The decimals are equivalent to given expression are 50.020 and 50.02.
Get x to one side by subtracting 2x by 5x.
-3x = -30
Then divide both sides by -3 to get x = 10
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Answer:
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Answer:
The height of the light pole to the nearest foot is approximately 50 feet
Step-by-step explanation:
The parameters given in the question are;
The length of the cable = 63 feet
The angle of elevation of the cable to the top of the light pole = 52°
With the assumption that the light pole is perpendicular to the ground, the figure formed by the light pole, the distance of the of the cable from the base of the light pole and the length of the cable form a right triangle
The question can be answered by using trigonometric relations for the sine of the given angle as follows;

The opposite leg length of the formed right triangle = The height of the light pole
The hypotenuse length = The length of the cable = 63 feet
The angle, θ = The angle of elevation = 52°
Plugging in the values, gives;

∴ The height of the light pole = 63 feet × sin(52°) ≈ 49.645 feet
The height of the light pole to the nearest foot ≈ 50 feet.
Answer:
A is (10,0)
B is (3, 3).
Step-by-step explanation:
First we calculate the coordinates of the point A.
Here, y = 0 so we have:
7(0) - 3x + 30 = 0
-3x + 30 = 0
x = -30/-3 = 10.
So A has coordinates (10,0).
Next we find the coordinates of the points where the line passes through the y axis. Here x = 0:
7x - 3(0) = 30
x = 30/7.
So the point is (0, 30/7).
Let the point B have coordinates (x1, y1)
Now x1 = y1 (given).
If we draw a line from B perpendicular to the x axis ( its length will be = y1) then we have 2 similar triangles.
So as corresponding sides are in the same ratio:
y1/ (30/7) = (10-x1) / 10
But as x1 = y1:
x1/ (30/7) = (10-x1) / 10
7 x1 / 30 = (10-x1) / 10
70 x1 = 30(10 - x1)
70x1 = 300 - 30 x1
100 x1 = 300
x1 = 3
So the coordinates of B are (3,3)
Checking the solution to the equation:
LHS = 3 / 30/7 = 3*7 / 30 = 21/30 = 7/10.
RHS = (10 -3 ) / 10 = 7/10.