Explain why the equation 6|x| + 25 = 15 has no solution. When one solves, they arrive at a step where |x| is equal to a negative number. Since | x| can never be negative, there is no solution. When one solves, they arrive at a step where |x| is equal to a fraction that may not be represented as an integer. Since | x| must be an integer, there is no solution. When one solves, they arrive at a step where x is equal to a negative number. Since x can never be negative inside of the absolute value bars, there is no solution. The statement is false. There is a solution.

Answers

Answer 1
Final answer:

The equation 6|x| + 25 = 15 has no solution because it implies that |x| equals a negative number after simplification, and absolute values cannot be negative.

Explanation:

The equation 6|x| + 25 = 15 has no solution because the absolute value of x, denoted by |x|, represents the distance of x from zero on the number line, and as such, it can never be negative. When we solve the given equation, we isolate the absolute value on one side which gives us 6|x| = -10 after subtracting 25 from both sides. Dividing by 6, we obtain |x| = -10/6, which is a negative number. However, since an absolute value cannot equal a negative number, this indicates that there is no valid solution to the equation.


Related Questions

Manda uses the recipe shown to make punch for a family party. amanda’s punch recipe 7 parts mixed fruit juice 2 parts lemonade how much lemonade will she need to make 180 fluid ounces of punch

Answers

7:2....added = 9

7/9(180) = 1260/9 = 140 fluid oz .....mixed fruit
2/9(180) = 360/9 = 40 fluid oz <== lemonade

Answer:

40 fluid ounces of lemonade.

Step-by-step explanation:

Amanda uses the recipe shown to make punch for a family party.

Amanda's punch recipe 7 parts mixed fruit juice 2 parts lemonade.

7 + 2 = 9  parts

She will need to make 180 fluid ounces of punch.

she will need lemonade = (180/9) × 2

                                        = 20 × 2

                                        = 40 fluid ounces lemonade

She will need fruit juice = (180/9) × 7

                                        = 20 × 7

                                        = 140 fluid ounces fruit juice.

Amanda will need 40 fluid ounces lemonade to make 180 fluid ounces of punch.

caryssa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost $45. In addition, the supplies for each bracelet cost her $3. She sells her bracelets for $5. What is the minimum number of braclets she must sell to make a profit?

Answers

She spent 48 dollars meaning she must sell at least 10 bracelets to make a profit (5.10)= 50

The scale of a map is 1 in. :500 mile. City A is 650 miles from City B. How far is it's distance on the map?

Answers

Thanks for the question!

650/500 * 1
1.3 * 1
1.3 in

Hope this helps!

one week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091. find the cost of a trumpet, a clarinet would, and a violin.

Answers

One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091.

Let x be the cost of trumpets  

y be the cost of clarinets

z be the cost of violins

Now we frame equations

2x +3y + 5z = 1240 ---> equation 1

3x + 1y + 4z = 1027---> equation 2

5x + 7y + 2z = 2091 ---> equation 3

Now we solve for x,y and z using elimination method

Multiply the second equation by -3 and with first equation

2x +3y + 5z = 1240  

-9x - 3y -12z = -3081

--------------------------------

-7x - 7z = -1841  ( divide both sides by -7)

x + y = 263 ----------> equation 4

Multiply the second equation by -7 and add it with third equation

-21x - 7y - 28z = -7189    

 5x + 7y + 2z = 2091  

------------------------------------

-16x - 26z = -5098 (divide the whole equation by -2)

8x + 13z = 2549  --------> equation 5

Now use equation 4  and 5 to eliminate x. Multiply equation 4 by 8

-8x - 8z = -2104

8x + 13z = 2549

------------------------------

5z = 445

z = 89

We know x + z = 263, replace z with 89

x + 89 = 263 ( subtract 89 on both sides)

x = 174

2x +3y + 5z = 1240 ---> equation 1 ( substitute the values of x  and z)

2(174) + 3y + 5(89) = 1240

348 + 3y + 445 = 1240

793 + 3y = 1240 ( subtract 793 on both sides)

3y = 447 ( divide by 3 on both sides)

y = 149

The cost of trumpets  = $174

The cost of clarinets = $149

The cost of violins = $89



Using a system of equations, it is found that:

The cost of a trumpet is of $174.The cost of a clarinet is of $149.The cost of a violin is of $89.

