All categories

3 years ago

Can someone answer this please

Mathematics

1 answer:

nlexa [21]3 years ago

6 0

Answer:

x = 31°

Step-by-step explanation:

All the angles given, a, 2x, and 3x, form a straight lines, so therefore, they add up to 180°. We can write an equation from the info:

a + 2x + 3x = 180°

We know a is 25°, so we can substitute that in:

25° + 2x + 3x = 180°

Combine like terms...

25° + 5x = 180°

And solve.

5x = 155°

x = 31°

You might be interested in

The matrix A = −14 −6 6 28 12 −4 0 0 4 has characteristic polynomial

rosijanka [135]

Answer:

Characteristic equation:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda$

Eigen values:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

Step-by-step explanation:

We are given the matrix:

$\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]$

The characteristic equation can be calculated as:

$det(A-\lambda I) = 0\\|A-\lambda I| = 0$

We follow the following steps to calculate characteristic equation:

$=det\Bigg(\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]-\lambda\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\Bigg)\\\\= det\Bigg(\displaystyle\left[\begin{array}{ccc}-14-\lambda&-6&6\\28&12-\lambda&-4\\0&0&4-\lambda\end{array}\right]\Bigg)\\\\=(-14-\lambda)[(12-\lambda)(4-\lambda)]+6[28(4-\lambda)]-6[(28)(0)-(12-\lambda)(0)]\\\\= -\lambda^3 + 2\lambda^2 + 8\lambda$

$p(\lambda)= -\lambda^3 + 2\lambda^2 + 8\lambda$

To obtain the eigen values, we equate the characteristic equation to 0:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda = 0\\-\lambda(\lambda^2-2\lambda-8) = 0\\-\lambda(\lambda^2-4\lambda+2\lambda-8) = 0\\-\lambda[(\lambda(\lambda-4)+2(\lambda-4)] = 0\\-\lambda(\lambda+2)(\lambda-4) = 0 \\\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

We can arrange the eigen values as:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4\\-2 < 0 < 4\\\lambda_2 < \lambda_1 < \lambda_3$

3 0

3 years ago

Which of Polygons B, C, D, E, and F are similar to Polygon A?

bearhunter [10]

Answer:

b and d

Step-by-step explanation:

3 0

3 years ago

IMAX theaters have the world’s largest screens. There are numerous IMAX theaters around the world. The Henry Ford Museum in Dear

SCORPION-xisa [38]

The dimensions would be 5 ft by 7 ft.

4 0

4 years ago

Read 2 more answers

2. State the negation of each of the following statements. a. √ is a rational number. b. 0 is not a negative integer. c. 111 is

maxonik [38]

The negation of the statements are:

a. √ is not a rational number.
b. 0 is a negative integer.
c. 111 is not a prime number.

<h3>How to determine the negation?</h3>

The negation of a statement x is represented as:

not x

This means that we simply introduce the "not" word in the statements or we remove the "not" word in them

So, we have the negation to be:

a. √ is not a rational number.
b. 0 is a negative integer.
c. 111 is not a prime number.

Read more about logic at:

brainly.com/question/14458200

#SPJ1

8 0

2 years ago

Find an equation of the plane. The plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0) Incorrect: Your answer is incorr

Andrei [34K]

Answer:

The equation of the plane is represented by $\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1$ .

Step-by-step explanation:

Algebraically speaking, a plane can be represented by following vectorial product:

$(a,b, c)\,\bullet\,(x,y,z) = 1$ (1)

Where:

$a$ , $b$ , $c$ - Plane coeffcients.

$x$ , $y$ , $z$ - Coordinates.

We need three distinct points to determine all coefficients. If we know that $(x_{1},y_{1},z_{1}) = (0,9,9)$ , $(x_{2},y_{2}, z_{2}) = (9,0,9)$ and $(x_{3},y_{3},z_{3}) = (9,9,0)$ , the system of equations to be solved is: