2)(0) = 0
x = -7 and the x intercept is at point (-7, 0)
(f) [tex]y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0[/tex]
Substitute for x = 0 to get y = (0+7)/(0-2) = -7/2
What is 22% of 150?
NEED FULL EXPLANATION pls
Answer:
Important note: "of" means to multiply!
22% of 150 is 33
Step-by-step explanation:
[tex]Y = P\% \times X\\Y = 22\% \times 150\\P = 22\%\div100 = 0.22\\Y = 0.22 \times 150\\Y = 33[/tex]
Hope this helps!
4. Jessica's cat eats 1 bags of food each week. How many whole bags of food does Jessica need
to buy to feed her cat for 42 days?
Answer:
Step-by-step explanation:
7 days= 1 week
42 days= 42/7 = 6 weeks
For 1 week 1 bag of food
For 6 weeks 6 bags of food
Which expression is the completely factored form of a³ +8y6 ?
O(x+2y²) (x² - 2xy² + 4y¹)
O (x+2y²) (x² + 4y¹)
○ (x+2y²) ³
O(x-2y²) (x² + 2xy² + 4y¹)
Step-by-step explanation:
[tex](a + 2 {y}^{2} )( {a}^{2} - 2a {y}^{2} + 4 {y}^{4} )[/tex]
Choose to use same variables next time to avoid confusions!!!!.
A side of the triangle below has been extended to form an exterior angle of 135°. Find
the value of x.
Using angle sum property for angles For, the given triangle, the value of x = 23°
What is the angle - sum property?The angle sum feature is a characteristic shared by all varieties of triangles. Triangles have an angle sum property of 180 degrees. This indicates that a triangle's internal angles add up to 180 degrees.
The angle 135 ,makes a linear pair with the line
So, the angle will be -
180 - 135
= 45°
Using angle - sum property,
x + 45 + 112 = 180
x + 157 = 180
x = 180 - 157
x = 23
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Solve y = ax² + c for x.
Answer:
[tex]x=\pm \sqrt{\frac{y-c}{a}}[/tex]
Step-by-step explanation:
[tex]y=ax^2 + c \\ \\ ax^2 =y-c \\ \\ x^2=\frac{y-c}{a} \\ \\ x=\pm \sqrt{\frac{y-c}{a}}[/tex]
Points A, B and C are collinear. Point B is between A and C. Suppose AB = x + 4 BC = 2x - 1, and AC = 4x - 7. Find x=, AB =, BC =, AC =
The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).
What are the values of a variable and the lengths of three line segments associated to it?
In accordance with geometry, three points are collinear if and only if these points lie on the same line. Then, the geometric system is represented by the following model:
AC = AB + BC
If we know that AB = x + 4, BC = 2 · x - 1 and AC = 4 · x - 7, then the value of x and the lengths of the line segments are, respectively:
4 · x - 7 = (x + 4) + (2 · x - 1)
4 · x - 7 = 3 · x + 3
x = 10
AB = 10 + 4
AB = 14
BC = 2 · 10 - 1
BC = 20 - 1
BC = 19
AC = 4 · 10 - 7
AC = 40 - 7
AC = 33
The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).
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Sam chose to buy the BLT bond rather than the stock. Based on Sam's purpose for making the investment, which
sentence provides a valid reason for his investment decision?
o Sam wants an investment that offers capital gains.
o Sam wants a steady income from his investment.
o Sam wants an investment that he can quickly sell to raise cash.
o Sam wants an investment that offers a higher return than stocks.
Correct answer is D. The statement that shows Sam's purpose for making the investment, is; Sam wants an investment that offers a higher return than stocks.
Sam desires an investment that delivers a larger return than stocks, which is the phrase that best demonstrates his motivation for making the investment.
What do bonds do?Bonds are a sort of investment that may be held for a time in the hopes of earning returns, as is common knowledge. The two most popular forms of investments traded on the stock market are bonds and stocks. Buyers just hold them in the belief that they will generate returns.
Bonds, however, are often safer investments than stocks. In actuality, stocks are a type of investment that is excessively volatile.
Sam desires an investment that delivers a larger return than stocks, which is the phrase that best describes his motivation for making the investment.
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Answer:
Sam wants a steady income from his investment.
Step-by-step explanation:
Got it right on edmentum
Given the functions:
f (x) = x³ + 8x
g(x)=√2x
h(x) = 4x+5
Evaluate the function (hf)(x) for x=3. Write your answer in exact simplified form. Select "Undefined" if applicable.
Answer:
h(x=8x)2x
dhhdndjeibdhxhdhsjzujdhdhxhdhhxbdnsj djjdndbzhhx
The album received the following ratings on a 1-to-10 scale from 10 music critics. What is the meaning of the ratings? 9.6, 9.8, 7.2, 6.4, 10.0, 8.9, 5.0, 9.8, 9.4, 6.8
The rating shows the quality and performance of the album.
What is the rating?A review or assessment of something in terms of quality, quantity, or a mix of the two is called a rating. A rating is something that indicates the performance or quality of anything. If the rating is higher then it is superior and if it is lower then it is poorer.
Given ratings are 9.6, 9.8, 7.2, 6.4, 10.0, 8.9, 5.0, 9.8, 9.4, 6.8. In the given ratings the highest rating is 10 which means that it is of superior quality and the lowest rating is 5 which means that the quality is poorer.
Therefore, the rating shows the quality and performance of the album.
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Find the length of the missing side. Leave your answer in simplest radical form.