------------------

For the system of equations, i will say that:

The cost of a trumpet is x.The cost of a clarinet is y.The cost of a violin is z.

------------------

2 trumpets, 3 clarinets, and 5 violins for $1240, thus:

[tex]2x + 3y + 5z = 1240[/tex]

3 trumpets, 1 clarinet, and 4 violins for $1027, thus:

[tex]3x + y + 4z = 1027[/tex]

5 trumpets, 7 clarinets, and 2 violins for $2091, thus:

[tex]5x + 7y + 2z = 2091[/tex]

------------------

From the second equation:

[tex]y = 1027 - 3x - 4z[/tex]

Replacing into the other two:

[tex]2x + 3y + 5z = 1240[/tex]

[tex]2x + 3(1027 - 3x - 4z) + 5z = 1240[/tex]

[tex]-7x - 7z = -1841[/tex]

Simplifying by 7:

[tex]x + z = 263 \rightarrow z = 263 - x[/tex]

Also:

[tex]5x + 7y + 2z = 2091[/tex]

[tex]5x + 7(1027 - 3x - 4z) + 2z = 2091[/tex]

[tex]-16x - 26z = -5098[/tex]

[tex]16x + 26z = 5098[/tex]

------------------

Solving for x:

[tex]16x + 26z = 5098[/tex]

[tex]16x + 26(263 - x) = 5098[/tex]

[tex]10x = 1740[/tex]

[tex]x = \frac{1740}{10}[/tex]

[tex]x = 174[/tex]

The cost of a trumpet is of $174.

------------------

Solving for z:

[tex]z = 263 - x = 263 - 174 = 89[/tex]

The cost of a violin is of $89.

------------------

Solving for y:

[tex]y = 1027 - 3x - 4z = 1027 - 3(174) - 4(89) = 149[/tex]

The cost of a clarinet is of $149.

A similar problem is given at https://brainly.com/question/22826010

What is 3a-2b if a=-1 and b=-2

Answers

3(-1) - 2(-2)

-3 + 4 = 1

your answer is 1

remember, two negatives become one postive

Write the domain of the function given in the graph in set builder notation.


a. {x|x<=10}
b. {x|x<=0}
c. {x|x>10}
d. {x|x>0}


I can't get a picture of the graph so I'll try to explain. Y axis 0-5, going up by 1's, x axis 0-50, going up by 5's. Line starts at 10 on the x axis, goes up at an angle and stops at 40.

Answers

Based on what I understood, the graph would look something like this (attached as a picture). I don't know what angle it would be but I just assumed simple conditions where in the function is linear. From the given graph, the domain (x-values) would start from 10 to 40.  Thus x would be equal to or greater than 10. The answer would be C.

Last year shantell bought a car for $24,000 the current value of the car is $21,000 find the percent decrease in the value of the car

Answers

24,000-21,000=3,000nThe decrease is 3,000 dollars. Now, put 3,000 over 24,000 which is 1/8, which is 12.5 percent.

Barbie is thinking of s number. Twenty less than one third of the number is 72. Find barbies number

Answers

 if you do inverse operations you get s=285
It is 285 because I got that one correct

What the simplified form of x- 1 +4+7x-3

Answers

Collect like terms (x + 7x) + (-1 + 4 - 3)

Simplify

Answer: 8x

Which is the best simplification of (24 x 32) / (2 x 3)?

Answers

(24*32)/(2*3)
(768)/(6)
=128
I hope this helped you!!
Final answer:

To simplify (24 x 32) / (2 x 3), perform the multiplication operations first. Then perform the division operation. This results in the simplification of the given expression to 128.

Explanation:

To simplify the expression (24 x 32) / (2 x 3), we'll first carry out the multiplication operations because of the BIDMAS or PEMDAS rule that gives the order of operations in maths. B or P stands for brackets, I or E stands for Indices or Exponents, D/M for Division/Multiplication and A/S for Addition/Subtraction. According to this rule, Division or Multiplication is performed from left to right. Therefore, we first multiply 24 x 32 which gives 768, and secondly multiply 2 x 3 which gives 6. Thus, the expression now becomes 768 / 6. This division gives us the final answer of 128.

