Expand each logarithm.
log m³/n⁴ p⁻²
After expanding logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]\frac{log_{10} m^3}{n^4 \\ p^-2} \\[/tex]
apply formula log a^x = x log a
[tex]= > \frac{3 log_{10} (m)}{\frac{n^4}{p^2} }\\ \\= > \frac{3 log_{10} (m) p^2}{{n^4} }[/tex]
Thus, after expanding the logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
To know more about logarithms, visit :
https://brainly.com/question/12049968
#SPJ4
Prompt: Tell me what you know about slope. Be as detailed
as possible and write in paragraph form. Some examples you
can expand on would be slope of parallel and perpendicular
lines, finding slope on a graph, using slope formula, etc.
Step-by-step explanation:
what did your teacher do in class ? nothing ?
it is really not that complicated :
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
it tells us how many units y changes when x changes by a certain number of units.
e.g. a slope of 2 = 2/1 means that when we increase x by 1, y increases by 2.
a positive slope means that the line goes up (seen while going from left to right).
a negative slope means that the line goes down.
therefore, a slope of 0 means a flat, horizontal line.
while for a vertical line the slope is the result of a division by 0 and is therefore undefined (some like to symbolize this by infinity).
parallel simply means to have the same slope. parallel lines imitate each other's behavior and attributes perfectly except for the absolute physical location.
perpendicular (at a 90° angle) slopes now simply turn x and y in the ratio upside-down and flip the overall sign of the slope.
e.g. the perpendicular slope of 2 = 2/1 is -1/2.
oh, and the slope of a function or curve that is not a line ?
then we go point by point, as the function does not have one slope for everything. and the slope of the function at a particular point is the slope of the tangent line at that point.
all clear now ?
write the number below (81) as a power with a base of 3 and a base of 9
Answer:
base of 3 --> 3^4 (three to the fourth); base of 9 --> 9^2 (nine squared)
Step-by-step explanation:
3 x 3 = 9 x 3 = 27 x 3 = 81 = 3^4
You multiply 3 by itself 4 times.
9 x 9 = 81 = 9^2
You multiply 9 by itself 2 times.
Please help me I am confused!!!!!!!!!!!
Answer: 202 ounces
Step-by-step explanation:
Because all you had to do is add all the ounces to get the amount he drank between 9 am and 2 pm!
Angles of Triangles #2: Find the angles below
The missing angles of the Triangle are; ∠1 = 62°; ∠2 = 45° and ∠3 = 22°.
How to find congruent angles?We know that the sum of angles on a straight line is 180 degrees. Thus, we can say that;
∠1 + 118° = 180°
∠1 = 180 - 118
∠1 = 62°
We also know that sum of angles in a triangle is equal to 180°. Thus;
∠1 + ∠2 + 73 = 180
Plugging in the relevant value gives;
62 + ∠2 + 73 = 180
∠2 = 180 - 135
∠2 = 45°
∠2 + ∠3 = 180 - (∠1 + 49)
∠2 + ∠3 = 180 - (62 + 49)
45° + ∠3 = 69
∠3 = 22°
Thus, we conclude that the missing angles of the Triangle are; ∠1 = 62°; ∠2 = 45° and ∠3 = 22°.
Read more about Congruent Angles at; https://brainly.com/question/14791175
#SPJ1
Let f(x)=3 x²-4 and g(x)=x-2 . Calculate (f ⁰ g⁻¹)(x) for x=-3 .
If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.
If x = -3 then (f ⁰ g⁻¹)(x) is 23.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Let the two functions be f(x) = 3x² - 4 and g(x) = x - 2
(g⁻¹)(x) = 1 - 2
(g⁻¹)(x) = -1
substitute (g⁻¹)(x) value in (f ⁰ g⁻¹)(x)
(f ⁰ g⁻¹)(x) = (f ⁰ ) (-1)
then f(x) equation is 3 x² - 4 substitute -1 in x
f(-1) = 3(-1)² - 4
f(-1) = -1
Now when x = -3 the (f ⁰ g⁻¹)(x) value is
f(-3) = 3(-3)² - 4
f(-3) = 23
Therefore, the value of (f ⁰ g⁻¹)(x) for x = -3 is 23.
To learn more about inverse formula refer to:
brainly.com/question/10219387
#SPJ4
Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 333 marbles into a marble jar. when the jar has 100100100 or more marbles, the students have a party. right now, the jar has 242424 marbles. write an inequality to determine the number of additional times, rrr, mrs. morton could reward the class in order for the students to have a party. will the students have a party if mrs. morton rewards them 313131 additional times?
