What is the equation of a circle with the same center but a radius that is twice as long ?

Complete the equation of the line through (−10,3) (−8,−8). Use exact numbers. y=

fomenos

Answer:

y = -11/2x - 52

Step-by-step explanation:

Now follow the equation for slope: m = change in y / change in x.

$\frac{y2-y1}{x2-x1}$

$\frac{-8-3}{-8--10}$

$\frac{-11}{2}$

The slope is -11/2. m=-11/2

Use slope-intercept form:

y=mx+b

Plug in a point and the slope:

-8 = (-11/2)(-8) + b

-8 = 44 + b

b = -52

y = -11/2x - 52

8 0

2 years ago

Find the inverse of this matrix. 1 -1 -1 -1 2 3 1 1 4

zheka24 [161]

Let's use Gaussian elimination. Consider the augmented matrix,

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]$

• Add row 1 to row 2, and add -1 (row 1) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]$

• Add -2 (row 2) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add -2 (row 3) to row 2:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add row 2 and row 3 to row 1:

$\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

So the inverse is

$\begin{bmatrix}1&-1&-1\\-1&2&3\\1&1&4\end{bmatrix}^{-1} = \boxed{\begin{bmatrix}5&3&-1\\7&5&-2\\-3&-2&1\end{bmatrix}}$

3 0

3 years ago

Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30.

aalyn [17]

The price of one hat is $2 and one pair of mittens is $5

Step-by-step explanation:

Hats and mittens are on sale at the store!

One woman was able to buy 5 hats and 4 pairs of mittens for $30
Another woman purchased 3 pairs of mittens and 2 hats for $19
The price of one hat is x
The price of one pair of mittens is y

We need to find x and y

∵ One woman was able to buy 5 hats and 4 pairs of mittens for $30

∵ The price of one hat is x

∵ The price of one pair of mittens is y

- Multiply 5 hats by x and 4 pairs of mittens by y and equate

their sum by 30

∴ 5x + 4y = 30 ⇒ (1)

∵ Another woman purchased 3 pairs of mittens and 2 hats for $19

- Multiply 2 hats by x and 3 pairs of mittens by y and equate

their sum by 19

∴ 2x + 3y = 19 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 and equation (2) by 5 to eliminate x

∵ -10x - 8y = -60 ⇒ (3)

∵ 10x + 15y = 95 ⇒ (4)

- Add equations (3) and (4)

∴ 7y = 35

- Divide both sides by 7

∴ y = 5

Substitute the value of y in equation (1) or (2) to find x

∵ 2x + 3(5) = 19

∴ 2x + 15 = 19

- Subtract 15 from both sides

∴ 2x = 4

- Divide both sides by 2

∴ x = 2

The price of one hat is $2 and one pair of mittens is $5

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

8 0

3 years ago

Clara's suitcase weighs 58 1/4 pounds, but the airline's weight limit for suitcases is 50 pounds. How much weight does she need

sergij07 [2.7K]

8 pounds and 4 oz. 58.04 - 8.04=50

5 0

2 years ago

Which two points on the number line represent numbers that can be combined to make zero? A B C D -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

maria [59]

Answer: B and D

Step-by-step explanation:

B=-2

D=2

The negative and positive signs cancel out, leaving you with zero.

Ex: you take two steps back, but then you take two steps forward so you're back where you started (0).

8 0

2 years ago