Learn more about Mathematical Simplification here:

https://brainly.com/question/33857870

#SPJ2

what is the answer to this problem?

Answers

Every two consecutive angles are supplementary

so x+115 = 180        x= 65

and x+y = 180         y = 115


you can pick the second choice 
X=65 or y =115, because they are supplementary meaning it must equal 180 degrees for adjacent angles. This would make it certain this is a parallelogram.
Hope it helped!

The product of a number and 7 is at most the difference of the number and 5. write an inequality and solve for the variable

Answers

       the inequality would be:    7n =< n - 5
(subtract n from both sides):      -n       -n   
                               
                                so then:    6n =< -5
       (divide both sides by 6):     6n/6 =< -5/6

                                answer:  n =< -5/6      OR      n =< -0.83


Hope this helps :)
                                                                           

Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university, however, she must pay in euros. How many euros can Varia expect to pay per month to the university? (Round to the nearest whole euro.)

Answers

It would be about 2938 Euros.
2940 euro's. i hope this helps

Suppose you are building a rectangular pen for your goats. You use 400 feet of fencing for the pen.

Answers

part A

The pen has a rectangular shape of length l and width, say w.

The perimeter (the fencing) of this rectangle is 2l+2w, as in the rectangle we have 2 opposing sides of length l and 2 opposing sides of length w.

This means that 2l+2w=400

subtract 2l from both sides:

2w=400-2l

divide by 2:

w=200-l, so we find that the width is 200-l.


part B

we are asked to find w when l=80 ft,

since we have w=200-l, we can find w for l=80 ft by substituting :

w=200-l=200-80=120  (feet)


Part C

The area of the pen when l=90 feet is:

[tex]A_{pen}=width \cdot length=(200-l) \cdot l=(200-90) \cdot 90\\\\=110 \cdot 90=9,900[/tex]  (square feet)

What is the equation of a horizontal line passing through the point (-7,5)

Answers

y=5x-(-7) that is the answer

The simplified version of what you’re asking, and by simolified i mean solved, is Y= 5

At 12 noon in anchorage Alaska Janice noticed that the temperature outside was 12
f. The temperature dropped at a steady rate of 2 F per hour.

Answers

I assume that you want to know the temperature at a certain timing.
Well, you know that at 12:00 pm, the temperature was 12 F and that it decreases by a steady rate of 2 F each hour.

This means that at 1:00 pm, the temperature was 12-2 = 10 F
At 2:00 pm, the temperature was 10-2 = 8 F
At 3:00 pm, it was 8-2 = 6 F
.......and so on

You can follow this sequence to the timing you are looking for.

Indicate the equation of the given line in standard form.

The line through (2, -1) and parallel to a line with slope of 3/4

Answers

Since the slope stays the same as it's parallel, we have y=(3/4)x+b. Plugging (2,-1) in, we get -1=3*2/4+b=6/4+b=1.5+b. Subtracting 1.5 from both sides, we get -2.5=b and our equation being y=(3/4)x-2.5 (since in y=mx+b, y and x remain as variables)

Diana received $35 worth in Starbucks gift cards for Christmas her favorite drink caramel macchiato costs about $4:00 help diana keep track of the balance left in her gift cards each time she buys a drink how many caramel macchiato will she be able to buy with her gift cards?

Answers

35/4=8.75
So she will be able to buy 8 caramel macchiatos.
:)

Diana can buy a total of 8 caramel macchiatos with her $35 Starbucks gift cards, and she will have a remaining balance of $3.

To help Diana keep track of the balance on her Starbucks gift cards after purchasing her favorite drink, the caramel macchiato, we need to perform a series of simple subtractions. She starts with a $35 balance, and each caramel macchiato costs $4.00.

After buying the first caramel macchiato, the new balance is $35 - $4.00 = $31.

After the second purchase, $31 - $4.00 = $27.

