Answer:
A) v = f(x) = 96 -32x
B)the velocity when x = 0
V = 96 ft/s
The velocity when x =4
V = -32 ft/s
C). Time when v= 0
3 seconds = x
Step-by-step explanation:
f(x) = 96x -16x^2
The above equation represents the position of the object at x time along the x axis.
The velocity will be determined by differentiating the equation with respect with x
f(x) = 96x -16x^2,
D f(x)/Dx= 96 -2(16x)
D f(x)/Dx= 96 -32x
v = f(x) = 96 -32x
The velocity when x = 0
v = f(x) = 96 -32x
V = f(0) = 96-32(0)
V = 96 ft/s
The velocity when x = 4
v = f(x) = 96 -32x
V = f(4) = 96-32(4)
V = 96 - 128
V = -32 ft/s
Time when v= 0
v = f(x) = 96 -32x
0= 96 -32x
-96= -32x
-96/-32=x
3 seconds = x
6(a+2b+3c) USE THE DISTRIBUTIVE PROPERTY TO CREATE AN EQUIVALENT EXPRESSION!!!!!!!!
Answer:
6a + 12b + 18c
Step-by-step explanation:
To solve, we distribute the 6 to all of the terms inside the parentheses.
[tex]6*a\\6*2b\\6*3c\\6a+12b+18c[/tex]
Our answer is 6a + 12b + 18c. Hope this helps!
Vocabulary:
Distribute: Give shares of something. In math: Divide / give to each term (in this case)
Answer:
6a+12b+18c
Step-by-step explanation:
To create an equivalent expression, we must distribute the 6. Multiply each term inside of the parentheses by 6.
6(a+2b+3c)
(6*a)+(6*2b)+(6*3c)
6*a=6a
6a+(6*2b)+(6*3c)
6*2b=(6*2)b=12b
6a+12b+(6*3c)
6*3c=(6*3)c=18c
6a+12b+18c
The equivalent expression using the distributive property is 6a+12b+18c
Find two numbers with difference 62 and whose product is a minimum.
Answer:
31 and -31
Step-by-step explanation:
The two numbers with a difference of 62 and whose product is a minimum are; 31 and -31
Let the two numbers be x and y.We are told that their difference is 62.
Thus; x - y = 62 ---(1)
We want their products to be minimum. Thus;f(x,y) = xy
From eq, making y the subject gives us;
y = x - 62
Thus;
f(x) = x(x - 62)
f(x) = x² - 62x
For the product to be minimum, let us find the derivative of f(x) and equate to zero. Thus;f'(x) = 2x - 62
At f'(x) = 0
2x - 62 = 0
2x = 62
x = 62/2
x = 31
Thus;
y = 31 - 62
y = -31
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Which value of x makes the equation 0.75( x + 20) = 2 + 0.5(x - 2) true?
Answer:
0.75x+15=2+0.5x-1
0.25x=1-15
0.25x=-14
x=-56
Step-by-step explanation:
is the perpendicular bisector of . What is the length of ?
A.
4
B.
6
C.
12
D.
7
Answer:
the answer is C. 12
Step-by-step explanation:
Which of the following is the product of the rational expressions shown here? X/x-2•3/x-2
Answer:
[tex] \boxed{\sf \frac{3x}{ {x}^{2} - 4x + 4}} [/tex]
Step-by-step explanation:
[tex] \sf Product \: of \: the \: rational \: expression: \\ \sf \implies \frac{x}{x - 2} \times \frac{3}{x - 2} \\ \\ \sf \implies \frac{3x}{(x - 2)(x - 2)} \\ \\ \sf (x - 2)(x - 2) = (x)(x - 2) - 2(x - 2) : \\ \sf \implies \frac{3x}{ \boxed{ \sf (x)(x - 2) - 2(x - 2)}} \\ \\ \sf (x)(x - 2) - 2(x - 2) = (x)(x) - (2)(x) - 2(x) - (2)( - 2) : \\ \sf \implies \frac{3x}{ \boxed{ \sf (x)(x) - (2)(x) - 2(x) - (2)( - 2) }} \\ \\ \sf \implies \frac{3x}{ \boxed{ \sf {x}^{2}} - 2x - 2x - (2)( - 2)} \\ \\ \sf (2)( - 2) = - 4 : \\ \sf \implies \frac{3x}{ {x}^{2} - 2x - 2x - \boxed{ \sf - 4}} \\ \\ \sf - ( - 4) = 4 : \\ \sf \implies \frac{3x}{ {x}^{2} - 2x - 2x + \boxed{ \sf 4}} \\ \\ \sf - 2x - 2x = - 4x : \\ \\ \sf \implies \frac{3x}{ {x}^{2} - 4x + 4} [/tex]
X/(x - 2) × 3/(x - 2) = 3x/(x² + 4x + 4). So, the correct option is A.
