40 POINTS!!!
All integers are either odd or even. Conceptually, an integer is odd if it has a remainder of 1 when dividing by 2. And an integer is even if it has a remainder of 0 when dividing by 2.

But when proving something rigorously, mathematicians use more precise definitions, like these: an integer is odd if it can be written in the form 2k + 1, where k is some integer. An integer is even if it can be written in the form 2k, where k is some integer. For example, 13 is odd because 13 can be written as 2(6) + 1.

With these definitions, use complete sentences to explain why zero is an even number.

Answer:

[tex]\int\limits {\int\limits_R {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]

Step-by-step explanation:

Given

[tex]x - y = 0[/tex]

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

[tex]x + y = 0[/tex]

[tex]x + y = 6[/tex]

Required

Evaluate [tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex]

Let:

[tex]u=x+y[/tex]

[tex]v =x - y[/tex]

Add both equations

[tex]2x = u + v[/tex]

[tex]x = \frac{u+v}{2}[/tex]

Subtract both equations

[tex]2y = u-v[/tex]

[tex]y = \frac{u-v}{2}[/tex]

So:

[tex]x = \frac{u+v}{2}[/tex]

[tex]y = \frac{u-v}{2}[/tex]

R is defined by the following boundaries:

[tex]0 \le u \le 6[/tex]  ,  [tex]0 \le v \le 7[/tex]

[tex]u=x+y[/tex]

[tex]\frac{du}{dx} = 1[/tex]

[tex]\frac{du}{dy} = 1[/tex]

[tex]v =x - y[/tex]

[tex]\frac{dv}{dx} = 1[/tex]

[tex]\frac{dv}{dy} = -1[/tex]

So, we can not set up Jacobian

[tex]j(x,y) =\left[\begin{array}{cc}{\frac{du}{dx}}&{\frac{du}{dy}}\\{\frac{dv}{dx}}&{\frac{dv}{dy}}\end{array}\right][/tex]

This gives:

[tex]j(x,y) =\left[\begin{array}{cc}{1&1\\1&-1\end{array}\right][/tex]

Calculate the determinant

[tex]det\ j = 1 * -1 - 1 * -1[/tex]

[tex]det\ j = -1-1[/tex]

[tex]det\ j = -2[/tex]

Now the integral can be evaluated:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex] becomes:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{x^2 - y^2}} \, *\frac{1}{|det\ j|} * dv\ du[/tex]

[tex]x^2 - y^2 = (x + y)(x-y)[/tex]

[tex]x^2 - y^2 = uv[/tex]

So:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{|det\ j|}\, dv\ du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *|\frac{1}{-2}|\, dv\ du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{2}\, dv\ du[/tex]

Remove constants

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 {\int\limits^7_0 {ue^{uv}} \, dv\ du[/tex]

Integrate v

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 \frac{1}{u} * {ue^{uv}} |\limits^7_0 du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 e^{uv} |\limits^7_0 du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{u*7} - e^{u*0}]du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{7u} - 1]du[/tex]

Integrate u

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7u} - u]|\limits^6_0[/tex]

Expand

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -(\frac{1}{7}e^{7*0} - 0)][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -\frac{1}{7}][/tex]

Open bracket

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} - 6 -\frac{1}{7}][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} -\frac{43}{7}][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{42} -\frac{43}{7}][/tex]

Expand

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]

Answer:

182.353745

Step-by-step explanation:

[tex]\frac{0.482 x61.2^2}{\sqrt{98.01} }[/tex]

Exponent First!

61.2^2 = 61.2 × 61.2 = 3745.44

Next, start multiplying it by 0.482

3745.44 × 0.482 = 1,805.30208

Then Solve for the Square root of 98.01

[tex]\sqrt{98.01}=9.9[/tex]    

Finally, divide 1,805.30208 by 9.9    

1,805.30208 ÷ 9.9 = 182.353745

Answer:

5. a) 5b

   b) 3b + 2b

Step-by-step explanation:

a) b + b + b + b + b is the same as

5 * b or 5b

b) 5b = 3b + 2b

or 3 * b + 2* b = 5b

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Bisector

Step-by-step explanation:

Answer:

the distance is called the circumference

I DONT SPEAK ENGLISH, I'M BRAZILLIAN

Answer:

brainllest if right

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is B.

It's a line that shows every point that satisfies the equation

y = 3x + 4  which is what I think you meant (but I'm not sure). If I am correct then there are a million possible points that could be the answer to this question.

If I am not correct, leave a comment that tells me so, and I'll revise my answer.

Never mind the question has the right equation. And my answer remains as given.

Answer:

A . Isosceles

Step-by-step explanation:

An isosceles triangle has both two equal sides and two equal .

Answer:

Length = 35

w = 5

Step-by-step explanation:

l x w = area

7y x y = 175

7y^2 = 175

y^2 = 175/7

y^2=25

y=5

The length is 7y, so it's 5 times 7 or 35.

The width is just y, so it's 5.

Answer:

Step-by-step explanation:

The two triangle are congruent for the rule SAS

QP congruent to TU

angle P and angle T are both right

side PR is in common

Answer:

Step-by-step explanation:

Hope this helps u !!

The LCM of 2a(4a² + 10a + 13)(4a² + 13 - 10a).

Least Common Multiple, often known as the Lowest Common Multiple, is denoted by the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It can also be computed using two or more numbers.

The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.

