The factored form of the equation -15w + 9wz - 6z + 10 is,
⇒ (3w - 2) (3z - 5)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ -15w + 9wz - 6z + 10
Now, Factor the equation as;
⇒ -15w + 9wz - 6z + 10
⇒ 3w (- 5 + 3z) - 2(3z - 5)
⇒ 3w (3z - 5) - 2 (3z - 5)
⇒ (3w - 2) (3z - 5)
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Find a particular solution of the following differential equations:
(a) y" + 3y + 2y = –20 sin(2x)
(b) y" – 4y + 13y = 2e21 [(1 + 6x) cos(3x) + (12.x – 8) sin(3x)]
The value of Differential Equation will be [tex]y_1=c_1 e^{-x}+c_2 e^{-2 x}+\sin (2 x)+3 \cos (2 x)[/tex]
[tex]$$\begin{aligned}& y^{\prime \prime}+3 y^{\prime}+2 y=-20 \sin (2 x) \\& \frac{d^2}{d x^2} y+3 \frac{d}{d x} y+2 y=-20 \sin (2 x)\end{aligned}$$[/tex]
A second order linear, non-homogeneous ODE has the form of ay"+b y'+cy=g(x).
General Solution can be written as y=y_h+y_p y_h is the solution to the homogenous ODE
a(x) y"+b(x) y'+c(x) y=0
Y_p is the particular solution to any function that Satisfies the non-homogenous equation.
Finding. y_n by solving
[tex]\frac{d^2}{d x^2}(y)+3 \frac{d}{d x}(y)+2 y=0 . \quad y=e^{y-t} .[/tex]
We can rewrite it as:
[tex]\frac{d^2}{d x^2}\left(\left(e^{x x}\right)\right)+3 \frac{d}{d x}\left(e^{y x}\right)+2 e^{y x}=0 \quad y=e^{y x}[/tex]
We will get it after solving as:
[tex]$\frac{d^2}{d x^2}\left(e^{8 x}\right)$[/tex] apply for chain role
we get [tex]$\Rightarrow r^2 e^{r x}$[/tex]
[tex]$$\begin{aligned}& \quad \frac{d}{d x}\left(e^{r x}\right) \Rightarrow \text { we get }=e^{r x} r \text { sob } \\& \therefore \quad r^2 e^{r x}+3 e^{r x} r+2 e^{r x}=0 .\end{aligned}$$[/tex]
Factor [tex]$e^{r x}\left(r^2+3 y+2\right)=0$[/tex]
By solving this we get r=-1, fr=-2
For two real roots [tex]$r_1 \neq r_2$[/tex].
The general solution will be:
[tex]$$y=c_1 e_2^{-x}+c_2 e^{-2 x}$$[/tex]
Similarly, further solving, we wll get: [tex]\frac{d^2}{d x}(y)+3 \frac{d}{d x}(y)+2 y=-20 \sin (2 x)[/tex]
We will get it as:
y=sin (2 x)+3 cos (2 x)
[tex]y_1=c_1 e^{-x}+c_2 e^{-2 x}+\sin (2 x)+3 \cos (2 x)[/tex]
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The correct question should be:
Find a particular solution of the following differential equations:
y" + 3y + 2y = –20 sin(2x)
Find the value of x in the given
right triangle.
37°
10
x = [?]
Enter your answer as a decimal rounded to the
nearest tenth.
The value of x ≈ 8.0 rounded to the nearest tenth.
What is a right-angled triangle?A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.
In the right-triangle,
The cosine ratio,
cos37° = perpendicular / hypotenuse
cos37° = x / 10
Using cross multiplication,
10 × cos37° = x,
x = 0.7986 × 10
x = 7.986
x ≈ 8.0 rounded to the nearest tenth.
Therefore, x ≈ 8.0 rounded to the nearest tenth.
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FOR EXAM! HELP
Determine if the two triangles are congruent. IF THEY ARE STATE HOW YOU KNOW!!!
According to the question, Triangles are said to be in SSS (Side-Side-Side) congruence if their third sides are the same length as the third sides of another triangle.