The product of the rational expressions shown here X/x-2•3/x-2
X/(x - 2) × 3/(x - 2)
3x/(x - 2)²
by the (a - b)² = a² + b² -2ab
(x - 2)² = x² + 4 - 4x
3x/(x² + 4 - 4x).
Therefore, the correct answer is 3x/(x² + 4 - 4x).
Learn more about rational expressions here:
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4. Considera la función f(x) = 2*. Determina la función g(x) que se obtiene al trasladar
f(x)
a.tres unidades a la izquierda y dos unidades hacia arriba
b. cinco unidades a la derecha y cuatro unidades hacia abajo
Answer:
a. [tex]g(x)=f(x+3)+2[/tex]
b. [tex]g(x)=f(x-5)-4[/tex]
Step-by-step explanation:
Como f(x) no está especificada correctamente, vamos a tratarla genéricamente.
Las transformaciones que se proponen son traslaciones en el eje x y en el eje y.
Cuando se traslada'la función en el eje x, la variable independiente se reemplaza por una variable auxiliar u que es equivalente a la variable original x mas el valor desplazado hacia la izquierda.
Cuando se traslada la función en el eje y, simplemente se suma una constante a la función con un valor equivalente a las unidades que la función se traslado hacia arriba (si es hacia abajo, este valor es negativo).
Entonces, para trasladar f(x) 3 unidades a la izquierda u 2 unidades hacia arriba, empezamos por reemplazar la variable independiente por u=x+3 y luego agregar una constante igual a 2:
[tex]g(x)=f(x+3)+2[/tex]
Si queremos trasladar f(x) 5 unidades a la derecha y 4 unidades hacia abajo, empezamos por reemplazar la variable independiente por u=x-5 y luego agregar una constante igual a -4:
[tex]g(x)=f(x-5)-4[/tex]
En la figura se puede ver un ejemplo de la transformación para f(x)=x^2.
express 11011 in base two
Answer:
27
Step-by-step explanation:
Hello,
11011 in base 2 is
1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 in base 10
which is 16 +8+2+1=27
Do not hesitate if you have any question
In the diagram, line a is the perpendicular bisector of KM. Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N. Line segment K L is 6 x + 4. Line segment K N is 9 x minus 5. Line segment N M is 7 x + 7. What is the length of KM? 22 units 40 units 44 units 80 units
Answer:
D. 80 :)
Step-by-step explanation:
The solution is : The value of segment LM is 9x + 5.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
Consider the image below.
A perpendicular bisector is a line segment that bisects another line segment into two equal parts and is perpendicular to this line segment.
So from the diagram below we know:
KL = LM
line a is ⊥ to KM
∠NLK = 90°
Since the angle measure of ∠NKL is not provided we cannot determine the value of x.
So, the value of segment LM is 9x + 5.
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Complete question:
Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N. Line segment K L is 9 x +5. Line segment K N is 14 x minus 3. What is the length of segment LM? units
Una masa de 16 libras viaja con una velocidad de 30 m/s . Cuál es su energía cinética?
