The logarithmic function log ( x³ y² ) when expressed in terms of log x and log y is 3 log ( x ) + 2 log( y).
The opposite of exponentiation is the logarithm. In other words, the exponent to which a fixed number, the base a, must be raised in order to create a specific number x, is represented by the logarithm of that number.
Consider the logarithmic function log x³ y⁴
Using the logarithmic formula,
log ( a b ) = log (a) + log (b)
We have,
log( x³ y² ) = log ( x³ ) + log( y² )
By applying the logarithmic property:
log ( xⁿ ) = n log x
We have,
log x³ y² = log ( x³ ) + log( y² )
log x³ y² = 3 log ( x ) + 2 log( y)
Therefore, the function log ( x³ y² ) in terms of log x and log y is 3 log ( x ) + 2 log( y).
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Find the charge Q that requires 96J of energy to be moved through a potential difference of 16V ?
6 Coulombs are needed to produce the 96J of energy.
Describe energy.Physics defines energy as the quantity of work or capability that may be applied to a thing to make it functional. Additionally, it refers to the capacity to exert force on an object as well as energy that is neither generated nor destroyed.
96 J of energy and a 16 V potential difference
Using the following formula, the work or energy is:
Work completed equals Charge x Potential Difference.
Charge = thus work completed/potential difference
Charge equals 96/16, or 6 Coulombs.
Therefore, 6 Coulombs of charged are needed to produce 96J of energy.
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Need help with this question! Need help with showing work.
You use a juice mix to make orange juice.
You combine 12 ounces of the mix with 36 ounces of water.
Answer:
48
Step-by-step explanaause tion:
because there are 12 ounces in orange juce and 36 ounces of water combime them together 48
Three-fourths of a box of chocolate is left over. Benjamin eats 2/3 of the leftover chocolate. What fraction of a box does Benjamin eat?
We will have that he ate the following amount:
So, he ate the following:
[tex]x=(\frac{3}{4})(\frac{3}{4})\Rightarrow x=\frac{1}{2}[/tex]He ate a total of 1/2 of the chocolate.
Determine whether the statement can be assumed from the given figure.
Yes/no
Share/do not share
Answer:
No
do not share
Step-by-step explanation:
Two rays make up angle 7 and two DIFFERENT rays make up angle 8 (angle 6 is in between them) If they were a linear pair with a shared side, it would look like a loooong line with a ray sticking out that makes two angles. In the image, Angle1 and Angle2 are a linear pair. And Angle1 and Angle4 also.
They do not share at all.
Simplify the fraction
18
60
as much as possible.
3
10
18
60
12
54
Answer:
3/10
Hope this helps!
Have a good day :)
What is the reason for each step in the solution of the equation?
4x−1=−2(x+1)
The solution of the equation 4 x - 1 = - 2 (x + 1) is x = [tex]\frac{-1}{6}[/tex]
4 x - 1 = - 2 (x + 1) (given)
4 x - 1 = - 2 x - 2 (applying distributive law to RHS)
4 x - 1 + 2 x = - 2 (transferring literal term from RHS to LHS)
6 x - 1 = - 2 (simplifying literal terms of LHS)
6 x = - 2 + 1 (transferring constant term from LHS to RHS)
6 x = - 1 (simplifying constant terms of RHS)
x = - 1 / 6 (transferring literal coefficient from LHS to RHS)
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Which values are in the solution set to this inequality? 3 x 4 < 9 and − x 6 ≥ − 3 x = 4 x = 11 x = 18 x = 12 x = 15
The value of x in the solution set is x = 4
How to determine the values in the solution setThe system of inequalities is given as
3x + 4 < 9
-x + 6 ≥ -3
The first step is to solve for x in both inequalities in the system of inequalities
So, we have
3x + 4 < 9
3x < 5
Divide by 3
x < 5/3
Also, we have
-x + 6 ≥ -3
-x ≥ -9
Divide by -1
x ≤ 9
So, we have
x < 5/3 and x ≤ 9
x ≤ 9 is a superset of x < 5/3
So, we have
x ≤ 9
This means that the values of x do not exceed 9
An example of this value (from the options) is 4
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g(4) please answer asap
A bag contains 7 red balls and 3 white balls. Andrew, Betsy, Cam and Doug, in that order are going to randomly pick a ball out of the bag and not replace it. The first person to draw a white ball wins $160. What is the probability that Doug will win the S160?
ANSWER
3/7 (the correct option is not there)
EXPLANATION
There are 7 red balls and 3 white balls in the bag.
