Skylar mowed 16 lawns in 12 hours. What was her rate of mowing in lawns per hour?

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

2 years ago

Find the length of the missing side. the triangle not drawn to scale. (Image attached)

3241004551 [841]

Answer: 8

Step-by-step explanation:

The triangle shown in the image attached is a right triangle.

Therefore, to calculate the missing lenght of the triangle you can apply the Pythagorean Theorem, which is shown below:

$a^2=b^2+c^2$

Where a is the hypotenuse and b and c are the legs.

The problem gives you the value of the hypotenuse and the value of one leg. Therefore, you must solve for the other leg from $a^2=b^2+c^2$ , as following:

$17^2=15^2+c^2\\c=\sqrt{17^2-15^2}\\c=8$

Therefore, the lenght of the missing side is: 8

6 0

2 years ago

Read 2 more answers

help me pls pls pls

sergiy2304 [10]

2, -3, -10 at the answers

3 0

2 years ago

What is the value of yearly compensation package that includes $65,000 salary the forecast of a $350 Dollar per month health ins

Klio2033 [76]

Answer:

$69560

Step-by-step explanation:

The yearly compensation package includes a yearly salary of $65000, the health insurance plan of $350 per month and a life insurance premium of $30 per month.

Total compensation in health insurance plan is $(350 × 12) = $4200

Total compensation in life insurance premium is $(30 × 12) = $360

Therefore, total yearly compensation package is $(65000 + 4200 + 360) = $69560 (Answer)

4 0

2 years ago

A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft.

Leviafan [203]

Answer:

T= 2.35 seconds

Step-by-step explanation:

⇒The question is on the time of flight.

⇒Time of flight is the time taken for a projected object to reach the ground.It depends on the projectile angle and the initial velocity of the projectile

Given;

Initial velocity of ball= 110ft./sec.

The projectile angle= 20°

Acceleration due to gravity, g=32 ft./s²

⇒Formulae for time of fright T= (2×u×sin Ф)/g

Where T=time of fright, u=initial velocity of projectile, Ф=projectile angle and g=acceleration due o gravity.

Substituting values

T= (2×u×sin Ф)/g

T=( 2×110×sin 20°) / 32

T= 2.35 seconds

3 0

2 years ago

Read 2 more answers