There are four basic properties of logarithms. The solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex].
What are the Properties of logarithms?There are four basic properties of logarithms:
[tex]\rm log_aU+ log_aV = log_a(UV)\\\\\rm log_aU - log_aV = log_a(\dfrac{U}{V})\\\\\rm log_aU^n = n\ log_aU\\\\\rm log_ab = \dfrac{log_xb}{log_xa}[/tex]
The given logarithmic problem can be solved in the following manner,
[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex]
By using the division law of logarithm, [tex]\rm log_a(\dfrac{x}{y}) = log_ax - log_ay[/tex]
[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5} = log_{12}\ {x^4\sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]
By addition law of Logarithm, [tex]\rm log_a(xy)= log_ax+ log_ay[/tex]
[tex]\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]
Using the logarithmic Property, [tex]\rm log\ a^m =mlog\ a[/tex]
[tex]=\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}\\\\=log_{12}\ x^4+ log_{12} (x^3-2)^{\frac12}-log_{12}{(x+1)^5\\\\[/tex]
[tex]=4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]
Hence, the solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]
Learn more about Logarithms:
https://brainly.com/question/7302008
Which number is a solution of 5m < 6m + 6? a. -8 b. -7 c. -6 d. -5
5m < 6m + 6
5m - 6m < 6
- m < 6
x > - 6
- 5 is ok
check
5 * (-5) = - 25
6 * (-5) + 6 = - 24
and - 25 < - 24 is correct
Key Features of Graphs of Functions - Part 1
1. The following statement is false. Highlight the two words that should be
interchanged to make it a true statement.
In a function, every output value corresponds to exactly one input
value.
2 The following graph fails the vertical line test and is not a function.
у
X
leg
Part A Explain how the vertical line test shows that this relation is NOT a
function. Because it has 2 lines interseding
Bart B: Name two points on the graph that show that this relation is NOT a
function. The reason its not a function is because
Answer:
See below
Step-by-step explanation:
Q1.
In a function, every output value corresponds to exactly one inputvalue.
The words to be interchanged are underlined. The function as per definition has exactly one output for each input.
Q2.
Part A
Because it has 2 same input value for 2 different output valuesPart B
The two points are (4, -2) and (4, 2)Answer:
below
Step-by-step explanation:
Question 1:
In a function, every output value corresponds to exactly one input value.
The words that should be switched around are "output" and "input". This is because every input should have have only ONE output.
Question 2:
The following graph fails the vertical line test and is not a function. (YES)
Using the vertical line test to test whether the vertical line passes through the graphed function more then once. If it does, its not a function. If it doesn't, it is a function. Sadly, the vertical lines pass the point on two separate occasions which makes it not a function.
The vertical line shows gives the points (4, 2) and (4, -2).
Best of Luck!
IS THIS RIGHT PLZZ HELP ME !!
Answer:
The answer would be D.
Step-by-step explanation:
The answer would be D since 3 and -3 are opposite numbers (they are the same distance in units away from 0) and they add up to 0.
Hope this helps :)
Answer: The correct answer is D
Step-by-step explanation:
It’s D because -3 and 3 equal 0.
How many 1 / 4 pound hamburgers can be made from 9 / 12 pound of meat?
More questions to come
Answer: Hi
Step-by-step explanation:
Due to festive season, the price of air tickets increased by 15%. If the price of one ticket was $575 during the festive season, what was its price before the festive season?
answer fast
The price before the festive season is $488.75
Data;
percentage increase = 15%ticket price = $575The Price before the festive seasonTo calculate the price before the festive season, we simply need to subtract 15% from $575.
[tex]\frac{15}{100} = \frac{x}{575} \\x = 86.25[/tex]
The increase in the ticket is $86.25., Let's calculate the price before the festive season.
[tex]$575 - 86.25 = 488.75[/tex]
The price before the festive season is $488.75
Learn more on percentage here;
https://brainly.com/question/25545513
#SPJ1
Plz i need help urgently I’ll mark brainiest the sum of a number, two thirds of the number and a quarter number of the number gives 5 3/4, find the number
Step-by-step explanation:
so you have to make an equation where you let x=the number, so it would be
x+(2/3)x+(1/4)x=5 3/4
you combine the like terms to get
(23/12)x = 5 3/4
multiply both sides by the reciprocal of 23/12 to isolate x, and you're left with
x=36/92, which simplifies to 9/23.
Eight more than the quotient of a number and 6 equals 3.
Hey there!
First of all, the quotient of a number and 6 means you divide that number by 6.
Let the number be x.
Then, eight more means you add 8:
8+(6÷x)=3
That's the answer.
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
In a school 3/5 of children are boys and the number of girls is 2000. Find the number of boys.
300
3000
400
4000
Answer:
3000
Step-by-step explanation:
Answer:
the answer is 3000
Step-by-step explanation:
5000 -2000=3000
How do u do this pls someone help me I’ve failed math for 3 quarters straight
Answer:
1. 84in³
2. 180cm³
3. 600ft³
4. 360cm³
5. 312cm³
6. 15.6kg
7. 1.95kg
Step-by-step explanation:
1: V = Bh = (7x3)x4 = 84in³
2: V = Bh = 1/2(8x5) x 9
= 20 x 9
= 180cm³
3: V = Bh = 1/2(b1+b2) h x 5
= 1/2(20+10) 8 x 5
= 15 x 8 x 5
= 15 x 40
= 600ft³
4: V = Bh = 1/2 (4x9) x 20
= 18 x 20
= 360cm³
5: Total volume = Volume of rectangular prism + Volume of triangular block
= (8.5 x 4 x 9) + 1/2(1.5 x 2) x 4
= 306 + 6
= 312cm³
6: divide 312cm³ by 20kg/cm³ to get the approx. mass:
312/20 = 15.6kg
7: first find the volume of the friends Display:
= (4.25 x 2 x 4.5) + 1/2(0.75 x 1) x 2
= 38.25 + 0.75
= 39cm³
Now divide by 20 to find the approx. weight of the friends display:
39/20 = 1.95kg
Have a nice day! :)
a circle with radius of 5cm sits inside a 11cm×11cm rectangle
Answer:
The area of the shaded region is
Step-by-step explanation:
Solve the inequality. 5+5(-7x+ 1) ≥ -130 write answer in the format variable inequality number
Answer:
x<_ 4
Step-by-step explanation:
first you distribute 5 to equal 5-35x+5 then you would carry the non variables to one side to be -35x>_-140 and the you would flip the sides because te variable is negative so it would be -35x<_ -140 the divid to get x<_4
At book fair, the ratio of adults to children is 7 : 3
The ratio of girls to boys at the book fair is 4 : 1
What percentage of the people at the book fair are boys?
The percentage of the boys at the book fair is 6%
What is a percentage?Percentages are used in mathematics as a decimal ratio expressed in a fraction of 100. It is represented with a symbol known as %.
At a book fair, the ratio of adults to children are:
7 : 3
The total number of people at the book fair = 7 + 3 = 10
The percentage of adults are:
[tex]\mathbf{=\dfrac{7}{10}\times 100\%}[/tex]
= 70% are adults
The percentage of children are:
[tex]\mathbf{=\dfrac{3}{10}\times 100\%}[/tex]
= 30% are children
However, if from the children, 4 are girls and 1 is a boy.
The total number of children at the fair = 4 + 1 = 5
The percentage of girls are:
[tex]\mathbf{=\dfrac{4}{5} \times 30\%}[/tex]
= 24%
The percentage of boys at the book fair is:
[tex]\mathbf{=\dfrac{1}{5} \times 30\%}[/tex]
= 6%
Learn more about percentages here:
https://brainly.com/question/24304697
What is the value of [3(−2)−7]÷(1.5+0.5)?
Answer: -13/2
Step-by-step explanation: hope this helps plz mark as brainliest:)
Is 2 greater than 2.5?
Answer:
2.5 means “two and five tenths”, or 2+5/10 . Adding two positive numbers together will make a number that’s larger than either of those two numbers, so 2.5 is greater than 2.
Step-by-step explanation:
2.5 is greater than 2.
Hopefully this helps you!
-Keira
I need help.. >w<
Which answer choice shows 36.95 written in expanded form?
