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If y = ax + 2a², then its derivative is dy/dx = a. Substitute y and dy/dx into the given equation and check if it results in an identity:

2 (dy/dx)² + x dy/dx - y = 0

2a² + ax - (ax + 2a²) = 0

0 = 0

This is of course true, so y = ax + 2a² is indeed a solution to the given equation.

Answer:

(A) 2^11

Step-by-step explanation:

Step-by-step explanation:

3(7x-9)-19x = -15

21x-27-19x = -15

2x-27 = -15

2x = -15+27

2x = 12

x = 6

prove x = 6

Substitute x=6 into the equation.

3(7(6)-9)-19(6) = -15

3(42-9)-114 = -15

3(33)-114 = -15

99-114 = -15

-15 = -15 True✓

Answer:

Value of [tex]x=-12[/tex]

Step-by-step explanation:

The given triangle is isosceles

Here

[tex]m\angle2+m\angle2+36^0=180^0\\\\2m\angle2=144^0\\\\m\angle2=72^0\\\\x+84=72\\\\x=72-84\\\\=-12[/tex]

[tex]m∠2+m∠2+36⁰= 180°[/tex]

[tex]2m∠2 = 144°[/tex]

[tex]m∠2 = 72⁰[/tex]

[tex]x +84 = 72[/tex]

[tex]x = 72 - 84[/tex]

[tex]x= -12[/tex]

Answer:

18225

Step-by-step explanation:

16200*0.025*5=2025

2025+16200 = 18225

Answer:

y= 1/3x + 3

Step-by-step explanation:

Answer:

Triangle 20, 30, and 15 will create a triangle

Step-by-step explanation:

In order for side lengths to make a triangle, the sum of the two shortest sides must be greater than the longest side

5+3 < 9 so it does not work

15+20>30 so it does work

Answer:

$110

Step-by-step explanation:

So first you have to do 15*4. We get the 4 from the admission fees and the 15 from the number of dances they attend. From this answer we can see the total of money they will be paying for admission for the 15 dances.

15*4=$60

However, our answer isn't just $50 as we are also told membership costs $50. So no we add $50 to $60, which gives us an answer of $110, which is the amount the member will pay if they attend 15 dances during the school year.

Answer:

True

Step-by-step explanation:

If you do this on paper, you can make a triangle but it will be close to a line, since the two side lengths are the same and that the last side length is 1.

Answer: 3Z

Step-by-step explanation:

Answer:

It's - 28

Step-by-step explanation:

6*-7=-42-4=-28

Answer:

y is -46

Step-by-step explanation:

y= 6x -4 ....means

y =6 *x -4......so replace x with -7

y = 6*-7 -4

y=-42 -4

y= -46

D) a side of one is congruent to side of the other

Coz in the question it specified that both the shapes are square so obviously all angles are equal (90°)

Now we only need one side of it congruent .

Answer:

12 minuts

Step-by-step explanation

If you divide 95 by ten you get 9.5, and 9.5 to 95 and you get 104.5 and it is 11 minuts. add it again and you are at 114 words and it is 12 minuts.

Answer:

4000 sqft

Step-by-step explanation:

you multiply 5*10 which equals 50 then 8*10 which equals 80 then to find area you multiply 50*80 which equals 4000 sqft

Answer:

I think it's -6x-18, this queston uses distributive property, so you must multiply each term inside the parenthesis to the number outside the parenthesis.

Answer:

The ratio of their radius is [tex]2:3[/tex]

Step-by-step explanation:

Volume of cylinder is [tex]\pi r^2h[/tex], where r is radius and h is height

We have

The heights of two cylinders are in the ratio of [tex]5:3[/tex]

[tex]\frac{h_1}{h_2} =\frac{5}{3}[/tex]

The volume are in the ratio [tex]20:27[/tex]

[tex]\frac{V_1}{V_2} =\frac{20}{27}\\\\\frac{\pi r_1^2h_1}{\pi r_2^2h_2} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2}\times \frac{3}{5} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2} =\frac{4}{9}\\\\\frac{ r_1}{ r_2} =\frac{2}{3}[/tex]

The ratio of their radius is [tex]2:3[/tex]

Answer:

2 : 3

Step-by-step explanation:

Let,

Radius of cylinder 1 = R

Radius of cylinder 2 = r

Now,

We know that

Volume of cylinder = πr²h

=> πR²h/πr²h' = 20/27

=> R² × 5/r² × 3 = 20/27

=> R²/r² = 20/27 × 3/5

=> R²/r² = 4/9

=> R/r = √(4/9)

=> R/r = 2/3

=> R : r = 2 : 3

Answer:

7/3

Step-by-step explanation:

Answer:

The answer is 3.

Step-by-step explanation:

Answer:

[tex]y=\frac{2}{5}x+2[/tex]

Step-by-step explanation:

(x1, y1) = (5, 4)

(x2, y2) = (0, 2)

First, find the slope. The slope formula is:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

I marked the 2 points above in that form, so you can plug those in here:

[tex]m=\frac{2-4}{0-5}\\\\m=\frac{-2}{-5}\\\\m=\frac{2}{5}[/tex]

The slope of this line is 2/5. Next, you can use that slope and whichever known point you want to find the y-intercept. Slope-intercept form is:

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept.

Plug in the slope we found for m and whichever point you want for (x, y):

[tex]2=\frac{2}{5}0+b[/tex]

Now, solve for b:

[tex]2=0+b\\b=2[/tex]

In this particular case, there wasn't much to be done. We already had a point at x = 0, and that is already our y-intercept. For similar problems though, that's how you would do it.

Finally, with both the slope and the y-intercept, you can write the equation:

[tex]y=\frac{2}{5}x+2[/tex]

Answer: (11x+12)(11x−12)

Step-by-step explanation: (11x+12)(11x−12)                                                       (11x+12)(11x+−12)                                                                                                       (11x)(11x)+(11x)(−12)+(12)(11x)+(12)(−12)                                           121x2−132x+132x−144                                                                                           121x^2-144

Answer:

y = -3/2x + 2

Step-by-step explanation:

Since you know it has a point at (0, 2) - the y intercept, put those values into the equation and solve. To be perpendicular it seems the reciprocal of the slope with the opposite sign, so 2/3 is the original slope, and -3/2 becomes the new slope.

y = 2/3x + 8 becomes

2 = -3/2(0) + b  We substitute in the x and y values, but we have to figure out what the last number will be.

2 = 0 + b

b = 2

So put the whole equation together

y = -3/2x + 2

Answer:

51.7%

Step-by-step explanation:

Because percent is out of 100, you multiply 0.517 by 100 and get 51.7, which is your percent.

Answer:

no I'm pretty sure it's wrong

Step-by-step explanation:

the y intercept for that to right us -4

Answer:

24 screeches = 20 meows.

Step-by-step explanation:

Calculate purrs:

12/3 = 4

4*2= 8

Use purrs to calculate screeches:

Answer:

Below.

Step-by-step explanation:

Here's an example.

What is 123 in base 5 converted to decimal.

123 base 5 =  3 * 5^0 + 2*5^1 + 1 * 5^2

= 3 + 10 + 25

= 38 in decimal.