This process continues until the balance is less than the cost of a caramel macchiato.

To find out how many drinks she can purchase in total, we divide the initial balance by the cost of one caramel macchiato:

$35 / $4.00 = 8.75

Since she cannot buy a fraction of a drink, Diana can buy a total of 8 caramel macchiatos with her gift cards and will have a remaining balance of $3, which is not enough for another drink.

A washer and a dryer cost $942 combined. The washer costs $42 more than the dryer. What is the cost of the dryer?

Answers

the dryer costs 900 because you subtract 942 from 42 and you get the total of the dryer. 
w + d = 942
w = d + 42

d + 42 + d = 942
2d + 42 = 942
2d = 942 - 42
2d = 900
d = 900/2
d = 450 <=== dryer costs $ 450

w = d + 42
w = 450 + 42
w = 492 <=== washer costs $ 492

Look at the diagram. Which of the following is another name for < 1

A. < CBA
B. < ACB
C. < CAB
D. < BAC

Answers

another name for ∠1 is
A. CBA 

Answer: A. ∠CBA

Step-by-step explanation:

We need three points to write a name of an angle. One point on each ray with the vertex lies in the middle.

There are total three ways to write a name of an angle.

For example :- M and N are points on each ray of an angle with vertex O.

Then, the name of angle can be ∠O, ∠MON or ∠NOM.

From the given picture , it can be observe that A and C are points on each ray of ∠1 with vertex B.

Then, the possible name of ∠1 will be ∠B , ∠ABC or ∠CBA.

Since, ∠CBA in given in option A.

Thus OPTION A is the correct option.

In which number is the digit 4 one hundred times larger than the value of 4 in the number 41?
A) 435
B) 540
C) 4,350
D) 9,400

Answers

A.435 I'm pretty sure
C, because the digit 4 represents 40 and in answer c the 4 represents 4,000, 40 times 100 is 4,000

A flower store has 42 carnations and 21 pansies. It puts the same number of flowers in each of 7 bouquets.

How many flowers are in each bouquet?

Answers

First you add 42 + 21 and that equals 63

Next you divide 63 by 7 which is nine

So the answer is that there are 9 flowers in each bouquet
42 carnations / 7 bouquets would equal 6 carnations per bouquet
21 pansies / 7 bouquets would be 3 pansies per bouquet

there would be 6 carnations and 3 pansies in each bouquet equaling in 9 flowers per bouquet 

Calculate f (-3) f (x)=-2x+3

Answers

Thanks for the question!


Substitute -3 as x:

f(x) = -2x + 3
f(-3) = -2(-3) + 3
f(-3) = 6 + 3
f(-3) = 9

Hope this helps!
solving for x)
x=-3/3f^2-2

△R′S′T′ is the image of △RST under a dilation through point C. RS=5 and R′S′=8 . What scale factor was used in the dilation?

Answers

Answer:

1.6

Step-by-step explanation:

To find the scale factor, we compare the image size to the pre-image size.

R'S' = 8 and RS = 5; this makes the scale factor 8/5, which is 1.6.

Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. The scale factor that was used in the dilation is 1.6.

What is dilation?

Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.

Scale factor = Dimension of the new shape/Dimension of the original shape

Given that △R′S′T′ is the image of △RST under a dilation through point C. Also, given that RS=5 and R′S′=8. Therefore, the scale factor that was used in the dilation is,

Scale factor = Dimension of the new shape/Dimension of the original shape

Scale factor = R′S′ / RS = 8/5

= 1.6

Hence, the scale factor that was used in the dilation is 1.6.

Learn more about Scale Factor:

https://brainly.com/question/22312172

#SPJ6

Are you smart enough to answer this??

Answers

y intercept: -3

Find the slope:
(0,-3)(4,0)

0-(-3)/4-0
3/4

Put into slope intercept form
y=3/4x-3

Because it is shaded above with a dashed line, the sign is >
Final answer: y>3/4x-3

The quotient of y and 3 is 25

Answers

This will become y/3=25.