What are Congruent Triangles?One of the following conditions must be satisfied for two triangles to be considered congruent: There is equality between all three pairs of corresponding sides. Two matching side pairs have identical angles between them, as well as equal sides between them. The corresponding sides between two sets of corresponding angles and their two pairs are equal.
If both of a triangle's three sides and three angles are equal in any orientation, the two triangles are said to be congruent.
When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent. Slides, rotations, flips, and turns can be used to make these triangles appear identical.
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Company B needs to hire 30 new employees. Ten percent (10%) of applicants do not meet the basic business requirements for the job. 12% of the remaining applicants do not pass the pre-screening assessment, 23% of those remaining applicants do not show up for the interview, and 5% of those applicants fail the backround investigation. How many applicants need to apply in order to meet the hiring target?
Multiply choice
O 30
O 45
O 50
O 52
O 60
The applicants that would have to apply in order to meet the target is 52. Option 4 is correct.
How to solve for the applicantsWe have to define x as the applications to meet target
The number of persons to hire is 30
10 percent do not meet requirements. Hence 90 meets the requirements. 90% of x
= 0.9X
12% fail the pre screening stage. Hence 88% have passed it. This would be 88% of 0.9x. = 0.792x
23% Did not come for the interview, hence 77% showed up. This would be 0.77*0.792x = 0.60984x
then 5% are said to have failed the background test. This means that 95% passed the test.
0.95 * 0.60984x = 0.579348X
We have to equate this to 30 in order to get the value of x
0.579348X = 30
divide through by 0.579348
X = 30 / 0.579348
X = 51.78
X ~ 52
The number of applicants is 52
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*need fast answer please * what are some numbers of pushups that bucky will never do in any game ?
It is impossible to determine with certainty which number of pushups Bucky will never do in any game, as this depends on Bucky's physical abilities, training, and determination.
It is possible that Bucky may be able to do a very large number of pushups in a game, or he may not be able to do very many. It is also possible that there may be certain numbers of pushups that Bucky finds more challenging or difficult to do than others, but this would depend on his individual physical abilities and strengths. Ultimately, the number of pushups that Bucky will be able to do in any given game will depend on a variety of factors, and it is not possible to predict with certainty which numbers he will never do.
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Number of push-ups Bucky will never perform in any game is impossible to predict with confidence because it relies on Bucky's physical prowess, training, and willpower.
In a game, Bucky might be able to perform a lot of push-ups or he might not be able to perform many at all. It's also likely that Bucky will find some numbers of push-ups harder or more difficult to complete than others; however, this will depend on his particular physical prowess and capabilities.
In the end, Bucky's ability to do a certain number of push-ups throughout a game will rely on a multitude of variables, and it is impossible to say with certainty certain numbers he will never complete.
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1.4+ (-3.1) + (-4.5)=
Answer:
-6.2
Step-by-step explanation:
1.4-3.1-4.5
=-1.7-4.5
=-6.2
Please help now ASAP
Answer:
A quadrilateral is a parallelogram if and only if opposite angles are equal.
So, to make the quadrilateral a parallelogram, we can set the following equalities:
(4x + 13) deg = (5x - 12) deg
(4y + 7) deg = (3x - 8) deg
Solving the first equation,
4x + 13 = 5x - 12
x = -5
Solving the second equation,
4y + 7 = 3(-5) - 8
4y + 7 = -17
4y = -24
y = -6
So, the values of x and y that make the quadrilateral a parallelogram are x = -5 and y = -6
Reduce to first order and solve. (1 - x2 )y" - 2xy' + 2y = 0, y1 = x. Use: -Sp dx = In [1/(1-x2)] find U with its integral. to get y2 = uyi. O a. Y2 = yıu = Y SU dx = 2 + 5 x In [(x+1)/(x-1)] O b. y2 = yıu = yısu dx = -1 + 0.5 x In [(x+1)/(x-1)]. O c. y2 = yıu = yılU dx = 10 + 20 x In [(x+1)/(x-1)] O d. y2 = yıu = YISU dx = 1 + 2 x In [(x+1)/(x-1)].
After converting the given differential equation into first order we will get it as [tex]\Rightarrow y_2=\frac{1}{2} x \ln |1+x / 1-x|-1[/tex]
The equation dy/dx =f (x,y) with two variables x and y with its function f(x,y) specified on a region in the xy-plane defines a first-order differential equation. There are no higher-order derivatives since it only contains the one derivative, dy/dx, making it a first-order equation.
The given differential equation is
[tex]\left(1-x^2\right) y^{\prime \prime}-2 x y^{\prime}+2 y=0----(i)[/tex] with y_1=x [tex]\Rightarrow & y^{\prime \prime}-\frac{2 x}{1-x^2} y^{\prime}+\frac{2}{1-x^2} y=0\end{aligned}$$[/tex]
Equation (1) is in the form of
[tex]$$y^{\prime \prime}+p(x) y^{\prime}+q(x) y=0$$[/tex]
where [tex]$p(x)=\frac{-2 x}{1-x^2}, \quad q(x)=\frac{2}{1-x^2}$[/tex]
As we know that if y_1 is given, we can find y_2 as:
y_2=4y_1, where u is a function of x and can be determined by
[tex]$U=\int \frac{e^{-\int p d x}}{y_1^2} d x$[/tex]
[tex]=\int \frac{e^{-\int \frac{-2 x}{1-x^2}} d x}{x^2} d x\\=\int \frac{e^{-\ln \left|1-x^2\right|}}{x^2} d x\\=\int \frac{1}{x^2\left(1-x^2\right)} d x\\=\int \frac{\left(1-x^2\right)+x^2}{x^2\left(1-x^2\right)} d x\\=\int\left(\frac{1}{x^2}+\frac{1}{1-x^2}\right) d x[/tex]
[tex]$$\begin{aligned}& =\int \frac{1}{x^2} d x+\int \frac{1}{1-x^2} d x \\& =-\frac{1}{x}+\int \frac{1}{1-x^2} d x\end{aligned}$$[/tex]
Now, [tex]$\int \frac{1}{1-x^2} d x=\int f(x) d x$[/tex] (say)
Where, [tex]$f(x)=\frac{1}{1-x^2}=\frac{1}{(1+x)(1-x)}$[/tex]
[tex]=\frac{A}{1+\eta}+\frac{B}{1-x} \\[/tex]
1=A(1-x)+B(1+x)
Putting x = 1, we will get B = 1/2
x = -1, we will get it as: A = 1/2
[tex]\therefore \int \frac{1}{1-x^2} d x=\int \frac{1 / 2}{1+n} d x+\int \frac{1 / 2}{1-x} d x[/tex]
[tex]=\frac{1}{2} \ln |1+x|-\frac{1}{2} \ln |1-x|\\=\ln \sqrt{1+x}-\ln \sqrt{1-x}\\\\=\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)\\\Rightarrow \int \frac{1}{1-x^2} d x=\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)[/tex]
Hence [tex]$u=-1 / x+\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)$[/tex]
[tex]\Rightarrow y_2=u \cdot y_1=x\left[-1 / x+\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)=x \ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)-1\right.\\\Rightarrow y_2=\frac{1}{2} x \ln |1+x / 1-x|-1[/tex]
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In art class, the students each made rectangular quilts using 24 paper
squares. They then glued a button onto each square and decorated the
squares with markers.
1. Create all of the possible arrays for modeling a rectangular quilt with
the 24 paper squares. Write an equation to accompany each array.
You can use the attached pre-made quilt squares by cutting and
pasting them, or you can draw the arrays with your own designs on a
separate sheet of paper?
ANSWER PLS AND U GET 30 POINTS
Answer:
There are many possible arrays that could be used to model a rectangular quilt with 24 paper squares. Here are a few examples:
A 3x8 array could be created by gluing the paper squares into a rectangle that is 3 squares wide and 8 squares long. This could be represented by the equation 3x8 = 24.