To find the probability of Doug being the first to draw the white ball, we have to assume that Andrew, Betsy and Cam all draw red balls.
There are a total of 10 balls there.
After Andrew Betsy and Doug pick their balls, there will be 7 balls left, that is:
4 red balls and 3 white balls.
Ther probaility of Doug picking the white ball will therefore be the number of white balls divided by the total number of balls.
That is:
P(Doug) = 3/7
That is the probability that Doug will win the $160.
a class has 30 cups of popcorn. they are filling individual bags with three-fourths cups of popcorn. write a number sentence to show how many bags they can fill with popcorn
If the clas has 30 cups and fills individual bags with three-fourths cups then the number of bags that can be filled
= 30 / (3/4)
= 30 * 4/3
= 40
Hence 40 bags can be filled with popcorn
I need help please it would help me a lot thank u
Her monthly payment will be $103.29.
Define simple interest.Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. Because simple interest keeps total interest payments lower than compound interest, it is better for borrowers. Simple interest is used in the monthly amortization of auto loans and retailer instalment loans. As the loan balance decreases with each monthly payment, so does the interest.
Given Data
Principal = $939
Time = 12 months
Rate = 11%
Simple interest = P(R)(T)
Simple interest = [tex]\frac{939(1)(11)}{100}[/tex]
Simple interest = 103.29
Her monthly payment will be $103.29.
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Lisa earns $39 for 3 hours of babysitting what does she earn per hour of babysitting?
Answer:
13$
Step-by-step explanation:
just divide 39 by three.
39 dive by 3=13
13 x 3=39
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x)=0.4x^2 - 104x + 13,586. How many cars must be made to minimize the unit cost? Do not round the answer
Answer:
130 cars
Step-by-step explanation:
You want the value of x (the number of cars made) that minimizes the unit cost, given by C(x) = 0.4x² -104x +13586.
VertexThe minimum cost will be found at the vertex of this quadratic cost function. For quadratic ax²+bx+c, the vertex is found at x=-b/(2a).
The cost function has a=0.4 and b=-104, so the number of cars that must be made to minimize the unit cost is ...
x = -b/(2a) = -(-104)/(2(0.4)) = 104/0.8
x = 130
130 cars must be made to minimize the unit cost.
__
Additional comment
A graphing calculator can plot the cost function and show you the coordinates of the minimum cost. The attachment shows the minimum cost per car is $6826 when 130 cars are made.
Which inequality is represented by the number line below?
An inequality which is represented by the number line above is: x < -7.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
The rules for writing an inequality.In Mathematics, there are four (4) rules that are generally used to write an inequality and these include the following:
The circle/dot on a number line should be filled when the inequality symbol is (≥ or ≤).The circle/dot on a number line should not be filled when the inequality symbol is (> or <).When the arrow points to the left on a number line, the inequality is either (≤ or <).When the arrow points to the right on a number line, the inequality is either (≥ or >).Next, we would apply the aforementioned rules to write the solution to the inequality shown in the number line above:
x < -7
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The word that has the/k/ sound
Answer:
kiss
i just thought of kiss I'm probably not correct to be honest
Zachary has a container of worms for fishing.
When empty, the mass of the container is 225 grams. With the worms in
it, the container has a total mass of 751.4 grams. Each worm has a mass
of 11.2 grams. How many worms are in the container? Write and solve an
equation to model this situation.
Answer:
there are 47 worms in the container
Step-by-step explanation:
empty container- 225 g.
full container- 751.4 g.
1 worm- 11.2 g.
equation
(751.4-225)/11.2
751.4-225= 526.4
526.4/11.2= 47 worms
The depth of a rain puddle D(t) is given in inches, and t is given in minutes. If the depth is changing with respect to time, which expression gives the rate of change at which the depth is changing at 1 minute? D″(1)D″(0) − D″(2)D′(1)D(0) − D(2)
The derivative evaluated at t=1 minute will give us the rate of change (or the slope) of the line equation which approximate the function at that point. In other words, the rate of change is given by
[tex]m=\frac{dD(t)}{dt}|_{t=1}=D^{\prime}(1)[/tex]Therefore, the answer is option 3 from top to bottom.
Carter budgets
18
% of his salary for food. His salary is $
3
,
900
. How much money does he need to budget for his food?