Yes the students have a party is mrs. Morton reward them 313131 additional times.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most of the time, size comparisons between two numbers on the number line are to be made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a > b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since a is apparently less than or solely greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
Read more about inequalities here:
https://brainly.com/question/20383699
#SPJ4
d(n)=-5(1/2)n-1 what is the third term in the sequence
Answer: d3 = - 17/2
correction: This is an explicit formula
All we have to do is plug n = 3 in the formula to find the 3rd term.
2. d(3)=-5(1/2)3-1
= -5/4
Step-by-step explanation:
What is the simplest form of the quotient √72 x⁵ y³ z⁸ / √3 x y²z² ?
(A) √24 x⁴ y z⁶
(C) 24 x⁴ y z⁶
(B) 2 x² z³ √6y
(D) 12 x² y z⁶
The simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.
What do we mean by simplest form?When the numerator and denominator have no common factors other than one, the fraction is in its simplest form. When the top and bottom cannot be any smaller while still being whole numbers, the fraction is in its simplest form. To simplify a fraction, divide the top and bottom numbers by the largest number that divides both numbers exactly (they must stay whole numbers).So,
Given: 72x⁵y³z⁸/√3xy²z²Then,
72x⁵y³z⁸/√3xy²z²Simplify the radical by dividing it into a product of known factors and assuming positive real numbers, which gives us:2x²z³√6yTherefore, the simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.
Know more about the simplest form here:
https://brainly.com/question/21298204
#SPJ4
The width of the rectangle is a+10 / 3 a+24 . Write an expression for the length of the rectangle in simplest form.
The required length of a rectangle in simplest form is (a + 10) / 3(a + 8).
What is a rectangle?
A rectangle is a geometrically closed figure with four sides in which the opposite pair of sides are equal to each other. The angle at all the vertices of the rectangle is 90 degrees.
The calculation for the length of a rectangle in simplest form.
Given the value of the width of a rectangle = (a + 10) / 3 a + 24
The length of a rectangle in the simplest form is given by: (a + 10) / 3(a + 8)
Hence, the required length of a rectangle is (a + 10) / 3(a + 8).
To learn more about the rectangle, visit here:
https://brainly.com/question/16239445
#SPJ4
I need like 3 more questions I will post seperately. Brainliest if correct *guaranteed*
[tex]y =\begin{cases}x + 1 \: \: \: \: \: \: \: \: x >2\\x + 2 \: \: \: \: \: \: \: \: x \leqslant 2\end{cases}[/tex]
Step-by-step explanation:According to the graph,
when x ≤ 2, the line passes through the points (-2,0) and (0,2).Let y = [tex]{m_1}[/tex]x + [tex]b_1[/tex] [[tex]b_1[/tex] = 2]
when x = -2 , y = 0
-2[tex]m_1[/tex] + 2 = 0 [[tex]{m_1}[/tex] = 1]
→ So when x ≤ 2 , y = x + 2
when x > 2, the line passes through the points (2,3) and (3,4).Let y = [tex]m_2[/tex]x + [tex]b_2[/tex]
[tex]m_2 = \frac{4 - 3}{3 - 2} = 1 \: \: \: \: \: \: \: \: \: \: [m = \frac{y_2 - y_1}{x_2 - x_1} ][/tex]
when x = 2 , y = 3
3 = 2 × 1 + [tex]b_2[/tex] , [tex]b_2[/tex] = 1
→ So when x > 2 , y = x + 1
So, the correct option is (c)[tex]y =\begin{cases}x + 1 \: \: \: \: \: \: \: \: x >2\\x + 2 \: \: \: \: \: \: \: \: x \leqslant 2\end{cases}[/tex]
The equation of the line through the point (2, 3) with slope -2 is
The correct answer is 2x - y +7 =0.
Various equations like equation of slope, y-intercept, slope- intercept must be known.
We have a line equation in the provided problem, and we must determine the slope and intercepts in order to create the graph. Assuming that m is the slope and c is the y-intercept, the slope intercept form is known as y=mx+c. We may determine the slope by utilizing the slope intercept formula.
