Expression written as a single natural logarithm 3 ln x-2 ln 2 x is [tex]ln(x^{} )[/tex] .
What is natural logarithm?3 ln x-2 ln 2 x is
= [tex]ln x^{3} - lnx^{2}[/tex]
= [tex]ln(x^{3} /x^{2} )[/tex]
=[tex]ln(x^{} )[/tex]
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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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
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Expand each logarithm. State the properties of logarithms used. log₂ (2 y-4)³
The expanded form of the equation log₂ (2 y-4)³ is 3log₂(2y -4).
What exactly are extended forms?An expanded form is a method of writing a number through adding the digit values. A place value chart can help us think about the worth of a number's digits. Logarithms can be expanded by writing them as a sum as well as difference of logarithms, using the power rule if necessary. The order summation rule, product rule, as well as power rule are frequently useful.
Expanding the equation log₂ (2 y-4)³:
log₂ (2 y-4)³
applying the log rule logₐxᵇ = b*logₐ(x)
so that
3log₂(2y -4)
The expanded form of the equation log₂ (2 y-4)³ is 3log₂(2y -4).
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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]
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.
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You buy 6 notebooks for $ 2.00 each, 10 folders at $1.00 each, 2 packs of pencils for $3.00 each and one lunch box for for $ 8:00 write an expression to final the cost of your school supplies
I rlly need help on this asap pls help :,)
Answer:
(6*2)+(10*1)+(2*3)+(1*8)
Step-by-step explanation:
6 notebooks for 2 dollars each: 6*2 dollars spent
10 folders for 1 dollar each: 10*1 dollars spent
2 packs of pencils for 3 dollars each: 2*3 dollars spent
1 lunch box for 8 dollars each: 1*8 dollars spent
Add all the dollars spent per item type for total dollars spent
An expression does not have an equal sign
Factor 5x2 + 7x + 2 completely (SHOW WORK)
please help me <3
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:
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]
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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
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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 ?
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
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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).
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use the following function rule to find f (70)
submit
Answer:
-70
Step-by-step explanation:
you didn't put the function so sorry if it is wrong
1 Name a linear pair. Describe the relationship of their measurements.
Answer:
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
Step-by-step explanation:
If there is a pair of adjacent angles, then this pair is a linear pair if the sum of the (measures of the) two angles will be 180°. So, linear pair of angles always add up to 180°. For example, the linear pair of 30° is 150°, the linear pair of 70° is 110°, etc.
These two angles form a linear pair. We have found all four linear pairs of angles. The four linear pairs formed by the intersecting lines ←→QR Q R ↔ and ←→ST S T ↔ are ∠SOQ ∠ S O Q and ∠QOT ∠ Q O T , ∠QOT ∠ Q O T and ∠TOR ∠ T O R , ∠TOR ∠ T O R and ∠ROS ∠ R O S , and ∠ROS ∠ R O S and ∠SOQ ∠ S O Q .
1. ¿Cuál de las siguientes expresiones representa el
producto de 9 por x, restado del cociente de 2
entre x?
2
(1) // - 9x
X
2
(2) -9x
(3) 2x(-9x)
(4) 9 - X-
(5) (2 + x) 9x
-
2
-
Answer:
(2/x) - 9x
Step-by-step explanation:
si una de las respuestas se ve así, elija esa.
4/9 x (-1/8)= ??
(MUST BE SIMPLIFIED FRACTION)
Answer: put 32x over 9 as a fraction and it would be a negative so put a - in front
Step-by-step explanation:
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.
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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.
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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
simplify this fraction
Answer:
1
Step-by-step explanation:
1 / 3-x
x - 2/x - 3
(x - 2)/x - 3
-3/x - 3
(x - 2) + -1/x - 3
= x - 3/x - 3
Cancel
= 1
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
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HELP!
Estimate 63% of 109.
6.6
88.2
66
91.3
Answer:
66
Step-by-step explanation:
63% of 109 is 68.67 the closest answer is 66
A triangle has a base of [tex]2^{-3}[/tex] units and a height of [tex]2^{-4}[/tex] units. What is the height of the triangle? Write your answer using a positive exponent.
The height of the triangle has a measure of 2⁻⁴ units, that is equivalent to a measure of 1 / 2⁴ units.
What is the height of a triangle?
The statement indicates the dimensions of a triangle, where the base and the height of the figure are expressed by exponential numbers with positive integer base and negative integer exponents and each of which must be rewritten with positive exponents, this can be done by using the following power property:
a⁻ⁿ = 1 / aⁿ
Then, if the height of the triangle has a measure of 2⁻⁴ units, that is equivalent to a measure of 1 / 2⁴ units.
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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!
Simplify this please!!!
Answer:1/8a^9b^12
or in other words, D. Last one
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]
Which of the following is equivalent to y + 8 = –3(x – 1)?
Answer:
Graph in the image above
Step-by-step explanation:
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°.
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Convert 0.074 to standard form.
Answer:
In standard form 7.4 × 10^-2
Step-by-step explanation:
Answer:
7.4×10^-2
Step-by-step explanation:
Firstly, to convert 0.074 to standard form you will bring the first significant figure and make it the first I.e 7.4 then count how many times you took it backwards to make it 7.4 then put a negative sign in front of it because you took it backwards
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
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