Write the equation below in standard form and then answer the following questions. If a value is a non-integer type your answer as a decimal rounded to the hundredths place. 4x^2+24x+25y^2+200y+336=0The center of the ellipse is (h,k). h= Answer and k= AnswerThe value for a is Answer . The value for b is Answer .The foci with the positive x value is the point ( Answer, Answer)The foci with the negative x value is the point ( Answer, Answer)

Write The Equation Below In Standard Form And Then Answer The Following Questions. If A Value Is A Non-integer

Answers

Answer 1

Given:

[tex]4x^2+24x+25y^2+200y+336=0[/tex]

Aim:

We need to convert the given equation into the standard form of the ellipse equation.

Explanation:

Consider the standard form of the ellipse equation.

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Consider the given equation.

[tex]4x^2+24x+25y^2+200y+336=0[/tex][tex]Use\text{ }336=36+400-100.[/tex]

[tex]4x^2+24x+25y^2+200y+36+400-100=0[/tex]

[tex]4x^2+24x+36+25y^2+200y+400-100=0[/tex]

Take out the common terms.

[tex]4(x^2+6x+9)+25(y^2+8y+16)-100=0[/tex]

Add 100 on both sides of the equation.

[tex]4(x^2+6x+9)+25(y^2+8y+16)-100+100=0+100[/tex]

[tex]4(x^2+6x+9)+25(y^2+8y+16)=100[/tex]

[tex]4(x^2+2\times3x+3^2)+25(y^2+2\times4y+4^2)=100[/tex][tex]\text{Use (a+b)}^2=a^2+2ab+b^2.[/tex]

[tex]4(x+3)^2+25(y+4)^2=100[/tex]

Divide both sides by 100.

[tex]\frac{4\mleft(x+3\mright)^2}{100}+\frac{25\mleft(y+4\mright)^2}{100}=\frac{100}{100}[/tex]

[tex]\frac{\mleft(x+3\mright)^2}{25}+\frac{\mleft(y+4\mright)^2}{4}=1[/tex]

[tex]\frac{\mleft(x+3\mright)^2}{5^2}+\frac{\mleft(y+4\mright)^2}{2^2}=1[/tex]

[tex]\frac{\mleft(x-(-3)\mright)^2}{5^2}+\frac{\mleft(y-(-4)\mright)^2}{2^2}=1[/tex]

The standard form of the given equation is

[tex]\frac{\mleft(x-(-3)\mright)^2}{5^2}+\frac{\mleft(y-(-4)\mright)^2}{2^2}=1[/tex]

Compare with the general form of the ellipse equation.

We get h=-3, k=-4, a=5 and b=2.

The centre of the ellipse is h= -3 and k = -4.

The value of a is 5.

The value of b is 2.

We need to find the eccentricity of the ellipse.

[tex]e=\sqrt[]{1-\frac{b^2}{a^2}}[/tex]

Substitute b=2 and a =5 in the formula.

[tex]e=\sqrt[]{1-\frac{2^2}{5^2}}=\sqrt[]{1-\frac{4}{25}}=\sqrt[]{\frac{25-4}{25}}=\sqrt[]{\frac{21}{25}}=0.9165[/tex][tex]e=0.9165[/tex]

The foci of the ellipse are

[tex]((h\pm a)e,0)[/tex]

Substitute h =-3, a=5 and e =0.9165 in the formula.

[tex]((-3\pm5)0.9165,0)[/tex]

The foci with a positive x value are the point

[tex]((-3+5)0.9165,0)\text{ =}(1.83,0)[/tex]

[tex](1.83,0)[/tex]

The foci with a negative x value are the point

[tex]((-3-5)0.9165,0)\text{ =}(-7.33,0)[/tex]

[tex](-7.33,0)[/tex]


Related Questions

If a girl has 7 skirts, 9 shirts, and 5 pairs of shoes, how many outfits canshe wear?

Answers

Okay, here we have a Combination Problem, we need just multiply to get the answer, of this mode:

[tex]C=7\cdot9\cdot5=315[/tex]

She can wear 315 outfits.

Which of the following is the position vector for a vector that has an initial point of (10, 2) andterminal point of (-8, -7)?

Answers

initial point = (10,2)

Terminal point = (-8,-7)

subtract the coordinates of the initial point from the coordinates of the terminal point

Position vector = ( -8-10 , -7-2 ) = <-18,-9>

use the graph to complete the ordered pair solution (0,_) for f.

Answers

we must look the value of the graph when x=0

the graph trought x=0 when y=-1 so, the point is

[tex](0,-1)[/tex]

Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000How much should they deposit now if they assume that they can earn 8.5% compounded annually?