O A) 3 + 6 + 9 + 5
OB) 30 + 6 + 0.9 + 0.5
OC) 30 + 6 + 0.9 + 0.05
OD) 30 + 6 + 0.9 + 0.005
Answer:
O C)30+6+0.6+0.05 hope this helps
Answer:
C) 30 + 6 + 0.9 + 0.05
Step-by-step explanation:
30. 0.9. 36
+6. +0.05. +00.95
---------. -------------. ---------------
36. 0.95. 36.95
----------. --------------. --------------
36+0.95=36.95
Solve the equation and enter the value of x below.
7x + (-2) = -44
X =
7x - 2 = - 44
7x - 2 + 2 = - 44 + 2
7x = - 42
x = -42/7
x = -6
check
7 * (-6) + (-2) = - 42 - 2 = - 44
Answer:
7x+ (-2)=-44
x= -6
Step-by-step explanation:
you're welcome
A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected Each person's weight is recorded before starting the diet and one year after it is concluded. Based on the data shown at right (weight in pounds), Can we conclude that the diet has a long-term effect, that is, that dieters manage to not regain the weight they lose? Include appropriate statistical evidence to justify your answer.
BEFORE
158 185 176 172 164 234 258 200 228 246 198 221 236 255 231
AFTER
163 182 188 150 161 220 235 191 228 237 209 220 222 268 234
Using the t-distribution, as we have the standard deviation for the sample, it is found that it cannot be concluded that the diet has a long-term effect.
What are the hypotheses tested?At the null hypotheses, it is tested if there is no difference in the weights, that is:
[tex]H_0: \mu_A - \mu_B = 0[/tex]
At the alternative hypotheses, it is tested if the weights decrease, that is:
[tex]H_1: \mu_A - \mu_B < 0[/tex]
What is the mean and the standard deviation of the distribution of the difference?Using a calculator, for each sample, we have that:
[tex]\mu_B = 210.8, s_B = 33.85, sE_B = \frac{33.85}{\sqrt{15}} = 8.74[/tex]
[tex]\mu_A = 207.2, s_A = 33.47, sE_A = \frac{33.47}{\sqrt{15}} = 8.64[/tex]
Hence, for the distribution of differences, we have that:
[tex]\overline{x} = \mu_A - \mu_B = 207.2 - 210.8 = -3.6[/tex]
[tex]s = \sqrt{sE_B^2 + sE_A^2} = \sqrt{8.74^2 + 8.64^2} = 12.3[/tex]
What is the test statistic?It is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Then:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{-3.6 - 0}{12.3}[/tex]
[tex]t = -0.29[/tex]
What is the decision?Considering a left-tailed test, as we are testing if the mean is less than a value, with a standard significance level of 0.05 and 15 + 15 - 2 = 28 df, the critical value is of [tex]t^{\ast} = -1.7[/tex].
Since the test statistic is greater than the critical value for the left tailed test, it cannot be concluded that the diet has a long-term effect, as the null hypothesis is not rejected.
To learn more about the t-distribution, you can check https://brainly.com/question/13873630
triangle JKL has vertices J(3,-7) K(7,-3) and L(3,6) What are the cordinates of point J after a 270° rotation counterclockwise about the orgin?
Answer:
(-7, -3)
Step-by-step explanation:
270° counterclockwise rotation is the same as a 90° clockwise rotationIf the point J (3, -7) is rotated 90° clockwise, ⇒ Point J' = (-7, -3)Could you show how to Graph X>2?
Answer:
I hope this helps!
what does x equal in the equation [tex]\frac{3}{5}x- \frac{1}{4}x=7\\[/tex]
Answer:
[tex] x = 20 [/tex]
Step-by-step explanation:
[tex] \frac{3}{5}x - \frac{1}{4}x = 7 [/tex]
The LCD is 20, so multiply both sides of the equation by 20.
[tex] 20(\frac{3}{5}x - \frac{1}{4}x) = 20 \times 7 [/tex]
[tex] 4 \times 3x - 5 \times x = 140 [/tex]
[tex] 12x - 5x = 140 [/tex]
[tex] 7x = 140 [/tex]
[tex] x = 20 [/tex]
Write an equation in Slope-Intercept Form of the line that is perpendicular to the graph of the given equation
and passes through the given point.
y= 4x + 8
(4,2)
Answer:
-1/4x
Step-by-step explanation:
A geometry test has 30 questions. 6 of the 30 questions are based on chapter 5. What is the ratio of questions from chapter 5 to the other questions on the test?
