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3 years ago

Find the value of x. then find the measure of each labeled angle. simplify your answer.

Mathematics

2 answers:

tankabanditka [31]3 years ago

5 0

11x + 7x = 180

When solved, x = 10.
Plug in the x to find the angle measurements

irina1246 [14]3 years ago

5 0

For this case we have that the sum of the internal angles of a quadrilateral is 360 degrees.

As we are told that the pairs of sides are congruent we have:

$7x + 11x + 7x + 11x = 360\\36x = 360\\x = \frac {360} {36}\\x = 10$

So, x = 10.

So:

$7x = 7 (10) = 70 \ degrees\\11x = 11 (10) = 110 \ degrees$

Answer:

$x = 10$

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Log_2(log_5 x) =3 show steps

alexandr1967 [171]

Use the definition of a logarithm
If Log(x) = y ; then b^y = x

$Log_{2} (Log_{5} (x)) = 3 \\ \\ 
2^{3} = Log_{5} (x) 
\\ \\ 8 = Log_{5} (x) 
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3 years ago

Can someone explain to me the letter or sign or variable after "Y"

sattari [20]

Answer:

It is a symbol used to denote an angle (or something else)

Step-by-step explanation:

Alpha(α) is a greek letter, it's one of the letters used to denote angles. Other such letters you'll often see in math are Beta (β), Gamma (γ), Delta (δ), these are used to denote angles. Also, pi (π), which is a mathematical constant. The letters phi (φ) and theta (θ) are also used for angles very often, especially in formulas. You'll see some of these in physics too.

It can be used as variable too, not necessarily for angles, but it's mostly used for them.

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3 years ago

The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo

shepuryov [24]

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY = $\sqrt{x^2+y^2}$

Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

= $\sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2} = \sqrt{20}$ = 4.472 units

Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

Length CD = $\sqrt{(-2)^2+5^2} = \sqrt{29}$ = 5.385 units

Length DA = $\sqrt{(8)^2+(-2)^2} = \sqrt{68}$ = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A = $\sqrt{(7)^2+(0)^2} = \sqrt{49}$ =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

= $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

$S_{{\bigtriangleup}ABC}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|$

= $=(\frac{1}{2})|-4-6 -8|= 9 units^2$

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

$S_{{\bigtriangleup}ACD'}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2}$ = 10.5 units²

Area of polygon = $S_{{\bigtriangleup}ABCD'}$ = $S_{{\bigtriangleup}ABC}$ + $S_{{\bigtriangleup}ACD'}$ = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

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3 years ago

Here are the first 4 terms in the sequences

balu736 [363]

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15. Given that each term has a common difference, this is an arithmetic sequence.

In this instance, the result is obtained by adding 6 6 to the prior term in the sequence.

What is the arithmetic progression formula?

a {n}=a {1}+(n-1) The nth term in the series is d a n.

The first term in the sequence is a 1.

d is the common distinction between the terms.

To learn more about Arithmetic progression refer to:

brainly.com/question/24191546

#SPJ13

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1 year ago

Given the quadratic equation ² + + = 0 where , , are real numbers and ≠ 0, which of the following is the sum of its roots? *

Morgarella [4.7K]

Answer:

Here is a more clearer version of the same question ;

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The proving of both a) and b) has been done

Step-by-step explanation:

The step by step explanation has been given in the attachment below.

Step-by-step explanation:

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3 years ago