A 4x6 array could be created by gluing the paper squares into a rectangle that is 4 squares wide and 6 squares long. This could be represented by the equation 4x6 = 24.
A 6x4 array could be created by gluing the paper squares into a rectangle that is 6 squares wide and 4 squares long. This could be represented by the equation 6x4 = 24.
A 8x3 array could be created by gluing the paper squares into a rectangle that is 8 squares wide and 3 squares long. This could be represented by the equation 8x3 = 24.
These are just a few examples, but there are many other possible arrays that could be created with 24 paper squares. Some other examples might include a 2x12 array, a 6x4 array, or even a 1x24 array. The key is to find combinations of width and length that will multiply together to equal 24.
Step-by-step explanation:
14. What is the value of x and y? Show all work. (3 points)
I’ll give 20 points
Answer:
x = 71
y = 71
Step-by-step explanation:
The value of x and y would be the same because this is an isosceles triangle.
38 + x + y = 180
x + y = 142
142/2 = 71
x = 71
y = 71
HELP PLEASE!
(Needed ASAP)
Which of the following graphs has a slope of negative two thirds and a y-intercept of 2?
i think its D but im not sure
if diagram d depicts the orbital occupancy of the cobalt ion in [cof6]n, what is the value of n?
The value that shows the occupancy for the cobalt ion is -1. Option B
What is the occupancy?We know that the electrons can be found in the orbitals that are contained in the atom. The d orbital diagram is the image that shows the occupancies of the d orbital of the atom. This is the number of the electrons that can be found in a particular orbital.
Let us note that the elements that have a d level that is not completely occupied as said to be the transition elements. As such the transition elements are the elements that have d orbitals that are incompletely filled.
We have a transition metal complex here and the number or the magnitude of the charge that is carried by the complex is what has been designated as n in the image that has been attached here.
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(Multiplying Linear Expressions LC)
Simplify five eights times a times three-sevenths times a.
30 over 56
15 over 56 times a squared
30 over 56 times a squared
15 over 56 times a
Answer:
(b) 15 over 56 times a squared
Step-by-step explanation:
You want the product of (5/8a) and (3/7a).
MultiplicationThe commutative and associative properties of multiplication help you find this product:
[tex]\dfrac{5}{8}a\,\times\,\dfrac{3}{7}a = \left(\dfrac{5}{8}\cdot\dfrac{3}{7}\right)\times (a\cdot a)=\dfrac{5\cdot3}{8\cdot7}a^2=\boxed{\dfrac{15}{56}a^2}[/tex]
Find the measure of angel b
Answer:
b = 138⁰ (Being alternate angles)
A student states that a triangle can be formed with side lengths 3 in, 5 in, and 9 in. Is the student correct? why, or why not?.
The student is not correct when he forms a triangle with side lengths 3 ,5 ,9 inches.
A triangle contains of 3 sides and 3 angles
The Triangle Inequality Theorem, which asserts that the total of any two sides must be greater than the third side, must be followed in order to determine whether a collection of integers is a legitimate measure of a triangle's sides.
as per the details stated above
Let a is 3 inches , b is 5 inches c is 9 inches
According to the triangle Inequality theorem
a + b > c
that is 8>9
which is incorrect
a + c > b
that is 12 > 5
which is correct
b + c > a
14 > 3
which is correct
as the theorem it does not satisfy one case so we can say that it will form a triangle
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No, the student is not correct. To form a triangle, all three sides must follow the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is not greater than 9, making it impossible to form a triangle.
No, the student is not correct. To form a triangle, all three sides must follow the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is not greater than 9, making it impossible to form a triangle. This theorem is based on the idea that the longer side of a triangle must always be opposite the largest angle. Therefore, the longest side of the triangle must be less than the sum of the other two sides. Essentially, this means that in order for a triangle to be formed with side lengths of 3 in, 5 in, and 9 in as the student suggests, the longest side must be less than 8 in, which is not possible. Therefore, the student is incorrect, and it is impossible to form a triangle with the side lengths they have provided.
