Scalar multiplication quiz

The number of sodas sold was three times the number of hot dogs sold, so if we set up an equation, it would be 3x + x = 220, where x is the number of hot dogs sold. To solve this equation, we can subtract x from both sides, leaving us with 2x = 220. Then, we can divide both sides by 2, leaving us with x = 110. This means that 110 hot dogs were sold and 3x = 330 sodas were sold.

The homogeneous equation and a particular solution of the given nonhomogeneous equation is [tex]& y=c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}[/tex].

The given nonhomogeneous equation is y" - 4y = 2

We are given [tex]$y_1=e^{-2 x}$[/tex]

Let [tex]$y_2=u y_1$[/tex]

Non-homogeneous differential equations are simply differential equations that do not satisfy the conditions for homogeneous equations. In the past, we’ve learned that homogeneous equations are equations that have zero on the right-hand side of the equation.

The two most common methods when finding the particular solution of a non-homogeneous differential equation are:

[tex]$$\begin{aligned}& y_2=u e^{-2 x} \\& y_2^{\prime}=u^{\prime} e^{-2 x}-2 u e^{-2 x} \\& y_2^{\prime \prime}=u^{\prime \prime} e^{-2 x}-2 u^{\prime} e^{-2 x}-2 u^{\prime} e^{-2 x}+4 u e^{-2 x} \\& y_2^{\prime \prime}=u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}+4 u e^{-2 x}\end{aligned}$$[/tex]

Substitute in [tex]$y^{\prime \prime}-4 y=0$[/tex], we get

[tex]$$\begin{aligned}& u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}+4 u e^{-2 x}-4 u e^{-2 x}=0 \\& u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}=0 \\& e^{-2 x}\left(u^{\prime \prime}-4 u^{\prime}\right)=0 \\& u^{\prime \prime}-4 u^{\prime}=0 \\& u^{\prime \prime}=4 u^{\prime}\end{aligned}$$[/tex]

Substitute [tex]$$u^{\prime}=v$ and $u^{\prime \prime}=v^{\prime}$[/tex], we get

[tex]$$\begin{aligned}& v^{\prime}=4 v \\& \frac{d v}{d x}=4 v \\& \frac{1}{v} d v=4 d x\end{aligned}$$[/tex]

Integrate both sides, we get

[tex]$u=\frac{1}{4} C_1 e^{4 x}+C_2$$[/tex]

put in [tex]$y_2=u y_1$[/tex]

[tex]$$y_2=\left(\frac{1}{4} C_1 e^{4 x}+C_2\right) e^{-2 x}$$[/tex]

Choose [tex]$$C_1=4$ and $C_2=0$[/tex], we get

[tex]$$y_2=e^{2 x}$$[/tex]

[tex]$$\begin{aligned}& y_c=c_1 y_1+c_2 y_2 \\& y_c=c_1 e^{-2 x}+c_2 e^{2 x}\end{aligned}$$[/tex]

Particular Solution

[tex]$$\begin{aligned}& y_y=A \\& y_y{ }^{\prime}=0 \\& y_y{ }^{\prime \prime}=0\end{aligned}$$[/tex]

Substitute in [tex]$y^{\prime \prime}-4 y=2$[/tex], we get

[tex]$$\begin{aligned}& 0-4 A=2 \\& -4 A=2 \\& A=-\frac{1}{2} \\& \therefore y_y=-\frac{1}{2}\end{aligned}$$[/tex]

General Solution

[tex]$$\begin{aligned}& y=y_6+y_y \\& y=c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}\end{aligned}$$[/tex]

Therefore, the second equation is [tex]& y_{2} =c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}[/tex].

For more such questions on homogeneous & nonhomogeneous equation

https://brainly.com/question/15839620

#SPJ4

Answer:

$6.36

Step-by-step explanation:

6 x 1.06 = 6.36

Food lion sells one can at $0.8 and Aldi sells one can at $1.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Food Lion sells 5- 15 ounce cans of beans for $4.00.

Aldi sells 4- 15 ounce cans for $4.00.

So, Food lion sell one can

= 4/5

= $0.8

and, Aldi sells one can at

= 4/4

= $1

Hence, Food lion sell at $0.8 and Aldi sells for $1.

Learn more about unitary Method here:

https://brainly.com/question/22056199

#SPJ1

The fourth graph (the right graph in the bottom row) is discovered to represent the function f using translation notions (x).

A sort of transformation called a translation involves moving each point in a figure the same distance in the same direction.

In terms of operations like multiplication or sum/subtraction in its definition, a translation is represented as a change in the function graph.

has a vertex at the origin and [tex]$f(x)=\sqrt{x}$[/tex] is the parent function.

