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3 years ago

Find the value of x in each case:

Mathematics

1 answer:

Eduardwww [97]3 years ago

7 0

Answer:

x = 45

Step-by-step explanation:

The angles labeled with the pink x are the same. Line V and Line X are parallel and alternate interior angles are equal when the lines are parallel.

We know the 3 angles inside the triangle and the sum of the angles of a triangle are 180

x+x+ 2x = 180

4x= 180

4x/4 = 180/4

x = 45

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2 years ago

Rod is paid $85 to install a screen door and $115 to install a wooden door. In one week he installed 18 doors and was paid a tot

Rainbow [258]

Answer:Rod installed 7 screen doors

Step-by-step explanation:

Step 1

Let the number of screen door = x

And the number of wooden doors = y

since he installed 18 doors , we have that

screen door + wooden doors = 18

x + y = 18------ equation 1

Also the cost to install a screen door -= $85

and to install a wooden door = $115

And he was therefore paid a total of $1850

Therefore

85x + 115 y = $1860------- equation 2

Step 2----- Solving

x + y = 18------ equation 1

85x + 115 y = $1860------- equation 2

Multiplying equation 1 BY 85

85x + 85y= 1530------- equation 3

85x + 115 y = $1860------- equation 4

subtracting from equation 1 from (2)

115y- 85y= 1860-1530

30y=330

y = 330/30 = 11

To find x

x+ y=18

x= 18-y

x= 18-11= 7

Rod installed 7 screen doors and 11 wooden doors.

8 0

3 years ago

Find all solutions to the equation. cos2x + 2 cos x + 1 = 0

yanalaym [24]

For cos(2x) * (2cos(x) + 1) = 0, use the double angle identity for cos(2x), which is cos^2 x - sin^2 x = cos^2 x - (1-cos^2) = 2cos^2 x - 1.
So we have (2cos^2 x - 1)(2cos x + 1) = 0. So 2cos^2 x -1 = 0 or x = 0 and 2pi.
For 2sec^2 x + tan^2 x - 3 = 0, use the identity sec^2 x = tan^2 x + 1, so we have
2(tan^2 x + 1) + tan^2 x - 3 = 0 or
2tan^2 x + tan^2 x - 1 = 0 or
3 tan^2 x = 1.

So x = pi/2, pi/2 + pi = 3pi/2.

5 0

3 years ago