Energía cinética = 1 / 2mv²
Donde m es la masa y v es la velocidad
De la pregunta
la masa es de 16 libras
la velocidad es de 30 m / s
16 libras es equivalente a 7.257 kg
Entonces la energía cinética es
1/2(7.257)(30)²
Que es 3265.65 juliosEspero que esto te ayude
6. Assume that the probability of a driver getting into an accident is 6.4%, the average cost of an
accident is $13,991.05, and the overhead cost for an insurance company per insured driver is $95.
What should this driver's insurance premium be?
Answer:
This driver's insurance premium should be at least $990.43.
Step-by-step explanation:
We are given that the probability of a driver getting into an accident is 6.4%, the average cost of an accident is $13,991.05, and the overhead cost for an insurance company per insured driver is $95.
As we know that the expected cost that the insurance company has to pay for each of driver having met with the accident is given by;
The Expected cost to the insurance company = Probability of driver getting into an accident [tex]\times[/tex] Average cost of an accident
So, the expected cost to the insurance company = [tex]0.064 \times \$13,991.05[/tex]
= $895.43
Also, the overhead cost for an insurance company per insured driver = $95. This means that the final cost for the insurance company for each driver = $895.43 + $95 = $990.43.
Hence, this driver's insurance premium should be at least $990.43.
Answer:115
Step-by-step explanation:
Which graph represents the equation?
Answer:
The bottom left
Step-by-step explanation:
the -4 tells you the y intercept and the 1/3 tells you slope
hope this helps!
As soluções da equação 2X² - 7 = 7 (x-1) + 2x são:
{A) x= 2 ou x= 7}
{B) x= 0 ou x= 2}
{C) x= 0 ou x= 9}
{D) x= 2 ou x= -7/2}
{E) x= 0 ou x= 9/2}
Answer:
E) x= 0 or x= 9/2
Step-by-step explanation:
You have the following equation:
[tex]2x^2-7=7(x-1)+2x[/tex] (1)
In order to find the solutions for x of the equation (1), you simplify it and factorize in a convenient way, as follow:
[tex]2x^2-7=7x-7+2x\\\\2x^2-9x=0\\\\x(2x-9)=0[/tex] (2)
Then, by the previous factors, it is necessary that either x=0 or 2x-9 = 0.
Thus, one of the solution is x=0. The other solution is:
[tex]2x-9=0\\\\x=\frac{9}{2}[/tex]
Hence, the solutions of the equation (1) are:
E) x= 0 or x= 9/2
an organisms population in the year 2000 was about 9 billion and was increasing with a double time of 20 years. Suppose the population continued this growth pattern from the year 2000 into the future. Complete part a through d
Answer:
For this case we know that at the starting year 2000 the population was 9 billion and we also know that increasing with a double time of 20 years so we can set up the following model:
[tex]18 =9(b)^20[/tex]
And if we solve for b we got:
[tex] 2 = b^20[/tex]
[tex]2^{1/20}= b[/tex]
And then the model would be:
[tex] y(t) = 9 (2)^{\frac{t}{20}}[/tex]
Where y is on billions and t the time in years since 2000.
And for this equation is possible to find the population any year after 2000
Step-by-step explanation:
For this case we know that at the starting year 2000 the population was 9 billion and we also know that increasing with a double time of 20 years so we can set up the following model:
[tex]18 =9(b)^20[/tex]
And if we solve for b we got:
[tex] 2 = b^20[/tex]
[tex]2^{1/20}= b[/tex]
And then the model would be:
[tex] y(t) = 9 (2)^{\frac{t}{20}}[/tex]
Where y is on billions and t the time in years since 2000.
And for this equation is possible to find the population any year after 2000
Esibu and Dela are in a part-time business manufacturing clock case. Esibu must work 4 hours and Dela 2 hours to complete one case for a grandmother clock. To build one case for a wall clock, Esibu must work 3 hours and Dela 4 hours. Neither partners wish to work more than 20 hours per week. If they receive GHC80.00 for each grandmother clock and GHC64.00 for each wall clock, how many of each should they build each week to maximize their profit?