In this issue, the translated function is [tex]$f(x)=2 \sqrt{x+1}$[/tex] It was left 1 unit relocated and vertically stretched by a factor of 2 units, resulting in a new vertex position of (0,-1).

As a result, the fourth graph, on the right side of the bottom row, represents the function f. (x).

To learn more about translation refer to:

https://brainly.com/question/1046778

#SPJ1

Answer:

1.5 or greater than 1.5

Step-by-step explanation:

First, we need to determine the total score of your opponent's dive:

40.8 points / 2.4 (degree of difficulty) = 17 (total score)

Now, we know that your total score needs to be greater than 17, and the scores awarded by the three judges are added together.

To calculate the scores from the third judge, we can use the following equation:

(Total score) - (score from judge 1) - (score from judge 2) = (score from judge 3)

Let's assume that you received scores of 8 and 7.5 from the first two judges.

We can plug in the values into the equation:

(Total score) - (8) - (7.5) = (score from judge 3)

We know that your total score needs to be greater than 17, so we have to find the score from the third judge, that when added to the scores 8 and 7.5, gives a total score greater than 17

17 - 8 - 7.5 = 1.5

The score from the third judge should be 1.5 or greater than 1.5 in order to give you more points than your opponent.

Therefore, the appropriate response for function problem  is Option B) This cat weighs 4 kilos at 7 months of age.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single variable, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x).

Here,

When the cat is m months old, w provides the cat's weight in kg.

the meaning of w(7) = 4 must be determined.

We already know that w represents weight in kilos.

When we enter the age in years, it returns the weight, which is what we consider to be the input.

W(7) stands for the weight of the cat at 7 months old.

where w(7) = 4 denotes the cat's weight at 7 months old, which is 4 kilograms.

Therefore, the appropriate response is Option B) This cat weighs 4 kilos at 7 months of age.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The series of transformations that would map figure D onto figure E is a

reflection over Y = -X.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The coordinates of Figure D are:

(4, 1), (1, 9), (5, 9), (7, 4), (6, 4).

The coordinates of Figure E are:

(-1, -4), (-9, -1), (-9, -5), (-4, -7), (-4, -6)

We see that,

The coordinates transformation:

(4, 1) → (-1, -4)

(1, 9) → (-9, -1)

(5, 9) → (-9, -5)

(7, 4) → (-4, -7)

(6, 4) → (-4, -6)

This is a reflection over Y = -X.

The reflection over Y = -X is (x, y) → (-y, -x).

Thus,

The transformations that would map figure D onto figure E are a

reflection over Y = -X.

Learn more about reflections here:

https://brainly.com/question/12463306

#SPJ1

Answer:

  176 cm

Step-by-step explanation:

You want the circumference of a wheel with a radius of 28 cm.

The circumference of a circle is given by ...

  C = 2πr

For r = 28 cm, this is ...

  C = 2π(28 cm) = 56π cm ≈ 176 cm

The circumference of the wheel is 56π cm, about 176 cm.

<95141404393>

The measure of the other two angles are 88 degrees and 22 degrees.

Let's call the two unknown angles x and y. Since the sum of all angles in a triangle is 180 degrees, we have:

x + y + 70 = 180

We also know that the ratio of the two angles is 4:7. We can set up a proportion to express this relationship:

x/y = 4/7

We can cross-multiply to get:

7x = 4y

We can substitute this equation into the first equation to eliminate one of the variables.

7x + y + 70 = 180

Now we have:

7x + y = 110

We can use the second equation to eliminate x:

7(4y/7) + y = 110

4y + y = 110

5y = 110

y = 22

Now that we know one of the angles is 22 we can substitute it back in the first equation

x+22+70 = 180

x = 88

Therefore, the measures of the other two angles are 88 and 22 degrees

Read more about the sum of all angles of a triangle:

https://brainly.com/question/22262639

https://brainly.com/question/8107050

[tex](7j+8)-(4j+6)[/tex]

Distribute negative sign:

[tex]7j+8+-1(4j)+(-1)(6)[/tex]

[tex]7j+8-4j-6[/tex]

Combine Like terms:

[tex](7j-4j)+(8-6)[/tex]

[tex]\fbox{3j + 2}[/tex]

Answer:

The Answer would be 0.6666 repeated

Step-by-step explanation:

I don't think that I have to explain the process. it would be too long to read!