Answer:
total question = 30
question from ch 5 = 6
remaining questions = 30-6 = 24
ratio = 6 : 24 = 1 : 4 answer
Plzz answer I will give you brainliest and 17 points
°F represents the
The temperature was 13° F. It dropped so that the temperature was o°F
change in temperature,
°F represents the change in temperature.
Write as a fraction
Step-by-step explanation:
it dropped to Celsius degree
(X+1)²+(x+1)(5x-3) factoriser
Answer:
Step-by-step explanation:
(x +1)² + (x +1)(5x - 3) = (x +1)(x+1) + (x +1)(5x - 3)
(x +10 is the common term. SO, we can take out (x+1)
=(x +1) [ x + 1 + 5x - 3]
=(x + 1) (x + 5x + 1 - 3) {Combine like terms}
= (x +1)(6x -2)
What is the slope of the equation y= 5/4 times -7/4
Answer:
5/4
Step-by-step explanation:
If the equation is
[tex] y = \dfrac{5}{4}x - \dfrac{7}{4} [/tex]
then the slope is the number multiplying x, so
slope = 5/4.
Answer:
5/4.
The x is a variable, not a multiplication sign.
The equation is
y=mx+b
the slope is the m.
ASAP NO LINKS SOLVE 2 QUESTIONS PLEASE
71. If March of a certain year has 5 Sundays, on what days of the week could St. Patrick's
Day fall? (St. Patrick's Day is March 17")
73. how many positive integers less than 1000 have the sum of the digits equal to four?
71 = When Is St. Patrick’s Day?
St. Patrick’s Day is officially observed on March 17 each year, though celebrations may not be limited to this date. The significance of March 17 is that it’s said to be the date of St. Patrick’s death in the late 5th century (circa A.D. 493).
St. Patrick’s Day Dates
Year St. Patrick’s Day
2021 Wednesday, March 17
2022 Thursday, March 17
2023 Friday, March 17
2024 Sunday*, March 17
73 = 28
Joanna and Kyle went to store. Joanna bought 2 erasers and 5 pens which altogether cost $17. Kyle
bought 4 erasers and 2 pens which he paid $10 for. Calculate the cost of one eraser and the cost of one
pen.
Answer: 2x + 3= 9
Step-by-step explanation: hope it's correct well your welcome
Answer:
Erasers are $1 and pens are $3
Step-by-step explanation:
2x+5y=17
4x+2y=10
y=5-2x
2x+5(5-2x)=17
2x+25-10x=17
8x=8
x=1
plug x in and get 3 for Y
if the square root of the natural number from 1 to 200 are calculated, the number of whole number will be
Answer:
first 15 no. only 1,2,3,4,5,6,7,8,9,10,11,12,13,14.
This is geometry, I need help! Please and thanks!!
Problem 8
Answer: angle LSO and angle MSN
--------------
Explanation:
Vertical angles form when we intersect two line segments, lines, or rays. Vertical angles are opposite one another and they are always congruent.
=============================================
Problem 9
Answer: angle LMS and angle SMN
--------------
Explanation:
Adjacent angles share a common line, line segment, or ray. Think of two adjacent rooms sharing a common wall between them. In the case of the answer above, the two angles share the common segment SM (note how S and M are part of LMS and SMN)
When it comes to naming angles, the middle letter is always the vertex of the angle. This is the hinge so to speak. Or you could picture a pair of scissors. For angle LMS, the arms LM and SM are the two blades of the scissors while point M is where the blades meet.
=============================================
Problem 10
Answer: angle LSM and angle MSN
--------------
Explanation:
Same idea as problem 9. Now we're making S the middle letter. Something like angle LSM is the same as angle MSL.
In this case, the two adjacent angles form a straight line. We consider these two angles a linear pair.
=============================================
Problem 11
Answer: angle LSO and angle OSN
--------------
Explanation:
The term linear pair was discussed back in problem 10. So you could list those two angles again, or you could go with another pair as shown above. All that matters is that they are adjacent angles and they are supplementary angles (they add to 180 degrees). There are many possible answers.
Something like the angle pair angle LOS and angle NOS are adjacent angles, but they aren't supplementary. So we don't meet the condition of a linear pair here.