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3 years ago

Given that the measure of ∠x is 73°, and the measure of ∠y is 90°, find the measure of ∠z.

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

3 0

The measure of ∠z is: 17

Why?

It is 17 because the triangle has to equal a total of 180°. To find the missing value, you have to subtract the values from the total.

180-73=107

107-90=17

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(2.5 • 10^4) - (1.5 • 10^3) Evaluate please, can you show the steps

Usimov [2.4K]

According to PEMDAS, you would look in the parenthesis first. In the first set of parenthesis we have an exponent. 10x10x10x10 is 10,000. Then we multiply this by 2.5. We now have 25,000. We put this to the side..

Next, we do the same thing on the other side -- 10x10x10 is 1,000 and then you multiply that answer by 1.5 and we have 1,500. Now we can subtract. 25,000 - 1500 = 23,500 :)

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3 years ago

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure

Umnica [9.8K]

Answer:

The solution of the Given matrix

( x₁ , x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:

Step(i):-

Given equations are x₁+4 x₂ = 11 ...(i)

2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

A X = B

$\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]$

Step(ii):-

$\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]$

The Augmented Matrix form is

$[AB] = \left[\begin{array}{ccc}1&4&11\\2&7&18\\\end{array}\right]$

Apply Row operations, R₂ → R₂-2 R₁

$[AB] = \left[\begin{array}{ccc}1&4&11\\0&-1&-4\\\end{array}\right]$

The matrix form

$\left[\begin{array}{ccc}1&4\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\-4\\\end{array}\right]$

The equations are

x₁ + 4 x₂ = 11 ...(a)

- x ₂ = - 4

x ₂ = 4

Substitute x ₂ = 4 in equation (a)

x₁ + 4 x₂ = 11

x₁ = 11 - 16

x₁ = -5

Final answer:-

The solution of the Given matrix

( x₁ , x ₂ ) = ( - 5 , 4 )

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