The equation for the line in the problem can be written using the point-slope formula. The linear equation's point-slope form is: (y-y1) = m(x-x1)
( y - (3))=-2(x-2)
y - 3 = 2x + 4
2x - y +7 =0
To learn more about slope-intercept refer the link:
https://brainly.com/question/12763756
#SPJ9
Which of the following interpretations for the given expression is correct
(x+y)^n/2
The correct interpretation for the given expression is the sum of x and y raised to the power of half n
How to determine the correct interpretations for the given expression?The expression is given as
(x + y)^n/2
To interpret the expression, we start by evaluating the expression in the bracket and the exponent
So, we have
(x + y): The sum of x and yn/2: n divided by 2Hence, the correct interpretation for the given expression is the sum of x and y raised to the power of half n
Read more about expressions at
https://brainly.com/question/8797023
#SPJ1
After four years of higher education, Marshall just graduated with a Bachelor's degree in Physics from NYU where the annual cost of tuition was $20,000. He paid for college by earning $11,000 annually through the work study program and receiving an annual scholarship. He covered the remainder of the costs by taking out $20,000 in student loans. If he didn't fund his education with savings or grant money, what was the amount of Marshall's annual academic scholarship?
The annual academic scholarship amount is $15000.
This problem can be solved by unitary method and also by addition and subtraction.
Total annual tuition fee of Marshal is $20000.
His annual earning through the scholarship is $11000.
He also took an loan of about $20000 from student loan.
Total fee for the four years Bachelor's degree in Physics is = $20000×4
= $80000
He cleared $20000 by student loan then remaining amount
=(80000-200000)
= $60000
Then the amount he earned through the scholarship program in total to clear the dues = $60000
Annual amount of scholarship is =$15000
To learn more about unitary method visit the link:
https://brainly.com/question/21648365
#SPJ9
What is the slope of a line parallel to the line whose equation is 2x-5y=302x−5y=30. Fully simplify your answer
Answer:
x = 30 + 5y / 2
Step-by-step explanation:
The slope of the line parallel to the given line is 2/5.
What is slope?Slope of a line is the measure of the steepness and the direction of the line.
Given that, an equation of a line, 2x−5y = 30
Converting the equation in slope intercept form,
2x−5y = 30
5y = 2x - 30
y = 2/5x - 30
We know that the slope of two parallel lines are equal.
Hence, The slope of the line parallel to the given line is 2/5.
For more references on slope, click;
https://brainly.com/question/3605446
#SPJ2
In a science lab, a number of rock samples are weighed. If the scientist finds one of the rocks to weigh 6 pounds and this is 38.7% of the total weight of all of the rocks, what is the weight of all of the rocks? If necessary, round your answer to the nearest tenth.
10.5 lb
2.3 lb
232.2 lb
15.5 lb
Answer:
15.5
Step-by-step explanation:
We are trying to find out:
38.7% of what number is 6?
38.7% as a decimal is .387
.387x = 6 Divide both sides by .387
x = 15.503875969
Round 15.5
a random two-digit number(10-99) is drawn.find the probability p(32)
Based on the sample space, the probability of P(32) is 1/90
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability?The sample space is given as
Space = two-digit numbers
There are 90 two-digit numbers
So, the sample size is
Size = 90
There is only one two-digit number with the value 32
So, we have
n(32) = 1
The probability of selecting 32 is
P(32) = n(32)/Size
So, we have
P(32) = 1/90
Hence, the probability of P(32) is 1/90
Read more about probability at
https://brainly.com/question/251701
#SPJ1
Which of the following is equivalent to y + 8 = –3(x – 1)?
Answer:
Graph in the image above
Step-by-step explanation:
Select the correct answer. Consider the formula for the slope between two coordinate points, m, shown below. m = y 2 − y 1 x 2 − x 1 Which of the following equations is equivalent to the slope formula? A. y 2 = m ( x 2 − x 1 ) + y 1 B. x 1 = m ( y 2 − y 1 ) + x 2 C. x 2 = m ( y 2 − y 1 ) + x 1 D. y 1 = m ( x 2 − x 1 ) + y 2
The equation that is equivalent to the slope formula is y₂ = m(x₂ - x₁) + y₁
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The slope between two points A(x₁, y₁) and B(x₂, y₂) is:
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
m = (y₂ - y₁) / (x₂ - x₁)
m(x₂ - x₁) = y₂ - y₁
y₂ = m(x₂ - x₁) + y₁
The equation that is equivalent to the slope formula is y₂ = m(x₂ - x₁) + y₁
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
Simplify this please!!!
Answer:1/8a^9b^12
or in other words, D. Last one
Step-by-step explanation:
Find the sum: 1/3+1/4
Answer:
7/12
Step-by-step explanation:
i used lowest common denomator
Answer:
answer is 7/12
Step-by-step explanation:
hope this helps
Natasha combines 6.54 liters of red paint with 6.09 liters of blue paint to make purple paint. she pours the paint equally into 3 containers, and has 1.68 liters of paint left over. how many liters of paint are in each container?
