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2 years ago

Line n intersects lines 1 and m, forming the angles shown in the diagram below.

Mathematics

1 answer:

bija089 [108]2 years ago

7 0

Answer:

B. 4.5

Step-by-step explanation:

(6x + 42)° and (18x - 12)° are alternate interior angles. If line l is parallel to line m, therefore,

6x + 42 = 18x - 12

Solve for the value of x. Combine like terms.

6x - 18x = -42 - 12

-12x = -54

Divide both sides by -12

-12x/-12 = -54/-12

x = 4.5

Therefore, x = 4.5 would prove lines l and m are parallel to each other.

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Find slope A.1/2 B.-1/2 C.-2 D.2

fomenos

Answer:

Option B, -1/2

Step-by-step explanation:

The slope is change in y over change in x.

Since this line is facing downward, we already know that the slope is negative.

To find the ratio, find the change in y and divide the change in x.

Change in y = -1

Change in x = 2

Change in y over change in x: -1/2

Answer: Option B, -1/2

6 0

2 years ago

Integrate this two questions

tankabanditka [31]

Simplify the integrands by polynomial division.

$\dfrac{t^2}{1 - 3t} = -\dfrac19 \left(3t + 1 - \dfrac1{1 - 3t}\right)$

$\dfrac t{1 + 4t} = \dfrac14 \left(1 - \dfrac1{1 + 4t}\right)$

Now computing the integrals is trivial.

$\displaystyle \int \frac{t^2}{1 - 3t} \, dt = -\frac19 \int \left(3t + 1 - \frac1{1-3t}\right) \, dt \\\\ = -\frac19 \left(\frac32 t^2 + t + \frac13 \ln|1 - 3t|\right) + C \\\\ = \boxed{-\frac{t^2}6 - \frac t9 - \frac{\ln|1-3t|}{27} + C}$

where we use the power rule,

$\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C ~~~~ (n\neq-1)$

and a substitution to integrate the last term,

$\displaystyle \int \frac{dt}{1-3t} = -\frac13 \int \frac{du}u \\\\ = -\frac13 \ln|u| + C \\\\ = -\frac13 \ln|1-3t| + C ~~~ (u=1-3t \text{ and } du = -3\,dt)$

$\displaystyle \int \frac t{1+4t} \, dt = \frac14 \int \left(1 - \frac1{1+4t}\right) \, dt \\\\ = \frac14 \left(t - \frac14 \ln|1 + 4t|\right) + C \\\\ = \boxed{\frac t4 - \frac{\ln|1+4t|}{16} + C}$

using the same approach as above.

5 0

1 year ago

Find the area of a circle circumscribing an equilateral triangle of side 15cm. Take pi = 3.14.

miskamm [114]

Answer:

236 cm²

Step-by-step explanation:

Height of an equilateral triangle (h) = √3 /2 (l)

l = side of the equilateral triangle.

h = √3 /2 (15)

In an equilateral triangle the orthocenter, centroid, circumcenter and incenter are in the same spot

The center of the circle is the centroid and height match with the median. The radius of the circumcircle is equal to two thirds the height.

Formula for the Radius of the circumcircle = 2/3 h

= 2/3 x √3 /2 (15)

= 5 √3 cm (=radius)

Area of the circle = πr^

= 3.14 x( 5 √3 ) ^

=3.14 x(25*3)

=3.14 x 75

=235.5

=236 cm²

8 0

2 years ago

How many ways are there to assign 8 visiting different studetns to one Stony Brook summer course, chossing from Calculus I, Line

Dmitry_Shevchenko [17]

Answer:

56 ways

Step-by-step explanation:

Number of ways is given by n combination r (n!/(n - r)!r!)

n = total number of students = 8, r = the number of summer courses = 3

Number of ways = 8 combination 3 = 8!/(8-3)!3! = 8!/5!3! = 8×7×6×5!/5!×6 = 8×7 = 56 ways

6 0

2 years ago

BRAINLIESTT ASAP! PLEASE HELP ME :) thanks!

nadya68 [22]

Answer:

Step-by-step explanation:

Please see the answer in the picture attached below.

" From Step 1: We find that Angle N1 equals to 75 gradius => Answers A and C wrong. Answers B and D are left.

" From Step 4: We find that Angle N2 equals to 129 gradius => Answer B is true.

You don't need to find the exact value of the angle N3 in oder to choose the right answers from A,B,C,D.

Hope this answer can help you. Have a nice day!

7 0

2 years ago