Answer:
1) 6 cm
2) 117°
Step-by-step explanation:
1) Draw a picture of the rhombus. The distance between opposite sides is the height of the rhombus. If we draw the height at the vertex, we get a right triangle. Using trigonometry:
sin 30° = h / 12
h = 12 sin 30°
h = 6 cm
2) Draw a picture of the rectangle.
∠KML is the angle the diagonal makes with the shorter side ML. This angle is 54°. ∠NKM is the angle the diagonal makes with the shorter side NK. ∠KML and ∠NKM are alternate interior angles, so m∠NKM = 54°.
The angle bisector of angle ∠NKM divides the angle into two equal parts and intersects the longer side NM at point P. So m∠PKM = 27°.
KLMN is a rectangle, so it has right angles. That means ∠KML and ∠KMN are complementary. So m∠KMN = 36°.
We now know the measures of two angles of triangle KPM. Since angles of a triangle add up to 180°, we can find the measure of the third angle:
m∠KPM + 36° + 27° = 180°
m∠KPM = 117°
Answer:
it is a+2b, the one you have selected.
Step-by-step explanation:
Yes they can. they can have any lengths
(-3, 7)
Explanation: the point (-5,8) moves to the left (x axis) 2 points and down (y axis) 1 point. Thus -5 + 2 = -3 and 8 - 1 = 7, so the answer is (-3, 7)
Solution of system of linear equation y = 2x – 4 and 3x - 2y = 8 is x = 0 and y = -4
<h3><u>Solution:
</u></h3>
Need to determine solution of following system of linear equation
y = 2x – 4 ------(1)
3x - 2y = 8 ------(2)
If we observe the equation (1), we can say that we are having value of y in terms of x. so substitution method is the best approach to solve the above system of linear equation.
In substitution method, we will substitute value of y in equation (2) in terms of variable x from equation (1)
On substituting y = 2x – 4 in equation (2) , we get equation in one variable that is x which is as follows
3x – 2 (2x – 4 ) = 8
=> 3x – 4x + 8 = 8
=> -x = 8 – 8
=> x = 0
On substituting x = 0 in equation (1), we get
y = 2 x 0 – 4
=> y = -4
Hence solution of system of linear equation y = 2x – 4 and 3x - 2y = 8 is x = 0 and y = -4