We have,

16[tex]a^4[/tex] + 4a² + 169 and 8a³ +2a(2a + 13) + 16a²

First, 16[tex]a^4[/tex] + 4a² + 169

= (4a²)² + (2a)² + (13)²

= (4a²)² + 2 . 4a² . 13 + (13)² + 4a² + 104a²

= (4a² + 13)² - (10a)²

= (4a + 13 - 10a) (4a + 13 + 10a)

= (13 - 6a)(13 + 14a)

Second, 8a³ +2a(2a + 13) + 16a²

= 8a³ + 4a² + 26a + 16a²

= 8a³ + 20a² + 26a

= 2a(4a² + 10a + 13)

So, the LCM is

= 2a(4a² + 10a + 13)(4a² + 13 - 10a)

Learn more about LCM here:

https://brainly.com/question/20739723

#SPJ2

Answer:

B: 112.5

Step-by-step explanation:

first, we split up the rhombus into two triangles, with the height of 15 and the length of 7.5. when you multiply these you will get 112.5, and normally if you are just getting the area of the triangle, then you would divide it by two, but seeing that we have 2 triangles here, we would multiply it by two afterwards so an easier way to do it is just to not divide.

Answer:

-8 is not a solution to the inequality

Step-by-step explanation:

[tex]3x + 13 \geqslant - 8 \\ 3x \geqslant - 21 \\ x \geqslant - 7 \\ [/tex]

Step-by-step explanation:

everything can be found in the picture

Answer: 5 billion pennies

Step-by-step explanation:

Answer:

1 and 2 only

Step-by-step explanation:

mark me as brainliest

Answer:

x   -   h(x)

0   -   1

1    -   3

2   -   5

3   -   7

Step-by-step explanation:

Just substitute the x value into the function

Answer:

Amount spent on food  = 510

Amount spent on entertainment = 720

Step-by-step explanation:

They have 3000 for vacation.

Amount spent on food = 17% of 3000

or 17/100*3000

17*30= 510

Amount spent on entertainment = 24% of 3000

or 24/100*3000

24*30= 720

Step-by-step explanation:

A shaded right rectangular pyramid is shown. where is the shade rectangular pyramid....how do I know the answer when you did post the full

question

Answer:

CO

Step-by-step explanation:

Conditional: If p, then q.

Converse: If q, then p.

Conditional: If the measure of an angle is 90 degrees, then it is a right angle.

If p, then q.

p = the measure of an angle is 90 degrees

q = it is a right angle

Converse:

If q, then p.

If it is a right angle, then the measure of the angle is 90 degrees.

Answer: CO

Answer:

B

Step-by-step explanation:

OEMJIGOVNarioendsdmarfwsipf JUST BELIEVE, also looking is good

The true statements on comparing Jasmine’s two drawings are B and C.

The sum of a finite traingle's interior angle is equal to 180° and this is called the Angle Sum Property of a Triangle.

It is given in the question

Jasmine drew triangles on a globe and on a flat map of the world

On comparing both the triangle the conclusions are

The triangle drawn on the globe is a spherical triangle and the angle sum of the interior angle will be greater that the two right angles or 180°.

Among the option given this is also true that

The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe

Therefore option B and C are both true statement comparing Jasmine’s two drawings .

To know more about Angle Sum Property

https://brainly.com/question/8492819

#SPJ2

Answer: 7

Step-by-step explanation:

find x

6x(6+4)=5x(1+x)

Then x=11

AB= 11-4=7

Answer:

B.) 7

Step-by-step explanation:

I got it correct on founders edtell

Answer:

Hello! answer: always

Step-by-step explanation:

And Isosceles triangle is a triangle with two sides that have the same length therefore the answer is always because as shown there are two sides with the same length hope that helps!

Answer is: always

since a  isosceles is a triangle with two equal sides and since two of the number is same(you know what i mean)

Answer:

a = -1  b=0  and c=1

Step-by-step explanation:

-x^2 +0x+1

This is in the form

ax^2 +bx+c

a = -1  b=0  and c=1

There for the diameter is 2(4.8 )= 9.6 ft

Given: Volume of the cone is 83.7 m³

We know that:

[tex]\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : \dfrac{\pi r^2h}{3}}}[/tex]

where r is the radius of the cone and h is the height of the cone

Given: Height of the cone = 5m

Substituting the values in the formula, we get:

[tex]\sf{\implies \dfrac{\pi r^2(5)}{3} = 83.7}[/tex]

[tex]\sf{\implies \pi r^2 = 83.7 \times \dfrac{3}{5}}[/tex]

[tex]\sf{\implies \pi r^2 = 83.7 \times 0.6}[/tex]

[tex]\sf{\implies \pi r^2 = 50.22}[/tex]

[tex]\sf{\implies r^2 = \dfrac{50.22}{\pi}}[/tex]

[tex]\sf{\implies r^2 = 16}[/tex]

[tex]\sf{\implies r = 4}[/tex]

We know that : Diameter is two times the radius

⇒  Diameter of the Cone is 8 meters

Answer: -64 Maybe

Step-by-step explanation:

It look like each term goes up by double of the last term.

Good question. It is supposed to be both the y-intercept and the x-intercept and is the only point on a graph that can be both. Something in wrong in that thing.

Answer:

2 miles

Step-by-step explanation:

Answer:

10,512 miles

Step-by-step explanation:

876 x 12 = d (d is distance)

Solving the multiplication above, 876 x 12 would equal 10,512 miles

Answer:

A.

Step-by-step explanation:

Vertical shifts are represented by - or +, and they are not within the parenthesis. Since the function is being shifted down by 2 units, the correct answer is A.

Answer:

6X(5 + 4)

6x(9)

54x

Answer:

the answer is 54x hope it will help full to you