Answer:
3900*18%=702
Step-by-step explanation:
Miss Jones mowed 1/4 of her lawn her son mowed 2/5 of it. who mowed most of the lawn? how much of the lawn still needs to be mowed
The son mowed most of the lawn
7/20 of the lawn still needs to be mowed
Explanations:Size of the lawn mowed by Miss Jones = 1/4
Size of the lawn mowed by her son = 2/5
To know who mowed the most lawn, find the LCM of the denominators
The LCM of 4and 5 = 20
Make the denominators of both fractions to be 20
Size of the lawn mowed by Miss Jones = 1/4 x 5/5 = 5/20
Size of the lawn mowed by her son = 2/5 x 4/4 = 8/20
Since 8/20 > 5/20, Miss Jone's son mowed more part of the lawn than Miss Jone
How much of the lawn still needs to be mowed:
[tex]\begin{gathered} \text{The part of the lawn that still n}eeds\text{ to be mowed = 1 -}\frac{1}{4}-\frac{2}{5}\text{ } \\ \text{The part of the lawn that still n}eds\text{ to be mowed = }\frac{7}{20} \end{gathered}[/tex]HELPPPP!
Does the frequency distribution given appear to be normal?
Score ---Frequency
65-69 4
70-74 5
75-79 6
80-84 4
85-89 6
90-94 4
95-99 5
Yes, the frequencies preceding the maximum are roughly a mirror image of those that follow the maximum
No, there is not a concentration of frequencies in the middle
Yes, there is symmetry in the distribution
No, the frequencies increase, reach a maximum, then decrease
It should be noted that the frequency distribution given appear to be normal as D. No, the frequencies increase, reach a maximum, then decrease.
How to illustrate the information?It should be noted that the graph that's illustrated shows that there is a concentration of the data points in the middle.
It should be noted that this illustrates that isn't not normal and the bell shaped curve was illustrated.
Therefore, based on the information, the correct option is D.
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Write a quadratic function for the following characteristics
Answer:
[tex]y=x^2+6x-16[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given points on the curve:
(-8, 0)(-6, -16)(2, 0)The x-intercepts of a quadratic function are the points at which the line crosses the x-axis, so when y = 0.
Therefore, the x-intercepts of the given function are -8 and 2.
Substitute these into the intercept formula:
[tex]\implies y=a(x-(-8))(x-2)[/tex]
[tex]\implies y=a(x+8)(x-2)[/tex]
Substitute the other given point (-6, -16) into the equation and solve for a:
[tex]\begin{aligned} y&=a(x+8)(x-2)\\\textsf{When }(-6,-16)\implies -16&=a(-6+8)(-6-2)\\-16&=a(2)(-8)\\-16&=-16a\\\implies a&=1\end{aligned}[/tex]
Therefore, the equation of the function in intercept form is:
[tex]y=(x+8)(x-2)[/tex]
Expand to standard form:
[tex]\implies y=x(x-2)+8(x-2)[/tex]
[tex]\implies y=x^2-2x+8x-16[/tex]
[tex]\implies y=x^2+6x-16[/tex]
Therefore, the quadratic function in standard form is:
[tex]\boxed{ y=x^2+6x-16}[/tex]
If A(2, 2), B(6, 4), C(4, 4) and D(8, 6) are four points then prove that: AB= CD
THE ONLY WAY WE CAN PROVE THAT AB IS EQUAL CD IS BY CALCULATING THE DISTANCES AND THEN COMPARING THEM.
FOR AB
[tex] = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } \\ = \sqrt{(( {6- 2})^{2} + ( ({4 - 2})^{2} } \\ = \sqrt{( {4})^{2} +( {2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]
THE DISTANCEAB IS GIVEN ABOVE.
NOW LET US CALCULATE DISTANCE CD
[tex] = \sqrt{ ({8 - 4)}^{2} + ({6 - 4})^{2} } \\ = \sqrt{ {(4})^{2} + ({2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]
WE CAN SEE THAT DISTANCE AB AND DISTAMCE CD ARE EQUAL THERE SE CAN NOW SAY
AB=CD
Use what you know about domain to select all of the following functions that could be the one graphed.
Using translation, the functions that could be the one graphed are given as follows:
y = sqrt(x) - 3.y = sqrt(x) - 1.What is a translation?A translation is when a function undergoes a change in it's definition, keeping the same shape and side length, just changing the position.
The possible translations are given as follows:
Translation down.Translation up.Translation left.Translation right.In the context of the graph of this problem, the parent function is the square root of x, defined as follows:
y = sqrt(x)
The domain of this function, as is the domain of the graph, is for non-negative values of x, hence:
x ≥ 0.
From the graph, the function was translated down a units, keeping the domain but changing the range, hence the translation has the following format:
y = sqrt(x) - a.
