Write a linear function f with f(5)=-1 and f(0)=-5

An ellipse has the general equation

(x/a)² + (y/b)² = 1

(actually, this is an ellipse whose semimajor and -minor axes are parallel to the x- and y-axes, but one can rotate any ellipse so that it has the same configuration, and the area remains constant)

Convert to a kind of rescaled polar coordinates, using

x = a r cos(t)

y = b r sin(t)

Then the interior of such an ellipse is the set

E = {(r, t) : 0 ≤ r ≤ 1 and 0 ≤ t ≤ 2π}

The area of E is then given by the integral

[tex]\displaystyle \iint_E dA[/tex]

Compute the Jacobian determinant for this change of coordinates. The Jacobian is

[tex]J = \begin{bmatrix}x_r & x_t \\ y_r & y_t\end{bmatrix} = \begin{bmatrix}a \cos(t) & -a r \sin(t) \\ b \sin(t) & b r \cos(t)\end{bmatrix}[/tex]

Then we have Jacobian determinant

|det(J)| = |a b r cos²(t) + a b r sin²(t)| = |a b r| = |a b| r

since r ≥ 0.

The area of E is then

[tex]\displaystyle \iint_E dA = \iint_E |ab| r \, dr \, dt[/tex]

[tex]\displaystyle \iint_E dA = \int_0^{2\pi} \int_0^1 |ab| r \, dr \, dt[/tex]

[tex]\displaystyle \iint_E dA = 2\pi |ab| \int_0^1 r \, dr[/tex]

[tex]\displaystyle \iint_E dA = \boxed{\pi |ab|}[/tex]

Answer:

90% off

Step-by-step explanation:

Your question is incomplete.

If these are the statement.. The answer is below:

The grocery bill before the coupons were used was 10 times as much as the bill after the coupons were used.

The grocery bill after the coupons were used was 10 times as much as the bill before the coupons were used.

The grocery bill before the coupons were used was 100 times as much as the bill after the coupons were used.

The grocery bill after the coupons were used was 100 times as much as the bill before the coupons were used.

Answer:

The grocery bill before the coupons were used was 10 times as much as the bill after the coupons were used.

Step-by-step explanation:

The price after coupons were used is $20, and the price before was $200. $20 · 10 =$200

Answer:

A. - This is my guess.

Answer:

A) 13

Step-by-step explanation:

If you recall the formula for finding a diagonal, or a^2 + B^2 = C^2, you will get 12^2 + 5^2 = C^2, if you solve that, you will get 13!

Answer:

-7x + 7y - 14

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{4.8}{1 \frac{7}{9} } = (1.2b) \div 6 \frac{2}{3} [/tex]

[tex] \frac{ \frac{48}{10} }{ \frac{16}{9} } = \frac{12b}{10} \div \frac{20}{3} [/tex]

[tex] \frac{48 \times 9}{10 \times 16} = \frac{12b}{10} \times \frac{3}{20} [/tex]

[tex] \frac{432}{160} = \frac{36b}{200} [/tex]

[tex]432 \times 200 = 160 \times 36b[/tex]

[tex]86400 = 5760b[/tex]

[tex]b = \frac{86400}{5760} [/tex]

[tex]b = 15[/tex]

Answer:

-26

Step-by-step explanation:

2 × 3 + 4 − 6^2

PEMDAS

exponents are first in this equation

2 × 3 + 4 − 36

Then multiply

6 +4 -36

Then add and subtract from left to right

10-36

-26

Answer:

A) -26

Step-by-step explanation:

2 * 3 + 4 - 6²

Use PEMDAS to figure out the equation.

Pass parenthesis since there are none in the equation.

Evaluate all of the exponents.

2 * 3 + 4 - 36

Evaluate all of the multiplication in the equation.

6 + 4 - 36

Pass division since there isn't any in the equation.

Evaluate all of the addition in the equation.

10 - 36

Evaluate all of the subtraction in the equation.

-26.

Answer:Possible Answers: 13.2%. 5.7%. 15.0%.

Step-by-step explanation:

Answer:

Line 1: Is parallel Line 2: Is Neither Line 3: Is parallel

Answer:

The constant factor between consecutive terms of a geometric sequence is called the common ratio. Example:  To find the common ratio  find the ratio between a term and the term preceding it. r=42=2. 2 is the common ratio.

Answer:

m ∠x = 81° and m ∠y = 109°

Step-by-step explanation:

m ∠R = 1/2 (arc REG)         m ∠G = 1/2(arc REF)

89° = 1/2 (arc REG)             81 = 1/2(arc REF)

178° = arc REG                    162° = arc REF

  m ∠x = 1/2 arc REF

  m ∠x = 1/2( 162°)

  m ∠x = 81°       or m ∠G = m ∠x  because these to angles intersect the same arc, therefore they are equal.

Now the polygon interior angles = 360° and you know the measure of three of the four angles, solve for the missing angle .

m ∠R + m ∠x + m ∠y + m ∠G = 360°

 89° +  81° + m ∠y + 89° = 360°

(89 + 81 + 81) + m ∠y = 360°

251° + m ∠y = 360°

m ∠y = 109°

Answer:

4 and 5

Step-by-step explanation:

Let's make an equation to solve. Let's call "one number" x. Another number is 1 more than x, so now we have x + 1. x plus x + 1 is equal to 9... and this gives us our equation:

x + (x + 1) = 9

We can now simplify by adding like terms together:

2x + 1 = 9

Now, let's take away 1 from both sides:

2x = 8

We can finally divide both sides by 2 to isolate x:

x = 4

One of our numbers is 4. Our other number is one more than 4, and 4 + 1 = 5. So our numbers are 4 and 5.