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a restaurant server averages $30 in tips for a 4 hour shift. At this rate, how many hours would the server have to work to earn $135 in tips?
There are 18 hours would the server have to work to earn $135 in tips.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A restaurant server averages $30 in tips for a 4 hour shift.
Now,
Since, A restaurant server averages $30 in tips for a 4 hour shift.
Hence, The time for a restaurant server averages in tips $1 = 4/30
So, The time for a restaurant server averages in tips $135 = 4/30 × 135
= 18 hour
Thus, The time for a restaurant server averages in tips $135= 18 hours
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What number is a multiple of 8?
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so forth.
A multiple of 8 is a sequence where the difference among each next number and the previous number is 8. In other words, multiples of 8 are numbers which can be divided exactly by 8. Multiples of 8 are found by counting up in eights.
We also can see that the multiples of 8 are in the table of 8. The first multiples of 8 are 8, 16, 24, 32, 40. And the prime factorization of 8 is 8 = 2 × 2 × 2 = 2³.
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how to put y=2x in a table
Answer:
Step-by-step explanation:
I got you. ( It's basically just y is double x.)
y x
2 1
4 2
6 3
8 4
10 5
Is t = 9 a solution to the inequality below? t ≤ 10 yes no
Answer:
Yes, t=9 is a solution to the inequality t ≤ 10. When t is equal to 9, the inequality is satisfied because 9 is less than or equal to 10.
Step-by-step explanation:
Answer:
I thing yes! because ≤ means less than or equal to, which 9 is less than 10.
Step-by-step explanation:
Hope it helps!
3. a. Given parallelogram ABCS, what are m is congruent to A and m is congruent to C?
The required measures of the angles of parallelogram ABCD as are follows m∠A = 66°, m∠B = 114°, and m∠C = 66°.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Given parallelogram ABCD,
m∠D = 114°
In a parallelogram, the opposite angles are congruent, so m∠A is congruent to m∠C. This means that m∠A and m∠C have the same measure.
If m∠D = 114°, then m∠A must be equal to 180° - 114° = 66°, since the measures of the adjacent angles of a parallelogram add up to 180°.
So, m∠A = m∠C = 66°
So, m∠B = 114°
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A parabola opening up or down has vertex (0,0) and passed through (-4,1). Write its equation in vertex form. simplify any fractions
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies y=a(x-0)^2+0\hspace{5em}\textit{we also know that} \begin{cases} x=-4\\ y=1 \end{cases} \\\\\\ 1=a(-4-0)^2 + 0\implies 1=16a\implies \cfrac{1}{16}=a~\hfill \boxed{y=\cfrac{1}{16}x^2}[/tex]
An angle measures 106° less than the measure of its supplementary angle. What is the measure of each angle
Answer:
143 degrees, 37 degrees
Step-by-step explanation:
Let's say the angle is x and the supplementary angle is x-106:
x + (x-106) = 180 ==> supplementary angles add up to 180 degrees
x + x - 106 = 180
2x - 106 = 180
2x = 286 ==> isolate x by adding 106 to both sides
x = 143 ==> divide 2 on both sides
x-106=
143-106 = 37
Answer: 143 degrees, 37 degrees
What is the domain of the function y=3sqrrt x?
Answer:
Step-by-step explanation:
it looks like squirt
so 33 = y
There are y yellow dogs out of a total of 12 dogs at obedience class. Write an expression that shows the number of dogs that are not yellow.
Answer: Don't use this if it is a test!
Step-by-step explanation:
Hello! An equation for this to represent the number of dogs that are not yellow is 12 dogs - yellow dogs = dogs that are not yellow. Make an expression out of this with numbers and variables! I hope this helps you!
4.Reason Alyssa has a CD that holds 700 megabytes
of information. She has saved 53 pictures, each using
2.24 megabytes, to the CD. How much space is left
on the CD? Elementary school
Analyzing the provided total storage for the CD and amount of pictures stored in it, Using simple difference , The answer is 581.28 megabytes.
