Expand the logarithm fully using the properties of logs. Express the final answer interms of log a, and log y.
Answers
To solve this problem, we will use these rules
[tex]\begin{gathered} \log ab=\log a+\log b\rightarrow(1) \\ \log a^n=n\log a\rightarrow(2) \end{gathered}[/tex]The given expression is
[tex]\log x^5y[/tex]By using rule (1)
[tex]\log x^5y=\log x^5+\log y[/tex]Use the rule (2) with log x^5
[tex]\log x^5=5\log x[/tex]Then the last answer is
[tex]\log x^5y=5\log x+\log y[/tex]The answer is 5 log x + log y
Related Questions
Davis make 720 a week he has spent 217 what fraction of his week pay has he spent.
Answers
Answer:
217/720
Explanation:
• The amount Davis makes in a week = $720
,• The amount he has spent = $217
,•
To determine the fraction of his week's pay that he has spent, divide the amount spent by the amount he makes weekly. That is:
[tex]\frac{217}{720}[/tex]Davis has spent 217/720 of his week's pay.
Jasmine is packing her bag for a four-day music festival. The weather forecast for each of the days states that the probability of rain is a constant value of 30%. Find the probability that it will rain on at least two of the four days.
Answers
The probability that it will rain for a particular day is 30 % .
Calculating the individual probabilities ,
[tex]\begin{gathered} P(\text{ two days ) = }2\text{ }\times\text{ 30 = 60 \%} \\ \text{ } \\ \end{gathered}[/tex]The required probability is calculated as ,
[tex]\text{Required probability = }\frac{60\text{ }}{100}\text{ = 0.60 }[/tex]Thus the probability that it rains for atleast 2 days is 0.60 .
Find an equivalent expression without parentheses -(6-n)=
Answers
Given the expression;
[tex]-(6-n)[/tex]Step 1: We multiply the expression in the parentheses by -1, we have;
[tex]\begin{gathered} =-1(6)-1(-n)_{} \\ =-6+n \end{gathered}[/tex]Hence, -(6-n)= -6+n
what is the answer to 13 /5/6 - 17 /3/8
Answers
When the fractions, 13 5/6 and 17 3/8 are subtracted, the answer would be -3 ⁵ / ₁₂
How to subtract mixed fractions?To subtract mixed fractions, the first thing to do is to convert the mixed fraction to an improper fraction.
To convert improper fractions, multiply the denominator by the whole number and then add the numerator. The result would be the numerator.
Converting the fractions gives:
13 5/6 = 83 / 6
17 3/8 = 139 / 8
Subtracting these fractions then gives:
= 83 / 6 - 139 / 8
Find a common denominator for 6 and 8 which will be 24 as this is their lowest common multiple.
Then, divide 24 by the denominator and multiply the result by the numerator of the fraction:
= 332 / 24 - 417 / 24
= -85 / 24
= - 3¹⁰ /₂₄
= -3 ⁵ / ₁₂
In conclusion, the answer would be -3 ⁵ / ₁₂
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According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=-4x^6 - 3x^5+2x² - 4x +1? Drag the choices to the boxes to correctly complete the table.
Answers
[tex] -4x^6 - 3x^5+2x^2 - 4x +1 = 0[/tex] has 1 or 3 Positive roots and one only Negative roots.
Descartes' rule of sign.Function has the same number of positive real zeroes as there are number of changes in the sign of the coefficients, or an even number less than the found number.
Now, here the given expression is : p(x) = [tex] -4x^6 - 3x^5+2x^2 - 4x +1 [/tex]
Now here, the number of sign changes are:
First : + to - in [tex] - 3x^5 => + 2x^2 [/tex]
Second : - to + in [tex]+2x² => - 4x [/tex]
Third: + to - in [tex] - 4x => +1 [/tex]
So, the total sign changes = 3
⇒ The total positive roots of p(x) = 3 or a EVEN NUMBER LESS THAN 3 = 1.
So, p(x) has either 3 or 1 POSITIVE ROOTS.
⇒ The number of negative roots p(x) has is either 4 or 6.
Hence has 1 or 3 Positive roots.
Now I look at f (−x). That is, having changed the sign on x, I'm now doing the negative-root case:
p(-x) = [tex] -4(-x)^6 - 3(-x)^5+2(-x)^2 - 4(-x) +1 [/tex]
= [tex] -4x^6 + 3x^5+2x^2 + 4x + 1 [/tex]
the number of sign changes are:
First : + to - in [tex] -4x^6 => +3x^5 [/tex]
So, the total sign changes = 1.
so there is exactly one negative root. (In this case, I don't try to count down by two's, because the first subtraction would give me a negative number.)