Answers

Compound interest formula:

[tex]A\text{ = }P(1+i)^n[/tex]

where:

A is the final amount, here = $250,000

P is the principal amount

i is the interest rate per year (in decimal form), here = 0.085

n is the number of years invested, here = 14

Replacing into the equation and solving for P, we get:

[tex]250000=P(1+0.085)^{14}[/tex][tex]\frac{250000}{1.085^{14}}=P[/tex]

P = $79,785.5

Michael bought groceries and spent $46.85 before including the sales tax of 7%. What is the total purchase price after tax?

Answers

We are told that a 7% tax is applied to the original sales price, in order to determine the tax amount we just have to multiply the original price ($46.85) by the tax percentage (0.07 as 7% in decimal form), then we get:

Tax amount = 0.07×46.85 ≈ 3.28

By adding the tax amount to the original price we should get the final price, like this:

Total purchase price = 46.85 + 3.28 = 50.13

Then, the total purchase price after tax is $50.13

how to find a volume of a cylinder that has a radius of 10 and a base of 4 Khan academy

Answers

Question:

Find a volume of a cylinder:

Solution:

Remember that the volume of the cylinder with radius r and height h is given by the following formula:

[tex]V\text{ = }\pi r^2h[/tex]

then, replacing the data of the problem into the previous equation, we get:

[tex]V\text{ = }\pi(4^2)(10)\text{ = 3.14 (16)(10) = 502.4}[/tex]

thus, we can conclude that the correct answer is:

[tex]V\text{ = 502.4}[/tex]

What is the answer to this question?

Answers

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

What is termed as the reflection of the point?A reflection point represents when a figure is built around a single point recognized as point of reflection or the figure's center. On the other side, per each point in the graph, some other point is observed directly opposite it.

For the given question.

Line m is the line along which reflection of point P is taken.

Then, line m is called the "perpendicular bisector" of line PP'.

P is the object and P' will be the image of the point P.

Thus, the complete definition of the reflection is given as-

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

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Evaluate the function f(p) = p2 + 3p + 1 for p = -2.

Answers

The result of the function f(p) = [tex]p^2[/tex] + 3p + 1  for p = -2 is -1

The function is

f(p) = [tex]p^2[/tex] + 3p + 1  

The function is the expression that represents the relationship between the one variable and another variable. If one variable is dependent variable then the another variable will be independent variable.

The values of p = -2

Substitute the value of p in the function and find the solution

f(p) = [tex]p^2[/tex] + 3p + 1  

f(-2) = [tex](-2)^2[/tex] + 3×-2 + 1

f(-2) = 4 - 6 + 1

f(-2) = -1

Hence, the result of the function f(p) = [tex]p^2[/tex] + 3p + 1  for p = -2 is -1


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A chocolate chip cookie recipe ask for 1 1/2 times as much flour as chocolate chips if 3 1/2 cups of flour is used what quantity of chocolate chips would then be needed according to the recipe

Answers

Given:

Amount of chocolate chips needed = 1 1/2 times as much floor.

Amount of floor used = 3 1/2 cups.

Let's find the quantity of chocolate chips that would be needed according to the recipe.

To find the amount of chocolate chips used, we have:

Amount of chocolate chips

[tex]undefined[/tex]

Which of the following is the number of sides a polygon can have to form aregular tessellation?O A. 9B. 3C. 5D.7

Answers

From the image, we are asked the number of sides a polygon can have to form a regular tesselation.

The first step is to understand what a regular tessellation is;

A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape. There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons.

This implies that it could either have 3 sides(triangle), four sides(square), six sides(hexagon).

From the given options we can clearly see that 3 sides is the only available option.

ANSWER: Option B

The Ruiz family took a summer trip.
In 4 days, they drove 1,600 miles. If they drove an equal
number of miles each day, how many miles did they drive
each day? Describe the basic fact you use to find your
answer and how many zeros you add from the dividend.

Answers

Answer:

400 miles each day

Step-by-step explanation:

You have 1600 miles divided into four days.

1600 / 4


We can use the basic fact that multiplying a number by ten simply means shifting everything to the left, for example 2 x 10 = 20, we just shifted 2 to the left and inserted a 0.

So for this problem, we can do the same. Divide 1600 by 100, or 10 x 10, then divide by 4.

1600/16 = 100

16/4 = 4.

Now, since we divided by ten twice before, we can get the right answer by multiplying by ten twice.

4 x 10 = 40

40 x 10 = 400

HELP PLEASEEEEE!!!!!!

Answers

-1 3/4, 14/8, 1.125 and -0.875 correspond to points 1, 8, 6 and 4 respectively on the number line.