What is 23% of 256? please help

Answers

So first you need to turn the percent into a decimal. So 23% would be 0.23 because you divide 23 by 100 to turn it into a decimal. Now you multiply 0.32 and 256. So:

[tex]0.23 *256=58.88[/tex] 

So your answer would be 23% of 256 is 58.88. I hope this helps! =)

Show that (2-√x)^2 divided by √x can be written as 4x^(-1/2)-4+x^1/2

Answers

hello : 
(2-√x)^2 = 4 - 4√x + x   ( identity : (a-b)² = a² - 2ab +b²  and : (√x)² = x )
now : 
(4 - 4√x + x)/(√x) = 4/√x - 4√x /√x + x /√x 
but : 
4/√x = 4/x^1/2 = 4x^(-1/2)
- 4√x /√x = - 4
 x /√x = (√x ×√x) / √x =  √x = x^1/2
conclusion : 
(4 - 4√x + x)/(√x) =4x^(-1/2) - 4 + x^1/2

Help please !! It’s geometry credit recovery

Answers

cross multiply? 9x2=18/3= 6

I need major help!!!!

What is the area of a circle with a diameter of 13.2 cm?
Use 3.14 for pi and round your final answer to the nearest hundredth.
Enter your answer in the box.

Which explanation can be used to derive the formula for the circumference of a circle?

A. Find the length of the diameter and double this amount. Subtract it from the length of the circumference. Set an equation to show the difference equaling the ratio between a circumference and radius. Then rearrange the equation to solve for the circumference.

B. Find the length of the radius. Then find the circumference. Use the square of the radius to set up an equation showing the relationship that the square of the radius equals the ​ π ​ times circumference. Then rearrange the equation to equal the circumference.

C. Find the length of the radius and the area of the circle. Divide the area by the radius to get a quotient of ​ π ​. Write an equation showing the area of a circle equals this quotient times the radius. Then substitute the area for 3 times the circumference and rearrange the equation to equal the circumference.

D. Find the length of the diameter and the length of the circumference of the circle. Divide the length of the circumference by the length of the diameter. Set up an equation showing the ratio of the circumference to the diameter equal to ​ π ​. Then rearrange the equation by solving it for the circumference. Substitute 2 times the radius for the diameter.


A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle.
Let s be the side length of the polygon,
let r be the hypotenuse of the right triangle,
let h be the height of the triangle, and
let n be the number of sides of the regular polygon.
polygon area = n(1/2*sh)

Which statement is true?

As h increases, the area of the regular polygon approaches the area of the circle.

As s increases, the area of the regular polygon approaches the area of the circle.

As n increases, the area of the regular polygon approaches the area of the circle.

As r increases, the area of the regular polygon approaches the area of the circle. (has picture)

What is the area of a circle whose radius is 5 ft?

5π ft²

10π ft²

20π ft²

25π ft²

The circumference of a circle is 5π cm.

What is the area of the circle?

​ 25π ​ cm²

​ 10π ​ cm²

​ 6.25π ​ cm²

​ 2.5π ​ cm²

Answers

1) Area of a circle = πr^2
Radius = 13.2 ÷ 2
= 6.6
Area = (3.14)(6.6)^2
= 136.78cm^2

