Answer:
x=7.5 and x=-12.5
Step-by-step explanation:
|2x+5|-4=16
|2x+5|=20
2x+5=20
2x=15
x=7.5
2x+5=-20
2x=-25
x=-12.5
Answer: Angle 4
Step-by-step explanation:
The angle of depression is formed by the line of sight and the horizontal line tangent to the top of the observer.
The answer is 3.14 m
The area (A) of the circle with radius r is: A = π · r²
The area of the quarter of the circle is: A1 = 1/4A = 1/4 · π · r²
We have:
A1 = ?
r = ?
π = 3.14
d = 4 m
A diameter d is the twice of the radius r: d = 2r.
Therefore, the radius is the half of the diameter: r = d/2
So, the area of the quarter circle would be:
A1 = 1/4 · π · r² = 1/4 · π · (d/2)² =1/4 · π · d²/2² = 1/4 · π · d²/4 = 1/16 · π · d²
A1 = 1/16 · π · d² = 1/16 · 3.14 · 4² = 1/16 · 3.14 · 16 = 3.14 m
Answer:
∠DRM=45°
Step-by-step explanation:
Given: PRST is a parallelogram, m∠T:m∠R=1:3, RD ⊥ PS , RM ⊥ ST.
To find: m∠DRM
Solution: Since, PRST is a parallelogram and then let m∠T=x then m∠R=3x.
From the figure, we get that m∠T+m∠R=180°(Adjacent angles)
x+3x=180°
x=45°
Therefore, m∠T=45° and m∠R=135°.
Also, in parallelogram, opposite angles are equal, therefore m∠R=m∠S=135°.
Now, We know that sum of all the angles of the parallelogram =360°, then
From the quadrilateral DRMS,
∠DRM+∠RMS+∠MSD+∠SDR=360°
∠DRM+90°+135°+90°=360°
∠DRM=360°-315°
∠DRM=45°
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

Where:
m: It's the slope
b: It is the cut-off point with the y axis
We manipulate the expressions to model them in the pending-intersection form
Line 1:

Line 2:

By definition, we have that if two lines are parallel then their slopes are equal. It is observed that the slopes of both lines are equal, so the lines are parallel.
ANswer:
The lines are parallel