MATHEMATICS HIGH SCHOOL

Math Homework about Trigonometry - Sine Rule.On a map whose scale is 8 cm to 1 km, an estate is shown as a quadrilateral ABCD. The length of the diagonal AC is 7 cm, BÂC = 55°, BĈA = 77°, DÂC = 90° and DĈA = 40°. (DRAW THE FIGURE)
Calculate:
a) the length, in cm, of the side AB on the map;
b) the length, in km, which represented by AD;
c) the area, in km², which represented by ΔADC.

Answers

Answer 1

Answer:

The length of the side AB in cm is 9.45.

The length of the side AD in km is 1.02.

The area of ΔADC is 3.56 km².

How to find exterior angle of a triangle ?

The exterior angle of a triangle is sum of two opposite interior angles.

The length of the side AB in cm on the map

∠B A C = 55 deg , ∠B C A = 77 deg

∴ ∠C A B is

We know the sum of all the interior angles of a triangle is 180 deg

So, ∠B A C + ∠B C A + ∠CAB = 180 deg

55° +77° + ∠CAB = 180 deg

∠C A B = 48°

∴ sin B= 7/AB

sin 48 deg = 7/AB

AB = 7/0.74

AB = 9.45 cm.

The length of AD in km is

Again from interior angle theorem ∠ADC is

= 60 deg

So,sin 60 deg = 7/AD

0.86 = 7/AD

AD = 8.14 cm

∴AD in km is 1.02 k m s.

The area of Δ ADC is

= 1/2 × AC × AD

= 1/2 × 7 × 8.14

= 28.5 cm²

So, the area in km²is

= 3.56 km².

Learn more about triangles here :

brainly.com/question/16886469

#SPJ2

Answer 2

Answer: The answer on un attached file.

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$3m(2m+9)=0 \n \n3m=0 \ \ \vee \ \ 2m+9 = 0\n \n m=0 \ \ \vee \ \ 2m= -9 /:2\n \nm=0 \ \ \vee \ \ m= -(9)/(2) \n \nm=0 \ \ \vee \ \ m= -4(1)/(2)$

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Identify the type of transformation given the rule M(x, y) = (x, –y), given the rule N(x, y) = (–x, y), and V(x, y) = (x, y – 1).

Answers

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Answers

Answer:

(-6,9,-3)

Step-by-step explanation:

-3x -y +z=6

-3x-y+3z =0

x-3z =3

Multiply the second equation by -1

-1 *(-3x-y+3z) =0*-1

3x +y -3z =0

Add this to the first equation

-3x -y +z=6

3x +y -3z =0

----------------------

0 + 0 + -2z = 6

Divide by -2

-2z/-2 = 6/-2

z = 6/-2

z=-3

Take the third equation to find x

x-3z=3

x-3(-3) = 3

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Subtract 9 from each side

x+9-9 =3-9

x=-6

Now we need to find y

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Add 9 to each side

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$\left\{\begin{array}{ccc}-3x-y+z=6\n-3x-y+3z=0\nx-3z=3&|\text{add 3z to both sides}\end{array}\right\n\nx=3+3z\n\n\text{Substitute it to the first and the second equation:}\n\n\left\{\begin{array}{ccc}-3(3+3z)-y+z=6\n-3(3+3z)-y+3z=0\end{array}\right\n\n\text{use distributive property}\n\n\left\{\begin{array}{ccc}-9-9z-y+z=6&|\text{add 9 to both sides}\n-9-9z-y+3z=0&|\text{add 9 to both sides}\end{array}\right\n\n\text{combine like terms}$

$\left\{\begin{array}{ccc}-8z-y=15\n-6z-y=9&|\text{change the signs}\end{array}\right\n\n\underline{+\left\{\begin{array}{ccc}-8z-y=15\n6z+y=-9\end{array}\right}\qquad\text{add both sides of the equations}\n.\qquad-2z=6\qquad\text{divide both sides by (-2)}\n.\qquad\boxed{z=-3}\n\n\text{Put the value of z to the second equation:}\n\n6(-3)+y=-9\n-18+y=-9\qquad\text{add 18 to both sides}\n\boxed{y=9}\n\n\text{Put the value of z to the equation}\ x=3+3z:\n\nx=3+3(-3)\nx=3-9\n\boxed{x=-6}$

$Answer:\ \boxed{x=-6,\ y=9,\ z=-3\to(-6,\ 9,\ -3)}$

Solve the equation. –x + 8 + 3x = x – 6

Answers

First group the coefficients together on their side of the equal sign.
-x + 3x = 2x.

Then, since it is a positive number, subtract it from that side and the other side.

On the other side, the x becomes -x.

Add the 6 from the other side to the 8 to make 14.

14 = -x

Divide both sides by -1, to get the answer.

x = -14

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8+2x=x-6
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14+2x=x
-2x -2x
14/-1=-x/-1
-14=x

On January 1 of a certain year, the price of gasoline was $2.29 per gallon. Throughout the year, the price of gasoline increased by 2.5% per month. What was the cost of one gallon of gasoline, to the nearest cent, one year after January 1?

Answers

Answer:

$3.08

Step-by-step explanation:

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