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2 years ago

If a pair of lines is intersected by Third line known as a transversal, then pairs of congruent angles are formed true or false

Mathematics

1 answer:

Olenka [21]2 years ago

3 0

Answer:

true

Step-by-step explanation:

it forms eight angles

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Find the value of x. Round to the nearest tenth.

nordsb [41]

Step-by-step explanation:

here,,

a=3,b=10,C=120°

c^2=a^2+b^2-2ab cos120°

=(3)^2 +(10)^2 _2 (3)(10)(-1/2) [cos120°=-1/2]

=9+100-(-30)

=109+30

=139

c=(139 )1/2=11.79

c=12

3 0

3 years ago

Write the equation in slope-intercept form then change it to standard form with integer coefficients.

SCORPION-xisa [38]

Answer:

1. Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

2. Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

3. Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

Step-by-step explanation:

Slope intercept form: $y = mx + b$

where:

$y$ = y-coordinate
$m$ = slope
$x$ = x-coordinate
$b$ = y-intercept

Standard form: $Ax + By = C$

$\textsf{1. as} \ m=2: \ \ y = 2x + b$

$\textsf{at} \ (6, 8): \ \ 8 = 2(6) + b$

$\implies b = -4$

Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

$\textsf{2. as} \ \ m = \dfrac12: \ \ y = \dfrac12x + b$

$\textsf{at} \ (4, 1): \ \ 1 = \dfrac12(4) + b$

$\implies b = -1$

Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

$\textsf{3. as} \ \ m = \dfrac45: \ \ y = \dfrac45x + b$

$\textsf{at} \ (1,5): \ \ 5 = \dfrac45(1) + b$

$\implies b = \dfrac{21}{5}$

Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

7 0

2 years ago

An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms. 3/4 of this weight is metal and the rest is wood.

Troyanec [42]

Answer:

Given is a sculpture that is built up of metal and wood, and the weight of this sculpture is 14.9 kilograms.

It says that three-fourth of the total weight is metal and says to find the weight of wooden part.

We can find the weight of metal part and then subtract it from the total weight to calculate the answer.

Total weight = 14.9 kilograms.

Metal part = three-fourth of total weight =

Wooden part = 14.9 - 11.175 = 3.725 kilograms.

Hence, the wooden part is 3.725 kilograms.

Step-by-step explanation:

8 0

2 years ago

Write the following series in sigma notation.<br> 7 + 16 + 25 +34 +43 +52 + 61

Solnce55 [7]

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: $\sum\limits^7_{n=1} {9n - 2}$

<h3>How to write the series in sigma notation?</h3>

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

First term, a = 7
Common difference, d = 9
Number of terms, n = 7

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7 - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

$\sum\limits^7_{n=1} {9n - 2}$

Read more about arithmetic series at:

brainly.com/question/6561461

3 0

2 years ago

Solve for x: |2x + 12| = 18

julsineya [31]

It can be x = 3 and x = -15

8 0

3 years ago