I hope this helps!
Other Questions
There isnt a civics section so its going in history.This Constitution, and the Laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land"The source of this quote is the Article I powers of the Constitution Reserved powers of the Constitution Supremacy clause to the Constitution Tenth Amendment to the Constitution NEED HELP ASAP!!!!!!! WILL GIVE BRAINLIEST THANKSIn the years just prior to the Depression, 75 percent of Americanfamilies were _____. If m = 4 and n = 4, then m = n What property is this? Which verb form correctly completes the conversation? Alberto: Dnde estudiabas cuando eras pequeo? Juan: Yo __________ en la escuela de mi barrio.estudibamosestudianestudiabaestudio The maintaining of a relatively stable internal environment by the body is called What is the length of AB? Question 1(Multiple Choice Worth 5 points)These lines from Kennedy's 1963 Civil Rights Address seek to most clearly define which idea?One hundred years of delay have passed since President Lincoln freed the slaves, yet their heirs, their grandsons, are not fully free. They are not yet free from the bonds of injustice; they are not yet free from social and economic oppression. And this nation for all its hopes and all its boasts will not be fully free until all its citizens are free. injustice A economics B freedom C nationality DQuestion 2(Multiple Choice Worth 5 points)"This is not a sectional issue. Difficulties over segregation and discrimination exist in every city, in every State of the Union, producing in many cities a rising tide of discontent that threatens the public safety. Nor is this a partisan issue. In a time of domestic crisis men of good will and generosity should be able to unite regardless of party or politics."In this excerpt from President Kennedy's 1963 Civil Rights Address the phrase "rising tide of discontent" most likely refers to: a sectional issue A difficulties over segregation and discrimination B every State of the Union C a time of domestic crisis DQuestion 3(Multiple Choice Worth 5 points)In this excerpt from President Kennedy's 1963 Civil Rights Address, he included the examples of President Lincoln's efforts to end slavery and social and economic oppression for what purpose? "One hundred years of delay have passed since President Lincoln freed the slaves, yet their heirs, their grandsons, are not fully free. They are not yet freed from the bonds of injustice. They are not yet freed from social and economic oppression. And this Nation, for all its hopes and all its boasts, will not be fully free until all its citizens are free." to revise the definition of freedom A to explain the bonds of injustice B to explain the rights of heirs and grandsons C to explain the passage of time DQuestion 4 (Essay Worth 10 points)In a paragraph of seven to ten sentences, answer the following questions in relation to this passage from John F. Kennedy's 1963 Civil Rights Address: What notion does Kennedy seek to reinvent in this passage? Why is it necessary for this notion to change? What long-term result does Kennedy expect to see through the reinventing of this notion? "One hundred years of delay have passed since President Lincoln freed the slaves, yet their heirs, their grandsons, are not fully free. They are not yet freed from the bonds of injustice. They are not yet freed from social and economic oppression. And this Nation, for all its hopes and all its boasts, will not be fully free until all its citizens are free. We preach freedom around the world, and we mean it, and we cherish our freedom here at home, but are we to say to the world, and much more importantly, to each other that this is the land of the free except for the Negroes; that we have no second-class citizens except Negroes; that we have no class or caste system, no ghettoes, no master race except with respect to Negroes?" During the worldwide economic depression of the 1930s, industrial output, farm production, and employment fell dramatically due to which of the following? What is syncopation? What type of music use syncopation? What type of plate boundary is forming the himalaya mountains, the tallest in the world?? How is an emulsion different from a solution Prove that the eigenvalues of a matrix squared are greater than the matrix eigenvalues Why might a bussiness want to gain influence over the goverment Insert parentheses so that the expression has a value of 67: 35+62+1 Our group struggled to discover the answer to the question; we felt like a tiny shriveled balloon drifting in a vast current over the planet. What does the author mean by the words in bold? The experience of discovering the answer was fun. The group members felt alone and without direction. The experience of discovering the answer was satisfying. The group felt its happiness could be seen from far away. What type of relationship existed betweenthe englishbetween the english and native americans around jamestown? Helpppppppppppppp historyyyy1) beginning in the 1660s what did wealthy Virginia tobacco planters buy?A)land in new jersey as an investment B)most of the native american land in the regionC)most of the good farmland near the coastD)most of the good farmland in the carolinas2)colonist most of whom were young men, could not vote without_____.A)owning propertyB)a proper eductionC)working the land for wealthy farmersD)a certain level of income or wealth3)farmers on the frontier demanded that the governor take strong measures against_____.A)the native americansB)other farmersC)the englishD)the rebels4)After 1644 native Americans living near the coast had to accept___.A)colonizationB)English ruleC)western ruleD)life as servants5)who became the leader of the frontier settlers around 1675?A)Charles masonB)Jeremiah DixonC)Virginia's governorD)Nathaniel bacon The ________ is a sequence of activities that determine the earliest date by which a project can be completed. If point a is located at (-12,6) on a coordinate plane, and point b is located at (4,6) what is the distance between the two points Give examples of needs, wants, and demands that fedex customers demonstrate, differentiating these three concepts. Steam Workshop Downloader