Hence has 1 or 3 Positive roots and one only Negative roots.
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. MODELING REAL LIFE You save $20 each week to
buy a smart watch that costs $229.95.
a. Describe the numbers of months you need to
save to buy the smart watch.
b. Your parents give you $50 to help you buy
the smart watch. How does this affect your
answer in part (a)? Use an inequality to justify
your answer.
Answers
After doing mathematical operations, we can conclude that it would take is 12 months to buy the smart-watch for $229.95 if we save $20 per month.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).A piece of cord 1.8 m long is cut evenly into smaller pieces of 0.05 m each. How many of these pieces can be cut?Number of pieces =
Answers
Solution:
We are given that :-
• A Piece of a cord = 1.8m long
,• need to cut into smaller pieces of 0.05m each
,• let ",n", be the number of smaller pieces to be cut
0.05 * n = 1.8
∴ n = 1.8/0.05
n = 36
• This means that 36 smaller pieces will be cut into 0.05m
equations with variables4w + 3 = 2w + 7
Answers
w = 2
Given 4w + 3 = 2w + 7
Collect like terms
4w - 2w = -3 + 7
2w = 4
Divide both sides by 2
2w/2 = 4/2
w = 2
please help this is for my study guide thanks! (btw it says simplify)
Answers
To simplify:
[tex](2b^2a)(4ba^2)[/tex]On simplification, we get
[tex]\begin{gathered} (2b^2a)(4ba^2)=8b^{2+1}a^{1+2} \\ =8b^3a^3 \end{gathered}[/tex]Hence, the answer is,
[tex]8b^3a^3[/tex]8. Multi-Step Willie bagged his potatoes
in 18 ten-pound bags, 16 five-pound bags,
and 4 twenty-five pound bags. He has
2 pounds of potatoes left over. How many
pounds of potatoes does Willie have?
Answers
The total pounds of the potatoes Willie have is 362 pounds.
What is defined as the term addition?Addition is a method of combining items and counting them as a single large group. In mathematics, addition is the method of integrating two or more numbers together. The numbers added are referred to as addends, and the result or final answer obtained after the method is referred to as the sum.For the given question.
Multi-Step Willie bagged his potatoes in -
18 ten-pound bags, 16 five-pound bags,4 twenty-five pound bags,2 extra pounds of potatoes.Thus, the total pounds of the potatoes are-
Total potatoes = 18×10 + 16×5 + 4×25 + 2
Total potatoes = 362
Thus, the total pounds of the potatoes Willie have is 362 pounds.
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Find the distance between the two points below. If your answer is not aninteger then type it as a decimal rounded to the nearest hundredth.(-4,1) and (3,-4)The distance between the two points is
Answers
The distance between two points is defined as follows:
[tex]d(a,b)=\sqrt[]{(x_2-x_1)^2-(y_2-y_1)^2}[/tex]Replacing the points in the equation:
[tex]\begin{gathered} a\to(-4,1) \\ b\to(3,-4) \\ d(a,b)=\sqrt[]{(3_{}-(-4))^2-(-4_{}-1_{})^2} \\ d(a,b)=\sqrt[]{(7)^2-(-5_{})^2} \\ d(a,b)=\sqrt[]{49-25} \\ d(a,b)=\sqrt[]{24} \\ d(a,b)=4.8989 \end{gathered}[/tex]The distance between the two points is 4.89 aprox 4.9
help me pleasee!!
thank you <3
Answers
And interval notation is [4.8, ♾)
The midpoint M of CD has coordinates (-2.5, 5.5). Point C has coordinates (4, 2). Find the
coordinates of point D.
Write the coordinates as decimals or integers.
D=(_____, _____)
Answers
could i have brainliest pls i'm trying to get to the next level?
The satang coin from Thailand has a radius of about 7 mm The diameter is mm The circumference in terms of his v mm 22 Using 7 for at the approximate value of the circumference is v mm Intro Donation. what is it
Answers
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
The values of the functions at x = 0 and x = 25/16 are f(0) = 0 and f(25/16) = 5/4
How to evaluate the function?The equation of the function is given as
f(x) = √x
The x values are given as
x = 0, 25/16
This means that
x = 0 and x = 25/16
Substitute x = 0 and x = 25/16 in the equation of the function
So, we have
When x = 0
f(0) = √0
Evaluate
f(0) = 0
When x = 25/16
f(25/16) = √25/16
Evaluate
f(25/16) = 5/4
Hence, the values are 0 and 5/4
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A walking trail is 3.8 miles long. If Gertrude walked the length of the walking trail 15 times, how many miles did Gertrude walk?