Hopefully this was helpful! If you need more help, let me know.

Answer:

$17.60

Step-by-step explanation:

Answer:

A) 115°

Step-by-step explanation:

if PQ || RS then those two angles are supplementary

Answer:

Step-by-step explanation:

`

Step-by-step explanation:

just think - what does it mean to translate (shift) a graph upward by 5 units ?

does the graph change in its content ? no. all the functional result value (= y values or coordinates) are still calculated as before, BUT before marking them on the chart the y values are moved up by 5 units. that means they are increased by 5 (that is the only way to move something "up" on a coordinate grid).

so, in other words, f(x) is nothing else but h(x), but it increases the results of h(x) consistently by 5.

h(x) = 2x² + 4

f(x) = h(x) + 5 = 2x² + 4 + 5 = 2x² + 9

Answer:

90

Step-by-step explanation:

Answer:

904.8 m²

Step-by-step explanation:

needed formulas:

surface of a circle: πr²

circumference of a circle: 2πr

The top and bottom are circles with radius 9, and surface π9² = 81π m²

The side is a rectangle of 2·π·9·7 long, so that is 126π m²

Brings the total to 81π + 81π + 126π = 288π ≈ 904.8 m²

Step-by-step explanation:

[tex] = - \frac{5}{3} + 2 \frac{1}{3} [/tex]

[tex] = - \frac{5}{3} + \frac{7}{3} [/tex]

[tex] = \frac{2}{3} [/tex]

Answer:

[tex] \sf \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] \sf = - \frac{5}{3} + 2 \frac{1}{3} [/tex]

[tex] \sf = 2 \frac{1}{3} - \frac{5}{3} [/tex]

[tex] \sf = \frac{7}{3} - \frac{5}{3} [/tex]

[tex] \sf = \frac{7 - 5}{3} [/tex]

[tex] \sf = \frac{2}{3} [/tex]

Answer:

A = 103°; B = 77°; C = 46°

Step-by-step explanation:

A + 45° + 32° = 180°

A + 77° = 180°

A = 180° - 77°

A = 103°

A + B = 180°

103° + B = 180°

B = 180° - 103°

B = 77°

B + C + 57° = 180°

77° + 57° + C = 180°

134° + C = 180°

C = 180° - 134°

C = 46°

I hope I've helped you.

Answer:

a. y = 3^x

yep

ype

pey

Answer:

a

Step-by-step explanation:

plug the points into the equations

3¹=3

3²=9

3³=27

3⁴=81

3⁵=243

these are all true equations, so the answer is a

Answer:

Option D is your answer.

Step-by-step explanation:

Remember that the x-values are the x coordinates and the y-values are the y coordinates in an ordered pair. Ordered pairs are written like this (x,y).

So for line r, you got (-6,4), (-3,0), and (0,-4).

But you only need two of these pairs to determine slope. Let's do that real quick, by using this formula. (Sorry if it's small)⤵⤵⤵

[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]

We'll use (-6,4) and ( -3,0).

0 - 4 = -4

-3 - (-6) = -3 + 6 = 3

So slope of line r is -4/3.

Now we'll do the same for line s:

Ordered pairs = (-5,-4), (5,0), and (20,6)

We'll use (-5,-4) and (5,0).

0 - (-4) = 0 + 4 = 4

5 - (-5) = 10

So slope of line s is 4/10 or 2/5.

Now we got to find the option choice that has these as the slopes.

We'll turn each into slope-intercept form.

A)

- Subtract 4x on both sides to get

3y = -4x - 12, then divide 3 on both sides to get y = -4/3 x - 4.

- Subtract 2x on both sides to get

-5y = -2x + 10, then divide -5 on both sides to get y = 2/5 x - 2.

B)

- Add 4x on both sides to get

3y = 4x + 12, the divide 3 on both sides to get y = 4/3 x + 4.

- Subtract 2x on both sides to get

-5y = -2x - 10, divide -5 on both sides to get y = 2/5 x + 2.

C)

- Subtract 4x on both sides to get

-3y = -4x - 12, then divide -3 on both sides to get y = 4/3 x + 4.

- Add 2x on both sides to get

-5y = 2x + 10, then divide -5 on both sides to get y = -2/5 x -2.

D)

- Add 4x on both sides to get

-3y = 4x - 12, then divide -3 on both sides to get y = -4/3 x + 4.

- Add 2x on both sides to get

5y = 2x + 10, then divide 5 on both sides to get y = 2/5 x + 2.

After all that writing we can tell that D is our answer, because both -4/3 and 2/5 appear as slopes.

Sorry this may seem like a lot, but the process really isn't that hard. Hope this helps :)

Answer:

Greater than 2+5

Answer:

On average, he exercises 2.875 hours per week.

Step-by-step explanation:

Just do 11 1/2 (11.5) divided by 4, and you get your answer of 2.875 hours per week.

Answer:

x= (5,0) y= (0,1)

Step-by-step explanation:

Answer:

Yes it is linear. Standard Form: 4x - y = -9

Step-by-step explanation:

Answer:

the answer is a

Step-by-step explanation:

the reason its a is because it just it