How can we match -1 3/4, 14/8, 1.125 and -0.875 on the number line?

Looking at the number line, there are 8 divisions between two points e.g 0 to 1.  

To know the value of  1 division, we divide the value of the distance between two points by the number of divisions:

= 1/8 = 0.125

To find the locations, we just divide the value of the locations with the value of 1 division:

-1 3/4 / 0.125 = -14  (Count 14 divisions to the left of 0) = point 1

14/8  / 0.125 = 14  (Count 14 divisions to the right of 0) = point 8

1.125/ 0.125 = 9 (Count 9 divisions to the right of 0) = point 6

-0.875 / 0.125 = -7  (Count 7 divisions to the left of 0) = point 4

Therefore, the positions of -1 3/4, 14/8, 1.125 and -0.875 on the number line are points 1, 8, 6 and 4 respectively.

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8 Madison has two plants. She waters the spider plant every 4 days and the cactus every 6 daysShe water bo November 30. What is the next day that she will water both plants?

Answers

Two plants

Spider plant 4 days

Cactus plant 6 days

Then find when

4X = 6Y

find m.c.m (minimum common multiple) of 4 and 6

m.c.m (4,6) = 12

SO therefore, if both plants were watered November 30, then

add 12 days to Nov 30

12 days after Nov 30 = December 12

Which of the following statements are equivalent to "Some politicians are not crooked"? Select all that apply:All politicians are crooked.Some politicians are crooked.Not all politicians are crooked.All politicians are not crooked.

Answers

SOLUTION

The given statement is

"Some politicians are not crooked"

The equivalent statement is

Not all politicians are crooked

And

All politicians are not crooked.

The equivalent statement is

Not all politicians are crooked

And

All politicians are not crooked.

Answer:  Not all politicians are crooked

It is equivalent to saying that  "Some politicians are not crooked". Both are implying that not every politician is crooked and some of them are good.

hope it helps, mark as brainliest :D

What is 2 2/3 - 3/5? 7/154 4/152 1/15 1 2/5

Answers

[tex]\begin{gathered} 2\text{ }\frac{2}{3}-\frac{3}{5}=\frac{8}{3}-\frac{3}{5} \\ \frac{8}{3}-\frac{3}{5}=\frac{40-9}{15}=\frac{31}{15}=2\text{ }\frac{1}{15} \end{gathered}[/tex]

Solve |x4|+6 = 13.
O A. x
11 and x = -11
OB. x = 11 and x = -3
OC. x = -11 and x = -3
OD. x = -11 and x = 3

Answers

Answer:

B

Step-by-step explanation:

| x - 4 | + 6 = 13

x - 4 + 6 = 13

x = 11

Or

4 - x + 6 = 13

x = -3

hi i'm stuck on diameter and radius and chord and the arc measure explanations. And i'm also stuck on this question

Answers

• Chord: ,a line segment connecting ,any two points, in a curve (circle).

,

• Diameter: ,a chord passing ,through the center ,of the figure.

,

• Radius: ,a line segment going ,from the center, to any point in the circumference.

The difference between them is that the chord is any two points touching the circumference, the diameter has to go through the center to any two points, and the radius goes from the center to just one point in the circumference.

Then, the line segment that meets the requirements of being the diameter in circle F is segment CD as it passes through the center.

The radius could be CF, DF, and EF. While a chord could be AB.

Answer: CD

Look at the photograph and if you need anything let me know

Answers

Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.

Therefore, the answer is the first option.

What is the value of p in the proportion below? 20/6 = p/12O 2 O 10O 40O 72

Answers

20/6 = p/12

cross-multiply

p x 6 = 20 x 12

6p = 240

divide both-side of the equation by 6

p = 240/6

p = 40

The equation of a curve is y=f(x)
The vertex of the curve is at (2,-3)
Write down the coordinates of the vertex of the curve with the equation
a) f(x)+5
b) -f(x)

Answers

The rigid transformations of the vertex of the curve are listed below:

(i) (2, 2).

(ii) (2, 3).

How to determine the coordinates of the vertex

In this problem we find the value of a point of a curve f(x), this point (the vertex) must be transformed by using rigid transformations. There are two cases: (i) Vertical translation, (ii) Reflection about the x-axis. The formulas for each case are described below:

Vertical translation

P'(x, y) = P(x, y) + (0, k)

Reflection about the x-axis

P'(x, y) = P(x, y) + (0, - 2 · p)

Where p is the y-coordinate of point P.

If we know that P(x, y) = (2, - 3), then the coordinates for each case are, respectively:

Vertical translation

P'(x, y) = (2, - 3) + (0, 5)

P'(x, y) = (2, 2)

Reflection about the x-axis

P'(x, y) = (2, - 3) + (0, 6)

P'(x, y) = (2, 3)

The transformations of the vertex of the curve are (i) (2, 2) and (ii) (2, 3).

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This table shows the top athletes that play both basketball and track. What is the intersection between the set of basketball players and the set of track athletes? Basketball Track Arnold Berenson Nickerson Eaton Yun Tadesse McDonald Jones Tadesse Nickerson Yang Martin​

Answers

The intersection between the set of basketball players and the set of track athletes is given by:

{Tadesse, Nickerson}

What is the intersection between two sets?

The intersection between two sets is the set containing the elements that belong to both sets which we are calculating the intersection.

In the context of this problem, the sets are given as follows:

List of basketball players: {Arnold, Nickerson, Yun, McDonald, Jones, Tadesse}List of track athletes: {Berenson, Eaton, Tadesse, Nickerson, Yang, Martin}.

The intersection is composed by athletes that are both basketball players and track athletes, hence it is given as follows:

{Tadesse, Nickerson}

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2. I want to find the area of a basketball free throw lane, and I am trying to use this formula:
Area =(6 ft) + (12 ft)(19 ft).
Clearly explain how you can tell this is wrong without knowing any area formulas.

Answers

Answer:

Down Here

Step-by-step explanation:

Hello!

Area is measured in units². Here, the units are feet, so the area would be written as feet² (ft²).

Simplifying the expression:

6ft + (12ft)(19ft)6ft + 228ft²

You can't simplify this because the units are not the same, and this can't measure area because all units of the area have to be squared. The term 6ft has non-squared units.

Which postulate or theorem could you use to prove (triangle)XYZ = (triangle)ABC?Choose the correct answer below.AAS theoremSSS postulateASA postulateSAS postulate

Answers

From the given figures in the 2 triangles XYZ and ABC

mXZ = AC

m

Since we have two equal angles and the sides between them are equal, then

The 2 triangles are congruent using ASA postulate

The answer is C

Which graph shows the same linear equation shown in the table below?

Answers

I'm drawing now

_______________________

Option C

Event A, Event B, and Event Care provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the union of A and B?

Answers

Given data:

The probability of A is P(A)=0.45.

The probability of B is P(B)=0.30.

The expression for the mutually exclusive events is,

[tex]P(A\cap B)=0[/tex]

The expression for the probability of A union B is,

[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =0.45+0.30-0 \\ =0.75 \end{gathered}[/tex]

Thus, the probability of (AUB) is 0.75.

LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit

Answers

The Solution:

Given the graph below:

We are required to find the perimeter of the triangle LMN rounded to the nearest unit.

Step 1:

Find the distance LM, where L(-3,2) and M(3,5)

By the formula for distance between two points, we have

[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where,

[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]

Substituting, we get

[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]

Step 2:

Find the distance LN:

[tex]LN=12[/tex]

Step 3:

Find the distance MN, where M(3,5) and N(9,2)

[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]

Step 4:

The perimeter is:

[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]

Therefore, the correct answer is 28 units.

rag the red and blue dots along the x-axis and y-axis to graph 10x - 7y=40

Answers

We were given the equation:

[tex]10x-7y=40[/tex]

We will proceed to graph this equation as shown below:

[tex]\begin{gathered} 10x-7y=40 \\ \text{Make ''y'' the subject of the equation, we have:} \\ \text{Subtract ''10x'' from both sides, we have:} \\ -7y=-10x+40 \\ \text{Divide through each term by ''-7'' to obtain the equation in terms of ''y'', we have:} \\ y=\frac{-10}{-7}x+\frac{40}{-7} \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ when\colon x=-7 \\ y=\frac{10}{7}(-7)-\frac{40}{7} \\ y=-10-\frac{40}{7} \\ y=-\frac{110}{7} \\ \\ when\colon x=0 \\ y=\frac{10}{7}(0)-\frac{40}{7} \\ y=-\frac{40}{7} \\ \\ when\colon x=7 \\ y=\frac{10}{7}(7)-\frac{40}{7} \\ y=10-\frac{40}{7} \\ y=\frac{30}{7} \end{gathered}[/tex]

We will proceed to plot these ordered pairs on a graph, we have:

Write the complex number in polar form with argument theta between 0 and 2 pie

Answers

[tex]=\text{ 7}\sqrt[]{2}\lbrack cos(tan^{-1}(-1)\text{ + isin}(tan^{-1}(-1)\text{ \rbrack}[/tex]Explanation:[tex]\begin{gathered} let\text{ z = -7 + 7i} \\ r\text{ = }\sqrt[]{(-7)^2+(7)^2} \\ r\text{ = }\sqrt[]{49+49\text{ }}\text{ = }\sqrt[]{98} \\ r\text{ = 7}\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ }\theta\text{ = }\frac{7}{-7}\text{ = -1} \\ \text{ }\theta=tan^{-1}(-1) \\ \end{gathered}[/tex][tex]\begin{gathered} z\text{= }r(\cos \theta+\text{ isin}\theta) \\ -7\text{ + 7i }=\text{ }r(\cos \theta+\text{ isin}\theta) \\ =\text{ 7}\sqrt[]{2}\lbrack cos(tan^{-1}(-1)\text{ + isin}(tan^{-1}(-1)\text{ \rbrack} \end{gathered}[/tex]

The answer in polar form:

[tex]=\text{ 7}\sqrt[]{2}\lbrack cos(tan^{-1}(-1)\text{ + isin}(tan^{-1}(-1)\text{ \rbrack}[/tex]

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 16° = ___

Answers

We have round of to 100th place means up to 3 places

[tex]\sin (16\text{ degre}e)=0.27563[/tex]

Now we will reduce the digit from right side upto 3 places

As last digit is 3 which is less than 5 so it will remove directly

[tex]\sin (16\text{ degr}e)=0.2756[/tex]

Now the last digit is 6 which is greater than 5. So and is even so change we will simply remove this

[tex]\sin (16\text{ degre}e)=0.275[/tex]

Graph transformation of the following line given the transformation: g(x)= -f(x) -2

Answers

Transformation of a Function

We are given the function:

[tex]y=f(x)=\frac{2}{3}x+8[/tex]

And it's required to find another function g(x) according to the transformation:

g(x) = -f(x) - 2

First, we calculate the negative of f(x):

[tex]-f(x)=-(\frac{2}{3}x+8)=-\frac{2}{3}x-8[/tex]

And now we subtract 2 to find g(x):

[tex]g(x)=-\frac{2}{3}x-8-2=-\frac{2}{3}x-10[/tex]

The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10

Answer:

[tex]g(x)=-\frac{2}{3}x-10[/tex]

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Give men in police uniforms stood in his living room with guns pointed at him.The captain shouted to the other officers, "You, go search the basement. You, search the garage. You, search the kitchen!""Wh-wh-where's your search warrant?" asked Johnny nervously."We don't need a warrant!" replied the police captain.After searching his house, the captain announced, "Johnny Q. Public, you are under arrest."Johnny was booked and led to a prison cell. He wondered what he had been arrested for. "Guard, why have I been arrested?" Johnny asked each day. But the guards said they didn't know.Months went by. Finally Johnny was told that if he could post one million dollars bail, he could get out of jail until his trial. "I Don't have that kind of money. Can I talk to an attorney?" He'd beg, but the answer was always, "No".A year passed and finally Johnny was transported from Virginia to Pennsylvania for trial. He found out that he was charged with shoplifting a t-shirt. As he entered the courtroom, he saw an empty jury box. He asked, "Where's my jury?" He was told he couldn't have a jury because judges were better at knowing when someone was guilty.Then the district attorney said, "The prosecution calls Johnny Q. Public to the stand." Johnny didn't want to testify, but he was told he would be sent back to jail if he did not. Johnny put on the best defense he could. By some miracle, he was found not guilty.A month later, Johnny was arrested again on the same charge. He had to prepare for another trail. The prosecution had new evidence this time. Johnny wanted to question the prosecution's witnesses, but the judge would not let him.When it was time for Johnny to present his case, Johnny said, "I'd like to call my neighbor to the stand. He knows that I was at home alone that night." But the judge said, "Your neighbor didn't want to get involved and so he would not agree to testify. There's nothing we can do."Johnny was found guilty. The judge asked Johnny to stand while he read the sentence: "Johnny Q. Public, since this is your first offense you have been sentence to five years in a maximum security prison." Johnny felt dizzy and sat down. He thought, "I wish there were something that could protect me from these abuses!" Suppose you have an Avogadros number of potassium. How many grams does this represent? 14. A waterway contains 10.3 milligrams of an impurity per gallon of water. How many micrograms of impurity arepresent per liter of water? what invention did american spies in new york use that the british had absolutely no idea of how has persuasion changed in the digital age? check all that apply. persuasive messages are targeted to very specific audiences persuasion is more complex and impersonal all businesses are in the persuasion business persuasive messages are slow to engage audiences persuasive techniques are more subtle and misleading 4. What is the main idea of the cartoon? DBQ statistics classifying samples (I am not sure if this is B or C)