Given the length of the perpendicular height and base length, the hypotenuse of the right triangle is 2√74 ft.
Hence option a)2√74 ft is the correct answer.
What is the length of the missing side?The Pythagoras theorem can be expressed as;
c = √( a² + b² )
Where c is hypotenuse, a and b are the other two sides of the right triangle.
Given the data in the image;
Length leg 1 of the right triangle a = 14ftLength leg 2 of the right triangle b = 10ftLength of hypotenuse c = ?Plug the given values into the above equation and solve for the hypotenuse 'c'.
c = √( a² + b² )
c = √( (14)² + (10)² )
c = √( 196 + 100 )
c = √( 296 )
296 can be written as 4 × 74, and 4 can further be written as 2²
Hence
c = √( 2² × 74 )
c = 2√74 ft
Given the length of the perpendicular height and base length, the hypotenuse of the right triangle is 2√74 ft.
Hence option a)2√74 ft is the correct answer.
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The product of two consecutive off integers is equal to 27 plus six times the sum of the integers . What is the largest integer?
Answer:
15
Step-by-step explanation:
x(x + 2) = 27 + 6(x + x + 2)
x^2 + 2x = 27 + 6(2x + 2)
x^2 + 2x = 27 + 12x + 12
x^2 + 2x - 12x - 12 - 27 = 0
x^2 -10x - 39 = 0
(x + 3)(x - 13) = 0
x + 3 = 0
x = -3 (extraneous solution)
x - 13 = 0
x = 13
x + 2 = 15
Taxpayers with an office in their home may deduct a percentage of their home-related expenses. This percentage is based on the ratio of the office's area to the area of the home. A taxpayer with a 2400-square-foot home maintains a 20-foot by 11-foot office. If the yearly electricity bills for the home come to $4500, how much of this is deductible?
$698.18 of his electricity is deductible
What is percentage ?A ratio or figure stated as a fraction of 100 is called a percentage. Although "pct," "pct," and occasionally "pc" are also used as acronyms, the percent symbol, "%," is most usually used to denote it. A % lacks dimensions and has no associated unit of measurement.
Given that : A taxpayer with a 2400 – square –foot home maintains a 20 – foot by 11- foot office . How much of the $4500 in annual electricity costs for the house is deductible?
Based on the ratio of the office's area to the home's area, this percentage was calculated.
A taxpayer keeps a 20 feet by 16 feet office in their 2200 square foot house.
How much of the $4800 in annual electricity costs for the house is deductible?
deduction =[tex]\frac{office area}{total area}total electric bill[/tex]
d = [tex]\frac{20.16}{2200}4800[/tex]
d = [tex]\frac{320}{2200}4800[/tex]
His electricity costs are deductible at d = $698.18
To learn more about $698.18 of his electricity is deductible
What is percentage ?A percentage is a number or ratio expressed as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as acronyms, the percent symbol, "%," is most usually used to denote it. A % lacks dimensions and has no associated unit of measurement.
Given that : A taxpayer with a 2400 – square –foot home maintains a 20 – foot by 11- foot office . How much of the $4500 in annual electricity costs for the house is deductible?
Based on the ratio of the office's area to the home's area, this percentage was calculated.
A taxpayer keeps a 20 feet by 16 feet office in their 2200 square foot house.
How much of the $4800 in annual electricity costs for the house is deductible?
deduction =[tex]\frac{office area}{total area}total electric bill[/tex]
d = [tex]\frac{20.16}{2200}4800[/tex]
d = [tex]\frac{320}{2200}4800[/tex]
His electricity costs are deductible at d = $698.18
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Answer gets brainliest PLS HELP!!
Based on the number of days that the health inspector and the fire inspector visits, the table for their next 4 visits is:
Number of visits Health Inspector visits Fire inspector visits
1 7 12
2 14 24
3 21 36
4 28 48
The number of days till both inspectors visit on the same day is 84 days.
What day will both inspectors visit?The model that would be best to use and solve the problem of the number of days till both inspectors visit is the Lowest Common Multiple.
This shows the number of days till both inspectors would visit based on their visiting interval.
The lowest common multiple of 7 and 12 is 84 which means that the health and fire inspectors would visit after 84 days on the same day.
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hello i need helpfffafafafa
Answer:2 x^2 + 7 x + 15
Step-by-step explanation:
Answer:
-2x^2-7x-5 or -(x+1)(2x+5)
Step-by-step explanation:
We combine -2x and 5x which becomes a -5x equaling to -7x
And then we add -10 and 5 to get -5.
which of the following numbers is best represented by point N? PLS HELP ME :( its my last question SAM HELP! PLSSSSS
Answer:
6.47
Step-by-step explanation:
all you have to so is count the number of black lines between 6.4 and 6.5. since there are 7, you add 0.07 to 6.4
6.4
+0.07
---------
6.47
A movie theater runs its films continuously. One movie runs for 70 minutes and a second runs for 105 minutes. The theater has a 15-minute intermission after each movie, at which point the movie is shown again. If both movies start at noon, when will the two movies start again at the same time?
Answer:
10:30 On the Next day
Step-by-step explanation:
This Is a Answer
HELP ME IM DESPERATE!!!!!!!!!!!What is the vector that results from transforming a⃗ by the transformation matrix?
Enter your answer by filling in the boxes.
Answer:
the vector is 24 OVER 67
Step-by-step explanation:
and never the less the vector is the number u Will have total of 67 and 24