The correct statement regarding the scatter plot is given as follows:

C. There were three athletes who had the same time in both races.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

The input and output variables for this problem are given as follows:

The points are given as follows:

(15, 15), (16, 15), (17, 15), (19, 15), (16, 16), (17, 16), (18, 16), (19, 16), (18, 18), (17, 19)

For example, the point (16, 15) means that the person took 16 seconds for the first race and 15 seconds for the second race.

Hence statement C is correct, as the points (15,15), (16, 16) and (18,18) means that there were three athletes who had the same time in both races.

The scatter plot is given by the image presented at the end of the answer.

More can be learned about scatter plots at brainly.com/question/6592115

#SPJ1

A homogeneous mixture with two or more substances is called a solution. Household remedies frequently take the form of substances that have been dissolved in water, like juice concentrate.

Solutions are any mixtures of substances that have been dissolved.

A solution can be diluted by adding more solvent or by removing solutes. You can concentrate it by removing solvent or adding more solutes.

The following are some illustrations of simple fixes:.

To know more about the solution, here

https://brainly.com/question/19587902

#SPJ4

Answer:

"A) 12n + 14m + 4" would be the standard form.

Step-by-step explanation:

the expression written correctly in standard form would be "A) 12n + 14m + 4"

10m + 3(n + 8) + 4(m - 5) + 9n you need to first clear the parenthesis by applying distributive property:

10m + 3(n + 8) + 4(m - 5) + 9n = 10m + 3n + 24 + 4m - 20 + 9n

After that you combine like terms

= 10m + 4m + 3n + 9n + 24 - 20 = 14m + 12n + 4

"A) 12n + 14m + 4" would be the standard form.

Gametes carry half the genetic information of an individual, one ploidy of each type, and are created through meiosis, in which a germ cell undergoes two fissions, resulting in the production of four gametes.

Mendel's Law I has another name, namely the Law of Segregation. In the Law of Segregation it states that "In the formation of gametes (sex cells) in the two genes which are partners, will be separated in two daughter cells". Mendel's Law I or the Law of Segregation applies to monohybrid crosses, aka crosses with one different trait.

Mendel's First Law also states that two alleles (gene variants) that regulate certain traits will separate in two different gametes (sex cells). Mendel's Law I includes several things, namely:

Learn more about Mendel's law https://brainly.com/question/23067535.

#SPJ4

The rate of change of the area of the right triangle at that instant is -1.5 sq km/h.

Make ABC a right triangle with a right angle to B.

BC = x on the side decreasing be

with AB = y being the rising side.

After that, AC = z = (x² + y2) (using Pythagoras theorem)

Given that dx/dt is equal to -5 km/h and dy/dt is equal to 14 km/h

When x = 3 and y = 9, respectively.

currently, the triangle's area equals xy/1/2.

A = 1/2 xy

dA/dt = 1/2 (y) (y).

dy/dt = dx/dt + x/2.

by inserting the values at x = 3 and y = 9,

(dA/dt) = 1/2 (9)(-5) + 3/2 (14) (14)

= -1.5

As a result, the right triangle's area is changing at a rate of -1.5 sq km/h at the moment when x=3 and y=9.

Your question is incomplete but most probably your full question was

One leg of a right triengle is decreasing at a tate of 5 kilometers per hour and the other leg of the triangle is increasing at a rete of 14 kilometers per hour. Ara certain anstant the decreasing leg is 3 kilometers and the increasing leg is 9 kilometers. What is the rate of change of the area of the right triangle at that instant (in square kilometers per hour)? 11 e 111 01.5 -1.5 Stuck?

know more about the area of a triangle here: brainly.com/question/19305981

#SPJ4

Answer: 3 : 8

Step-by-step explanation:

red to blue is 3 : 5

blue to yellow is 3 : 8

red to yellow is 3 : 8

The fraction of the marble in the bag are blue is 4/15

The term fraction can be found by dividing part of a whole by the whole. Here the example if 2 students out of a total of 4 are picked, then the part is 2 and the whole is 4 while the fraction is 2 by 4.

Here we have given that a bag has 16 blue, 20 red, and 24 green marbles.

And we need to find the fraction of the marbles in the bag are blue

While looking into the given question, we have identified that the number of blue marbles is 16.

And the total number of marbles is calculated by adding the number of each marbles, then we get,

=> 16 + 20 + 24 = 60.

Here we know the the resulting fraction is obtained by the number of blue marbles out of the total marbles is,

Then it can be written as

=> 16/60

When we simplify this one then we get,

=> 4/15

To know more about Fraction here.

https://brainly.com/question/10354322

#SPJ4

Options A and B are the correct answers.

The exponent or power to which a base must be raised to yield a given number is called a logarithm.

x is the logarithm of n to the base b if bx = n, in which case one writes

x = logb n.

