Mackenzie borrowed some money from her
friend in order to help buy a new video game
system. Mackenzie agreed to pay the friend back
some amount every week until her loan was paid
off. Let L represent the amount Mackenzie owes
her friend after t weeks. The table below has
select values showing the linear relationship
between t and L. Determine how many weeks
when the amount of money Mackenzie owed her
friend was $100.

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!

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)

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

Translation 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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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!

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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Answer:

don't know if I am correct but,

18<n<20

so must be 19.

The diagonal length of the figure, to make sure the base of his tree house is a rectangle, is given as follows:

15 feet.

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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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

The value of x ≈ 8.0 rounded to the nearest tenth.

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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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]

Answer:

Step-by-step explanation:

it looks like squirt

so 33 = y

The expression 6wy-2wz+3xy-xz can be factorized into (2w+x) ( 3y-z). The value of a and b are 2 and 3 respectively

To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In another word, the reverse process of expansion of an algebraic expression is its factorization.

to factorize 6wy-2wz+3xy-xz , we firstly collect like terms, 6wy + 3xy -2wz - xz

The next step is to group the expression into two

(6wy+3xy)(-2wz-xz)

bringing out the factors in each parentheses

3y( 2w+x) -z(2w+z)

therefore 6wy-2wz+3xy-xz = (3y-z)(2w+z)

comparing the expression (aw+x)(by-z)

Therefore a = 2 and b= 3

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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!!

If the dot plot is converted to a box plot, the first quartile would be drawn at 61 and the third quartile would be drawn at 63.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the dot plot, the average daily temperatures include the following:

Temperature                  frequency            

  59                                   0

  60                                   2

  61                                    3

  62                                   3

  63                                   4

  64                                   2

  65                                   1

Total                                 15

By grouping the average daily temperatures, we have:

(60, 60, 61), 61, (61, 62, 62), 62, (63, 63, 63), 63, (64,64,65)

First quartile = 61.

Median = 62.

Third quartile = 63.

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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:

Answer:

-6.2

Step-by-step explanation:

1.4-3.1-4.5

=-1.7-4.5

=-6.2

Answer:

  (b)  15 over 56 times a squared

Step-by-step explanation:

You want the product of (5/8a) and (3/7a).

The 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]

Answer:

27

Step-by-step explanation:

Answer:

it is a one-to-one function

Step-by-step explanation:

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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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

There are 18 hours would the server have to work to earn $135 in tips.

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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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

The required measures of the angles of parallelogram ABCD as are follows m∠A = 66°,  m∠B = 114°, and m∠C = 66°.

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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Each student must work 14 hours on the project.

To solve this problem, we need to isolate the variable x on one side of the equation.

First, we can get rid of the fraction on the left side of the equation by multiplying both sides by 5:

5 * (x + 28) / 5 = 5 * (3x) / 5

This simplifies to:

x + 28 = 3x

Then, we can subtract x from both sides to get:

x + 28 - x = 3x - x

This simplifies to:

28 = 2x

Finally, we can divide both sides by 2 to find the value of x:

28 / 2 = 2x / 2

This simplifies to:

14 = x

Therefore, each student must work 14 hours on the project.

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Each student must work 14 hours on the project.

this is a question of set of equations, the solution is as follows,

we can get rid of the fraction on the left side of the equation by multiplying both sides by 5:

5 * (x + 28) / 5 = 5 * (3x) / 5

x + 28 = 3x

Then, we can subtract x from both sides to get:

x + 28 - x = 3x - x

28 = 2x

2x=28

Finally, we can divide both sides by 2 to find the value of x:

2x/2 = 28/2

x = 14

Therefore, each student must work 14 hours on the project.

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The area of the triangle and the square are the same = 4 square units

How to determine the area?

You should know that the area talks about the floor space occupied by each shape.

The square occupies 2 units on the base and two units on the height

The triangle occupies two grids on the base and four grids on the height

Area of square is S² and Area of a triangle is 1/2base*height

⇒Area of square is = 2² = 4 ²square units

Area of triangle = 1/2 * 2 * 4 = 4 square units.

In conclusion the area of the triangle is equal to the area of the square with 4 units square each

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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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Answer:

b = 138⁰ (Being alternate angles)