Hence the first two options can be correct, either with a = 1 or with a = 3.
What is the missing information?The information to solve this problem is given by the image at the end of the answer.
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a seventh-grade student does not believe that -5 is greater than -2. the student argues that a debt of $5 is greater than a debt of $2 how do you respond?
Answer:
it is greater then -2
Step-by-step explanation:
heres how I was taught, if you have a number say like 8 then its greater the day 5 same for -8 and -5 the long it is away from 0 the greater it is
PLEASE HELP GEOMETRY 50 POINTS
Answer:
See below
Step-by-step explanation:
Alternate exterior angles are equal if the lines crossed by the transversal are parallel
15x + 9 = 21x - 27
9 + 27 = 21x - 15 x
x = 6 °
Express 4+-4as a complex number ( term of i) 4+-4
Complex numbers are numbers in the form
[tex]z=a+bi[/tex]where i represents the imaginary number defined as the square root of minus one.
[tex]i=\sqrt{-1}[/tex]We call a as the real part of the complex number and b the imaginary part.
We want to rewrite the number
[tex]\sqrt{4}+\sqrt{-4}[/tex]in terms of the imaginary constant.
Using the following property
[tex]\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}[/tex]We can rewrite the second term of our sum as
[tex]\sqrt{-4}=\sqrt{(-1)(4)}=\sqrt{-1}\sqrt{4}[/tex]Then, our number can be rewritten as
[tex]\sqrt{4}+\sqrt{-4}=\sqrt{4}+\sqrt{-1}\sqrt{4}[/tex]Using the definition of the imaginary unit we can rewrite our number as
[tex]\sqrt{4}+\sqrt{-1}\sqrt{4}=\sqrt{4}+\sqrt{4}i[/tex]Then, we can rewrite the square roots as
[tex]\sqrt{4}=2[/tex]The simplified version of our number is
[tex]\sqrt{4}+\sqrt{-4}=2+2i[/tex]2. A rectangle with a length of 20 centimeters and an unknown width of x centimeters has a
smaller rectangle cut out of it. The smaller rectangle has a length of 16 cm and a width of
x-3. The area of the shaded region (what remains) is 80 square centimeters.
Set up
and solve an equation for the value of x.
X
x-3
20 cm
16 cm
The value of x is 8 cm.
What is the area of a rectangle?The area of a rectangle is the space occupied by the rectangle inside its perimeter. A rectangle's area is calculated by multiplying its length by its width.
Given:
Length of rectangle = 20 cm
Width of rectangle= x cm
Area of rectangle = length × width
= 20x cm²
The dimensions of the smaller rectangle cut out of it are,
Length = 16cm
Width = x-3
Area of the smaller rectangle = length × width
= 16(x - 3) cm²
The area of the shaded portion will be equal to the difference between both areas which is given as 80 square centimeters.
20x - 16(x-3) = 80
Now, we need to solve this equation to obtain the value of x.
20x - 16x + 48 = 80
4x = 80 - 48
4x = 32
x = 32/4
x = 8
Therefore, the value of x is 8 cm.
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One leg of a right triangle is 8 inches less than the hypotenuse. The other leg is 12 inches. Find the length of hypotenuse.
Answer:
13 in
Step-by-step explanation:
Let the hypotenuse be x. Then, by the Pythagorean theorem,
[tex](x-8)^2 + 12^2=x^2 \\ \\ x^2-16x+64+144=x^2 \\ \\ 16x=64+144 \\ \\ x=4+9 \\ \\ x=13[/tex]
If rocks along the furnace creek fault have been offset 30 miles over 10 million years, what is the rate of plate motion in cm/year. (Hint: Rate x Time = Distance, and there are 5280 feet in one mile, and 2.54 cm. in one inch.)
The rate of plate motion in cm/year is equal to 3.3528 × 10⁻³ cm/year.
What is a conversion factor?A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.
Conversion:
1 mile = 5280 feet
30 miles = X feet
Cross-multiplying, we have:
X = 30 × 5280
X = 158,400 feet.
Next, we would convert the value in feet to inch and then to cm as follows:
Distance = 158,400/12 = 13,200 inches.
In centimeters (cm), we have:
1 inch = 2.54 cm
13,200 inches = Y cm
Cross-multiplying, we have:
Distance, Y = 13,200 × 2.54
Distance, Y = 33,528 cm.
Now, we can determine the rate of plate motion in cm/year:
Rate = Distance/Time
Rate = 33,528/10,000,000
Rate = 3.3528 × 10⁻³ cm/year.
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