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Serga [27]
3 years ago
5

The measure of Angle E, the angle of elevation from point A to point B, is ( 3 x plus 1 ). The measure of Angle D, the angle of

depression from point B to point A, is 2 ( x plus 8 ) Find the measure of each angle.
Mathematics
1 answer:
ryzh [129]3 years ago
3 0
Let
E----------------> angle of elevation
D----------------> angle of depression
we know that
E=(3x+1)
D=2(x+8)
remember that
angle of elevation is equals to angle of depression------> by alternate angles
then 
E=D
(3x+1)=2(x+8)-----------> 3x+1=2x+16----------> 3x-2x=16-1-----> x=15
E=3*15+1-------> 46°
D=2*15+16-----> 46°

the answer is
the measure of angle of elevation and angle of depression is 46°

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An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref
Deffense [45]
To minimize the cost, we take the straight distance from the refinery to the other side of the river as 2 km. Also, the 7 km will be the distance that has to be traveled by the pipeline in land. The total cost, C, is therefore,
               total cost =   (2 km)($800,000/km) + (7 km)($400,000 /km)
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Thus, the total cost of the pipeline is approximately $4,400,000.00. 
 
4 0
4 years ago
Prove the polynomial identity. (2x−1)2+2(2x−1)=(2x+1)(2x−1) Drag and drop the expressions to correctly complete the proof of the
Alex_Xolod [135]

Answer:

Step-by-step explanation:

Given expression is,

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

To prove this identity we will take the left hand side of the equation and will prove equal to the right side.

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

4x² - 4x + 1 + 4x - 2 = (2x - 1)(2x + 1)

4x² - 1 = (2x - 1)(2x + 1)

(2x - 1)(2x + 1) = (2x - 1)(2x + 1) [Since a² - b² = (a - b)(a + b)]

6 0
4 years ago
Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.​
koban [17]

Answer:

x^2 + 4x + y^2 +8y  =  0

Step-by-step explanation:

Given

A = (-1,-2)

B = (2,4)

AP:BP = 1 : 2

Required

The locus of P

AP:BP = 1 : 2

Express as fraction

\frac{AP}{BP} = \frac{1}{2}

Cross multiply

2AP = BP

Calculate AP and BP using the following distance formula:

d = \sqrt{(x - x_1)^2 + (y - y_1)^2}

So, we have:

2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

Take square of both sides

4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2

Evaluate all squares

4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16

Collect and evaluate like terms

4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20

Open brackets

4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20

Collect like terms

4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y  + 20 - 20 =  0

3x^2 + 12x + 3y^2 +24y  =  0

Divide through by 3

x^2 + 4x + y^2 +8y  =  0

3 0
3 years ago
Help please thanks math is hard
leonid [27]
X= 25
Explanation:
The two lines are equal. Since 48+16= 64,
the other line has to equal 64 as well.
64-39= 25
8 0
3 years ago
Where can I find the shaded area of this diagram?
erik [133]

To find the area of the figure, we divide it into two rectangles as follows:

And we find the area of each rectangle, which is given by:

\begin{gathered} A=b\cdot h \\ \text{where b = base and h = height} \end{gathered}

Area rectangle 1:

A=3\cdot10=30m^2

Area rectangle 2:

A=4\cdot6=24m^2

Therefore, the shaded area of the diagram is:

A=30+24=54m^2

Answer: 54 m^2

7 0
2 years ago
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