“The logarithm of a positive real number a with respect to base b, and a positive real number not equal to 1^[nb 1], is the exponent by which b must be raised to yield a”.

b^y=a ⇔logba=y

To calculate the value of log₁₂81 we use the formula of

log ab=logb/loga=ln b/ln a

log₁₂81=log₁₀81/log₁₀12

           =log81/log12

Also, log e81=loge81/loge12

                    =ln81/ln12

So, choose log81/log12 and ln81/ln12

To know more about Logarithms:

https://brainly.com/question/10208274

#SPJ4

Answer:

see photo, they change out answer order to look close.  :-)

Step-by-step explanation:

Plato/Edmentum

The four parts of a polygon are: sides, vertices, diagonals, and interior angles.

Polygon is a closed figure in a plane made of of straight line or curved line that insert in pairs a polygon has at least three side of angle the height can be of any length and the angle can be of any measure polygon or classified according to the number of side they have such as triangle.

A polygon is a closed, two-dimensional shape with three or more straight sides. The four parts of a polygon are: sides, vertices, diagonals, and interior angles. The sides are the straight line segments that make up the shape. The vertices are the points where the sides meet. The diagonals are line segments joining any two non-adjacent vertices. The interior angles are the angles inside the polygon, which are determined by the number of sides the polygon has.

To know more about polygon click-
https://brainly.com/question/26583264
#SPJ4

The daily increase in Mrs. Miller's daily class is $2 more than it is in Mr. Taylor's class.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Mr. Taylor:

The coordinates from the graph.

(1, 10), ), (2, 20), (3, 30)

The rate of change.

= (20 - 10) / (2 - 1)

= 10

This means,

Each day the amount is increased by $10.

Mrs. Miller:

From the table,

(3, 24), (5, 60)

Rate of change.

= (60 - 24) / (5 - 3)

= 36 / 2

= 12

This means,

Each day the amount is increased by $12.

Thus,

Mrs. Miller's daily increase is $12.

Mr. Taylor's daily increase is $10.

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction number is given below.

⇒ 35 / 80

⇒ 7 / 16

⇒ 21 / 48

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ1

The hourly rate of Sheila Blige if she worked for 40 regular hours and 8 overtime hours and paid a gross of $884.00 is $17

Total regular hours worked = 40

Total overtime hours worked = 8

Total gross pay = $884.00

Let

Hourly rate = x

Overtime rate = 1.5x

So,

40x + 8(1.5x) = 884

40x + 12x = 884

52x = 884

divide both sides by 52

x = 884 / 52

x = $17

Therefore,

Hourly rate = x

= $17

Overtime rate = 1.5x

= 1.5(17)

= $25.5

Read more on gross pay:

https://brainly.com/question/13793671

#SPJ1

The quotient of the given expression is calculated by dividing one fraction by another fraction. The result is 0.75.

When two numbers are divided, a new number called a quotient is produced. The formula to calculate this quotient is Quotient = Dividend÷Divisor. Consider the expression 40÷4. Here, 40 is the dividend, 4 is the divisor, 10 is the quotient, and 0 is the remainder.

The given expression is (-2/3)/(-8/9). This can be solved using the formula   [tex]\frac{A}{B}\div\frac{C}{D}=\frac{A}{B}\times\frac{D}{C}[/tex]. Here, A is -2, B is 3, C is -8, and D is 9. Substituting these values, we get,

[tex]\begin{aligned}\frac{A}{B}\div\frac{C}{D}&=\frac{A}{B}\times\frac{D}{C}\\\frac{-2}{3}\div\frac{-8}{9}&=\frac{-2}{3}\times\frac{9}{-8}\\&=\frac{3}{4}\\&=0.75\end{aligned}[/tex]

The required answer is 0.75.

The complete question is -

What is the quotient (-2/3)/(-8/9)?

To know more about quotient:

https://brainly.com/question/29786626

#SPJ4

Answer:

78 that he added

Step-by-step explanation: not needed

The school's population in the year 2017 is given by the equation A = 1620

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the school's population in 2017 be represented as A

Now , the equation will be

The school's population in 2016 = 1500 students

The percentage of increase in population = 8 %

So , school's population in 2017 A = school's population in 2016 + ( 8/100 ) x school's population in 2016

Substituting the values in the equation , we get

The school's population in 2017 A = 1500 + ( 0.08 x 1500 )

On simplifying the equation , we get

The school's population in 2017 A = 1500 + 120

The school's population in 2017 A = 1620 students

Hence , the population is 1620 students

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1