Answer:
Correct Answer:
To maximize their profit, Esibu must build 6 (2 grandmother clock and 4 wall clock) while Dela must build 8 (6 grandmother clock and 2 wall clock).
Step-by-step explanation:
Since they don't want to work for more than 20 hrs in a week
In-order to maximize the profit,
For Esibu,
2 grandmother clock = 4 hours ×2 = 8 hours
4 wall clock = 3 hours × 4 = 12 hours
Total hours = 20 hours.
For Dela,
6 grandmother clock = 2 hours × 6 = 12 hours
2 wall clock = 4 hours × 2 = 8 hours
Total hours = 20 hours.
convert the equation y= -4x + 2/3 into general form equation and find t the values of A,B and C.
Answer:
Standard form: [tex]12x+3y-2=0[/tex]
A = 12, B = 3 and C = -2
Step-by-step explanation:
Given:
The equation:
[tex]y= -4x + \dfrac{2}3[/tex]
To find:
The standard form of given equation and find A, B and C.
Solution:
First of all, let us write the standard form of an equation.
Standard form of an equation is represented as:
[tex]Ax+By+C=0[/tex]
A is the coefficient of x and can be positive or negative.
B is the coefficient of y and can be positive or negative.
C can also be positive or negative.
Now, let us consider the given equation:
[tex]y= -4x + \dfrac{2}3[/tex]
Multiplying the whole equation with 3 first:
[tex]3 \times y= 3 \times -4x + 3 \times \dfrac{2}3\\\Rightarrow 3y=-12x+2[/tex]
Now, let us take all the terms on one side:
[tex]\Rightarrow 3y+12x-2=0\\\Rightarrow 12x+3y-2=0[/tex]
Now, let us compare with [tex]Ax+By+C=0[/tex].
So, A = 12, B = 3 and C = -2
rationalize root six divided by root three minus root two. [tex]\frac{\sqrt{6} }{\sqrt{3}-\sqrt{2} }[/tex]
Answer:
the answer is
[tex]3 \sqrt{2} + 2 \sqrt{3} [/tex]
Step-by-step explanation:
the explanation is given in the image.
Answer:
[tex]\huge\boxed{\dfrac{\sqrt6}{\sqrt3-\sqrt2}=3\sqrt2+2\sqrt3}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt6}{\sqrt3-\sqrt2}\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\\dfrac{\sqrt6}{\sqrt3-\sqrt2}\cdot\dfrac{\sqrt3+\sqrt2}{\sqrt3+\sqrt2}=\dfrac{\sqrt6(\sqrt3+\sqrt2)}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}=\dfrac{(\sqrt6)(\sqrt3)+(\sqrt6)(\sqrt2)}{(\sqrt3)^2-(\sqrt2)^2}[/tex]
[tex]\text{use}\ \sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\ \text{and}\ (\sqrt{a})^2=a[/tex]
[tex]=\dfrac{\sqrt{(6)(3)}+\sqrt{(6)(2)}}{3-2}=\dfrac{\sqrt{18}+\sqrt{12}}{1}=\sqrt{9\cdot2}+\sqrt{4\cdot3}\\\\=\sqrt9\cdot\sqrt2+\sqrt4\cdot\sqrt3=3\sqrt2+2\sqrt3[/tex]
Write the partial fraction decomposition of the rational expression. Check your result algebraically.
Answer:
See below.
Step-by-step explanation:
First, distribute:
[tex]=\frac{1}{x(x+1)}[/tex]
Now, perform partial fraction decomposition. This is only two factors, so we only need linear functions:
[tex]\frac{1}{x(x+1)} =\frac{A}{x}+\frac{B}{x+1}[/tex]
Now, multiply everything by x(x+1):
[tex]1=A(x+1)+B(x)[/tex]
Now, solve for each variable. Let's let x=-1:
[tex]1=A(-1+1)+B(-1)[/tex]
[tex]1=0A-B=-B[/tex]
[tex]B=-1[/tex]
Now, let's let x=0:
[tex]1=A(0+1)+B(0)[/tex]
[tex]A=1[/tex]
So:
[tex]\frac{1}{x(x+1)}=\frac{1}{x}-\frac{1}{(x+1)}[/tex]
Double Check:
[tex]\frac{1}{x}-\frac{1}{(x+1)}=\frac{(x+1)}{x(x+1)}-\frac{x}{x(x+1)}[/tex]
[tex]=\frac{x-x+1}{x(x+1)} =\frac{1}{x^2+x}[/tex]
An arrow is shot upward at a rate of 220 feet per second. Use the projectile formula h=−16t^2+v_0t to determine when the height of the arrow will be 400 feet. Round your answer to the nearest tenth.