What do you mean by storage?Storage refers to the process of preserving data in a computer or other electronic device for later retrieval. This can include both short-term storage, such as in RAM, and long-term storage, such as on a hard drive or in the cloud. Data can be stored in various formats, including text, images, videos, and audio. Storage devices come in different forms including internal storage, external storage, removable storage, and cloud storage.
What do you mean by difference?The term "difference" in mathematics can refer to a few different concepts, depending on the context. In subtraction, the difference between two numbers is the result of subtracting one number from the other. For example, the difference between 8 and 3 is 8 - 3 = 5. In set theory, the difference between two sets is a new set that contains all the elements that are in the first set, but not in the second set. In geometry, the difference between two shapes is the area left over when one shape is subtracted from the other.
total = 700 MB
used by pictures = 53 * 2.24 = 118.72 MB
Space left = 700 - 118.72 = 581.28 MB
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The side lengths of a 30-60-90 triangle are in the ratio 1: √3:2. What is tan 60°?
A. √3/2
B. 1/2
C. √3/3
D. √3
Answer:
D [tex]\sqrt{3}[/tex]
Step-by-step explanation:
tan60 is the same for all values when you plug it into a calculator you will get [tex]\sqrt{3}[/tex]
Use the distributive property with factoring to find the equivalent expression.
21x + 39z = (7x + z)
Answer:
x = -19/7 z
z = -7/19 x
Lets solve for x in 21x + 39z = (7x+z):
Step 1: Add -7x to both sides.
21x+39z+−7x=7x+z+−7x
14x+39z=z
Step 2: Add -39z to both sides.
14x+39z+−39z=z+−39z
14x=−38z
Step 3: Divide both sides by 14.
14x/14 = −38z/14
x = −19/7 z
Lets solve for z in 21x 39z = (7z+z):
Step 1: Add -z to both sides.
21x+39z+−z=7x+z+−z
21x+38z=7x
Step 2: Add -21x to both sides.
21x+38z+−21x=7x+−21x
38z=−14x
Step 3: Divide both sides by 38.
38z/38 = −14x/38
z = −7/19 x
Hope this helps!!
bob is building a treehouse he was locations for four holes that will hold his corner post they form a figure with a long side with 12 feet and a short side of 9 feet wha must the diagnol of the figure be to make sure the base of his tree house is a rectangle
The diagonal length of the figure, to make sure the base of his tree house is a rectangle, is given as follows:
15 feet.
How to obtain the diagonal of the figure?We want for the figure in this problem to represent a rectangle. For a rectangle, the diagonal is the hypotenuse of a right triangle in which the side lengths are the same as the side lengths of the triangle, and there is an angle of 90º between them.
Hence the Pythagorean Theorem can be used to obtain the diagonal, which states that the length of the hypotenuse squared is equals to the sum of each of the sides of the triangle squared.
Then the diagonal length is calculated as follows:
d² = 12² + 9²
d = square root (12² + 9²)
d = 15 feet.
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The graph of g(x) is a transformation of the graph of f(x)=3x.
Enter the equation for g(x) in the box.
g(x) =
Considering the graph of g(x) which is a transformation of the graph of
f(x) = 3ˣ, the equation for g(x) is
g(x) = 3ˣ ⁺ ¹- 2
How to interpret the transformationTranslation say x units to the left is represented by positive x units while to the right is represented by negative x values. the left and right translation is restricted to the x values.
Translation say x units up is represented by positive x units while to the down is represented by negative x values. the top and down translation is restricted to the y values or the function itself.
The transformation of f(x) = 3ˣ include
translation 1 unit to the left = x + 1 putting to the equation yields 3ˣ ⁺ ¹
translation 2 units to the down = "the equation itself" - 1 putting to the equation yields 3ˣ ⁺ ¹- 2
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Please help as fast as you can
Answer:
b
production of pancakes depends on batter
Answer:
b, because they are asking how much batter(b) they will need to make pancakes(p), which the dependent variable is what happens as a result of the independent variable, which in this case it is, b, or the batter to make the pancakes, so the dependent variable would be b.
Step-by-step explanation:
Hope it helps!