After dividing the paint in each container there are 3.65 liters of paint in each container.
what is division?
in the process of dividing a number up into equals parts and getting how many same numbers can be made. this process opposite of multiplication.
Quantity of red paint = 6.54 liters
Quantity of blue paint = 6.09 liters
by addition, quantity of purple paint = 12.63 liters
According to the question 1.68 liters paint left over then remaining paint by Subtraction = 10.95 liters 10.95 liters paints divided into 3 containers then the paint in each container is 3.65 liters.
Read more about Subtraction here:
https://brainly.com/question/2346316
#SPJ4
this multi answer so please put multi
The pair of numbers that have the greatest common factor of 3 will be:
18 and 15
6 and 9
3 and 9
How to illustrate the information?It should be noted that the factor of a number can be multiplied with another number that get the original number.
Therefore, the of pair of numbers that have the greatest common factor of 3 will be:
18 and 15
6 and 9
3 and 9
It should be noted that they have 3 as a common factor.
Learn more about factor on:
brainly.com/question/25829061
#SPJ1
5 - (x - 2)² for x =- 1
Answer: -4
Step-by-step explanation:
5 - (x - 2)²=
5 - (-1 - 2)²=
5 - (-3)²=
5 - (3)²=
5-9=-4
Answer:45
Step-by-step explanation:
Select the correct answer. The square of y varies directly as the cube of x. When x = 4, y = 2. Which equation can be used to find other combinations of x and y? A. B. C. D.
The direct variation equation can be used to find other combinations of x and y is y² = 4x³/27
What is direct variation?Direct variation is variation in which one quantity increases as another quantity increases or decreases as anothe rquantity decreases.
How to find equation can be used to find other combinations of x and y?Since we have that the square of y varies directly as the cube of x.
Writing this as a direct variation mathematically, we have
y² ∝ x³
So, the direct variation equation is
⇒ y² = kx³ where k = constant of proportionality
Now, given that when x = 4, y = 2.
Substituting the values of x and y into the equation, we have
y² = kx³
2² = k(3)³
4 = k(27)
k = 4/27
Substituting the value of k into the expression, we have
y² = kx³
y² = 4x³/27
So, the direct variation equation can be used to find other combinations of x and y is y² = 4x³/27
Learn more about direct variation equation here:
https://brainly.com/question/28596613
#SPJ1
what is (18+x) x 28=326?
Answer:
x = -6.36
Step-by-step explanation:
(18 + x) × 28 = 326
Divide both sides by 28
18 + x = 11.64
Subtract 18 from both sides
x = -6.36
Expand each logarithm.
log₃[(xy 1/3)+z²]³
After expanding logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]log_3[xy^\frac{1}{3} + z^2]^3[/tex]
apply formulas log a^x = x log a
=> [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
Thus, after expanding the logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
To know more about logarithms, visit :
brainly.com/question/5956809
#SPJ4
A florist buys a dozen roses for $12.96 and sells them for $48.48. Find the amount of markup on a single rose.
The amount of markup on a single rose is $2.96
What is profit?Profit = Selling Price – Cost Price.
We have,
We can consider the cost price as:
Bought amount = $12.96
We can consider the selling price as:
Selling amount = $48.48
Now,
Markup price can be considered as the profit:
Profit = Sellin price - Cost price
Profit = $48.48 - $12.96
Profit = $35.52
Since in a dozen we have 12 roses the markup price for each rose is:
= $35.52 / 12
= $2.96
Thus the amount of markup on a single rose is $2.96
Learn more about profits here:
https://brainly.com/question/14930773
#SPJ1
help i need help with this maths question
x add 3 = 8
Answer:
i guess X=5 because 3+5=8?
Step-by-step explanation:
Please Help acellus is torture.
The angle made by the vector is [tex]\theta[/tex] such that
[tex]\tan(\theta) = \dfrac{18.4\,\rm m}{-28.7\,\rm m} \approx -0.6411[/tex]
Before taking the inverse tangent of both sides, recall that [tex]\arctan[/tex] returns a number between -π/2 and π/2 radians, or -90° and +90°. The vector in the diagram clearly makes an angle between 90° and 180°, however, so we use the fact that tangent has a period of π rad / 180° to write
[tex]\theta \approx \arctan(-0.6411) + 180^\circ n[/tex]
where [tex]n\in\Bbb Z[/tex].
Now,
[tex]\arctan(-0.6411) \approx -0.5701 \,\mathrm{rad} \approx -32.6639^\circ[/tex]
Add 180° to this to recover the correct angle.
[tex]\theta = \arctan(-0.6411) + 180^\circ \approx \boxed{147.34^\circ}[/tex]