Answer:Explanatory help v
Step-by-step explanation:The question gives you V0 as 220, so plug that in first.
h=-16t2+220t.
Then it says to find the time (solve for t), when the height is 400 ft. Plug 400 ft in as h and solve for t.
400=-16t2+220t.
To solve this, set the quadratic equal to 0 by subtracting 400 from both sides (0=-16t2+220t-400) and use the quadratic formula!
Answer:
The arrow reaches 400 feet in its way up at about 2.2 seconds after being launched.
Step-by-step explanation:
Since we want to find the time at which the arrow will reach 400 feet, we use this information in the equation for the height;
[tex]400=-16\,t^2+220\,t\\16\,t^2-220\,t+400=0[/tex]
and now use the quadratic equation to solve for the unknown time (t). Notice that been a quadratic equation we expect up to two answers, and then we will need to decide which answer to pick.
[tex]t=\frac{220}{2\,(16)} +/- \frac{\sqrt{(-220)^2-4 \,(16)(400)}}{2\,(16)} \\ \\t= 2.156\,sec\,\,\,or\,\,\, t=11.594\,sec[/tex]
This means that as the arrow goes up, it takes 2.156 seconds to reach 400 feet, and afterwards, after the arrow reaches it maximum height, it falls back due to acceleration of gravity, going through the same 400 feet height before reaching the ground.
We round the answer to the nearest tenth as requested.
Customers can pick their own pumpkins at the great pumpkin patch. They pay $4 to enter and $3 per pound for the pumpkins they pick. Write an equitation to model the total cost, y, for x pounds of pumpkins.
Answer:
y=3x+4
Step-by-step explanation:
4 is the y intercept and 3 is the slope which is how much per pound. The equation you can use is y=mx+b, m is the slope so you fill it in with 3 and b is the y intercept so you fill it in with 4.
What point lies on the line described by the equation below? Y+3=2 (x-1
Answer:
[tex]\boxed{(1, -3)}[/tex]
Step-by-step explanation:
[tex]y+3=2 (x-1)[/tex]
Put equation in slope-intercept form.
[tex]y=mx+b[/tex]
[tex]y=2(x-1)-3[/tex]
[tex]y=2x-2-3[/tex]
[tex]y=2x-5[/tex]
Let x = 1
[tex]y=2(1)-5[/tex]
[tex]y=2-5[/tex]
[tex]y=-3[/tex]
The point (1, -3) lies on the line.
in the diagram AB =AD and
Answer:
AC ≅ AE
Step-by-step explanation:
According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.
Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.
Answer:
A). AC ≅ AE
Step-by-step explanation: took test on edge
Write the point slope equation of the line with the given slope that passes through the given point
M= -3, (3,5)
Answer:
y - 5 = -3(x - 3).
Step-by-step explanation:
The point-slope form is y - y1 = m(x - x1).
In this case, y1 = 5, x1 = 3, and m = -3.
y - 5 = -3(x - 3).
Hope this helps!
Answer:
[tex]\boxed{y-5= -3(x-3)}[/tex]
Step-by-step explanation:
Point-slope is in the general form:
[tex]y-y_1 = m(x-x_1)[/tex]
The values are given.
[tex]m=-3\\x_1=3\\y_1=5[/tex]
Plug in the values,
[tex]y-5= -3(x-3)[/tex]
What is the measure of JOK, given that GH=JK ?
A.
288
B.
108
C.
72
D.
18
Answer:
72 degrees.