Answers
Explanation:
If Gertrude walked the length of the walking trail 15 times, it means that she walked 3.8 miles 15 times. Therefore to find the total distance we have to multiply the length by the times she walked the trail:
[tex]3.8\times15=57[/tex]Answer:
Gertrude walked 57 miles
Find the area. I'll add picture
Answers
The area of a triangle is represented below
[tex]\text{area}=\frac{1}{2}bh[/tex]where
b = base = 14 mm
h = height = 8.2 mm
[tex]\begin{gathered} area=\frac{1}{2}\times14\times8.2 \\ \text{area}=\frac{114.8}{2} \\ area=57.4mm^2 \end{gathered}[/tex]Does the table show a proportional relationship? If so, what is the value of y when x is 3/5?
Answers
There is a directly proportional relationship between "x" and "y" which is y=5x i.e., for every "x", value of "y" is "5x" hence the value of "y" if value of x=3/5 will be y = 3.
As per the question statement, we are supposed to find out a proportional relationship between "x" and "y" and also find the value of "y" when x=3/5.
After observing the given data, we conclude that y = 5x i.e., for every value of "x", value of "y" is "5x".
So we derive a formula y = 5x and the proportionality constant is 5
Now when x = 3/5
Then by the formula, y = 5x,
y = 5*(3/5)
y = 3
Hence, there is a directly proportional relationship between "x" and "y" which is y=5x i.e., for every "x", value of "y" is "5x" hence the value of "y" if value of x=3/5 will be y = 3.
Direct Proportionality. When two values are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage.To learn more about direct and inverse proportionality, click on the link given below:
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Which tree diagram shows the possible outcomes of choosing either black or gray shorts and a blue,green,white, or red T-shirt
Answers
The second option is the correct answer
Outcome can be
Point H(-7, 5) is rotated 270° clockwise to create H a.write a rule for transformation. B.give thelocation of each.
Answers
The image of the point after the rotation is (-5, 7)
What is a 270 degrees rotation?A 270 degrees rotation is a rotation that has the same effect as the 90 degrees counterclockwise of a figure.
How to determine the image of the rotation?The coordinate of the point is given as
H = (-7, 5)
The rotation is given as 270° clockwise
As mentioned above,
The algebraic rule of its rotation to be changed from (x, y) to (-y, x) i.e. (x, y) => (-y, x)
So, we have
(x, y) => (-y, x)
Substitute (-7, 5) in (x, y) => (-y, x)
So, we have
(-7, 5) => (-5, 7)
Rewrite as
H' =(-5, 7)
Hence, the coordinates of the image using the rotation rule is (-5, 7)
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x² + 8x + 17, x ≤ -5X+4,x>-52B) Does not exist.5) lim f(x), f(x) =x->-5
Answers
Evaluate each limit separately:
[tex]\begin{gathered} \lim_{x\to-5}x^2+8x+17 \\ \\ \lim_{x\to-5}(-5)^2+8(-5)+17=25-40+17=2 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \lim_{x\to-5}-\frac{x}{2}+4 \\ \\ \lim_{x\to-5}-\frac{-5}{2}+4=\frac{5}{2}+4=\frac{5+8}{2}=\frac{13}{2}=6.5 \end{gathered}[/tex]As the one-sides limits are different, the limit doesn't existAnswer: Does not exist.What is 3/8 x 3/8 x 3/8 written as a power
Answers
Answer:
3/8^3
Step-by-step explanation:
its like 1/2 x 1/2 x1/2 its 1/2^3
or 7x7x7x7x7=7^5 its the same concept....
While shopping at his local home improvement store, Chen notices that the directions for an extension ladder state, “This ladder is most stable when usedat a 75° angle with the ground." He wants to buy a ladder that will reach a height of 26 feet to paint a two-story house. How long does his ladder need tobe? Draw a diagram and set up an equation for this situation. Show all work.
Answers
hello
to solve this question, we need to draw a diagram to illustrate their positions
to solve this question, we can simply use trigonometric ratio
SOHCAHTOA
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp} \\ \cos \theta=\frac{adj}{hyp} \\ \tan \theta=\frac{opp}{adj} \end{gathered}[/tex]from this, we can use the sine angle to solve this since the parameters of interests are hypothenus, opposite and angle
[tex]\begin{gathered} \theta=75 \\ \text{hpy}=x \\ \text{opp}=26 \end{gathered}[/tex][tex]\begin{gathered} \sin 75=\frac{26}{x} \\ x=\frac{26}{\sin 75} \\ x=26.917\text{feet} \end{gathered}[/tex]from the calculations above, the length of the ladder is 26.91 feet
d 2 6.28 3 9.42 5 15.7 What is the constant of proportionality? Type your answer below as a number texample: 5.3.1. + H2. or 3/2):
Answers
Ok,we can calculate the constant of proportionality as the slope of a line
with this equation
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) is a point to the right compared to (x1, y1)
for this case I will choose the points (2,6.28) and (3,9.42)
where (3,9.42) is (x2,y2)
[tex]\begin{gathered} m=\frac{9.42-6.28}{3-2} \\ m=\frac{3.14}{1} \\ m=3.14 \end{gathered}[/tex]if we want a more exact number we can divide one number by another
[tex]\begin{gathered} \frac{6.28}{2}=3.14 \\ \frac{9.42}{3}=3.14 \\ \\ \frac{15.7}{5}=3.14 \end{gathered}[/tex]so the correct constant of proportionality is 3.14
Suppose f(x) represents the amount of money in a bank account after x weeks.If you want to represent the amount of money in a bank after 7 weeks, what should you write instead of f(x)?
Answers
Since f(x) represents the amount of money in a bank account after x weeks and we want to know the money after 7 weeks we need to plug x=7 in the function, that is we need to write f(7).
6 more than the quotient of a number and five is eight use the variable B for the unknown number
Answers
Let B the unknown number.
The quotient of this number and five can be express as:
[tex]\frac{B}{5}[/tex]Six more than the quotient of a number and five can be express as:
[tex]\frac{B}{5}+6[/tex]Finally we know that this is equal to eight, then we have the equation:
[tex]\frac{B}{5}+6=8[/tex]Solving for B we have that:
[tex]\begin{gathered} \frac{B}{5}+6=8 \\ \frac{B}{5}=8-6 \\ \frac{B}{5}=2 \\ B=5\cdot2 \\ B=10 \end{gathered}[/tex]Therefore the unknown number is 10
Please answer question 11, 12, And 13 there different word problems.
Answers
radius= 12 meters
Explanation
11)the area of the sector is given by:
[tex]A=\frac{5}{18}\pi r^2[/tex]
where r is the radius ( in meters)
then
Step 1
Let
[tex]\begin{gathered} \text{radius}=r \\ \text{Area}=\text{ A=}40\pi(m^2) \end{gathered}[/tex]
now replace and solve for r
[tex]\begin{gathered} A=\frac{5}{18}\pi r^2 \\ 40\pi=\frac{5}{18}\pi r^2 \\ \text{the }\pi\in\text{ both sides is eliminated,so} \\ 40=\frac{5}{18}r^2 \\ \text{now,multiply both sides by 18/5} \\ 40\cdot\frac{18}{5}=\frac{5}{18}r^2\cdot\frac{18}{5} \\ 144=r^2 \\ \text{square root in both sides} \\ \sqrt{144}=\sqrt{r^2} \\ 12=r \end{gathered}[/tex]therefore, the answer is
radius= 12 meters
I hope this helps you
A sweater is on sale at the mall for 75% off the original price of $38.00. What is the new price of the sweater?
Answers
We have:
Original price = $38.00
Off = 75% = 0.75
Then:
[tex]0.75\times38.00=28.5[/tex]So, the new price of the sweater is:
[tex]38.00-28.5=9.5[/tex]Answer: $9.5
A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze, and the second brand is 55% pure antifreeze. In order to obtain 60 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answers
36 gallons of the 55% brand and 24 gallons of the 30% brand of antifreeze must be used.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Let x denote the amount of 30% pure antifreeze required in the combination.
The quantity of the 55% brand is then calculated (60-x).
The pure antifreeze content of the combination as:
⇒ 0.30x +0.30(60 -x) = 0.45 (60)
When we subtract 0.30(60), we get
x(0.55 -0.30) = 60(0.45 -0.30)
To simplify, divide by the coefficient
x = 9/0.25 = 36 .
Therefore, 36 gallons of the 55% brand and 24 gallons of the 30% brand of antifreeze must be used.
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A 12-in.-long steel cable weighs 0.428 lb.How much does an 11.4-ft-long cableweigh?
Answers
4.8792 lb
1)Since a 12 inch weighs 0.428 lb
2) We need to convert a 11.4 ft to lb
1 ft -----12 inches
11.4 -----x
x=136.8 inches
3) If a 12 inches long steel weighs 0.428 lb, let's calculate the weight of 136.8 inches cable
12 inches -----------------0 .428 lb
136.8 inches ------- y
12y =0.428 x 136.8
12y =58.5504
y=4.8792 lb