Step-by-step explanation:
The angle marked as 72 degrees and the angle of JOK are considered vertically opposite angles in relation to each other. This relationship means that the angles are equal.
Answer:
[tex]\boxed{Option \ C}[/tex]
Step-by-step explanation:
Congruent arcs subtend congruent central angles.
So,
∠GOH ≅ ∠JOK
∠JOK = 72 degrees
Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
(A) If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.
(B) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.
Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) = [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]
= [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]
= [tex]\frac{0.3025}{0.4825}[/tex]
= 0.63
Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid passwords are there with the given restriction(s)? Length is 13. No character repeats.
Answer:
2310789600
Step-by-step explanation:
10 digits + 26 letters = 36
₃₆C₁₃ = 2310789600
Hope this helps, although i am not 100 percent sure its right.
Use all the information below to find the missing x-value for the point that is on this line. m = - 1 / 3 b = 7 ( x, 4 )
Answer:
[tex]\boxed{x = 9}[/tex]
Step-by-step explanation:
m = -1/3
b = 7
And y = 4 (Given)
Putting all of the givens in [tex]y = mx+b[/tex] to solve for x
=> 4 = (-1/3) x + 7
Subtracting 7 to both sides
=> 4-7 = (-1/3) x
=> -3 = (-1/3) x
Multiplying both sides by -3
=> -3 * -3 = x
=> 9 = x
OR
=> x = 9
Answer:
x = 9
Step-by-step explanation:
m = -1/3
b = 7
Using slope-intercept form:
y = mx + b
m is slope, b is y-intercept.
y = -1/3x + 7
Solve for x:
Plug y as 4
4 = 1/3x + 7
Subtract 7 on both sides.
-3 = -1/3x
Multiply both sides by -3.
9 = x
6th grade math help me, please :D
Answer:
option: D
51200
Step-by-step explanation:
64000 x 80/100 = 51200
Answer:
Hi there!!!
your required answer is option D.
explanation see in picture.
I hope it will help you...
Use the Product Rule of Logarithms to write an expression equivalent to In(6a+ 9b). Make sure to use parenthesis around your logarithm functions In(x +y)
Answer:
The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].
Step-by-step explanation:
Let be [tex]r = \ln (6\cdot a + 9\cdot b)[/tex], which is now solved as follows:
1) [tex]\ln(6\cdot a + 9\cdot b)[/tex] Given.
2) [tex]\ln [3\cdot (2\cdot a + 3\cdot b)][/tex] Distributive property.
3) [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex] ([tex]\ln (x\cdot y) = \ln x + \ln y[/tex]) Result.
The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].
We want to find an equivalent expression to ln(6a + 9b). We will get:
ln(6a + 9b) = ln(3) + ln(2a + 3b)
Here we will be using the rule:
ln(x) + ln(y) = ln(x*y)
Now let's see our expression:
ln(6a + 9b) = ln(3*(2a + 9b))
Now we use the above rule to write:
ln(3*(2a + 3b)) = ln(3) + ln(2a + 3b)
Then the equivalent expression is:
ln(6a + 9b) = ln(3) + ln(2a + 3b)
If you want to learn more, you can read:
https://brainly.com/question/9280855
Complete the point-slope equation of the line through (3,-8) (6,-4)
Answer:
y + 4 = 4/3(x - 6).
Step-by-step explanation:
The point-slope formula is shown below. We just need to find the slope.
(-4 - (-8)) / (6 - 3) = (-4 + 8) / 3 = 4 / 3
m = 4/3, y1 = -4, and x1 = 6.
y - (-4) = 4/3(x - 6)
y + 4 = 4/3(x - 6).
Hope this helps!
x^2-y^2=3y in polar form
Answer:
Step-by-step explanation:
put x=r cos θ
y=r sin θ
r²cos²θ-r²sin²θ=3rsin θ
r²(cos²θ -sin²θ)=3r sin θ
r²cos 2θ=3rsinθ
r cos 2θ=3 sin θ
r=3sec 2θ sin θ