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2 years ago

If 5y = 6x + 16 and 9x = 7y-20, what is the value of 3x - 2y?

Mathematics

2 answers:

Law Incorporation [45]2 years ago

5 0

The value of 3x-2y is -4. From the equation 5y=6x=16 and 9x=7y-20 the values of (x,y) is (4,8).

Step-by-step explanation:

The given equations are,

5y=6x+16.......................(1)

9x=7y-20......................(2)

3x-2y...............................(3)

Step:1

Modify the equations (1) and (2) in (x+y=constant) format,

6x-5y=-16.....................(4)

9x-7y=-20....................(5)

Step:2

Equation (4) is multiplied by 7 ( ∵ 7×Eqn(4))

42x-35y=-112..............(6)

Step:3

Equation (5) is multiplied by 5 (∵ 5×Eqn(5))

45x-35y=-100.............(7)

Step:4

Subtracting Equation (6) and (7)

42x-35y=-112

45x-35y=-100

( - )

(42x-45x)+(35y-35y)=(100-112)

(-3x)+(0)=(-12)

x=4

Step:5

Substitute X value in Equation (1),

5y=6x+16...................(1)

where, x=4,

5y= (6×4)+16

5y=40

y= 8

Step: 6

Check for solution, substitute x and y values in equation (2).

9x=7y-20.......................(2)

(9×4)=(7×8)-20

36=36

Step:7

From given, 3x-2y

where, X=4 and y=8

3x-2y = (3×4)-(2×8)

= 12-16

3x-2y = -4

Result:

The value for 3x-2y is -4. The values of (x,y) are (4,8).

Scrat [10]2 years ago

5 0

Answer:

-4

Step-by-step explanation:

When you graph the system, the 2 lines intersect at the point (4,8). Therefore, the x is 4 and the y is 8. If you plug in 4 and 8 into 3x-2y, you get 3(4)-2(8)=12-16=-4.

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The tallest tree in the world is reputed to be a giant redwood named Hyperion located in Redwood National Park in California, US

dlinn [17]

Answer:

114.02 meters

Step-by-step explanation:

The information you're given about the tree will form a triangle, with the three corners being the top of the tree, the point where the tree meets the ground, and the specified point 41.5 meters from the tree. The angle of elevation (70°) is the angle made where the line representing the ground and the line connecting the top of the tree to the ground at the specified point connect.

The angle where the tree meets the ground is 90°, so the triangle a right triangle.

So this all means you know one angle of a right triangle (70°) and the side adjacent to this angle (41.5 meters). You're solving for the height of the tree, which is the side opposite of the angle you know. You can solve using either Sine, Cosine, or Tangent.

Use the acronym SOHCAHTOA to figure out which of those three functions to use. Feel free to look this up for more information if you haven't heard of it before. In this case, we're using Tangent (TOA = Tangent, Opposite side, Adjacent side)

To solve using any of those three functions, you'll need a scientific calculator. On your calculator, you'll see the buttons SIN, COS, andTAN. For this problem, press TAN and you'll see something appear that says tan (___). You'll need to input a number to get your answer, and here's how to find that number:

Again referencing SOHCAHTOA, the "TOA" part lists Opposite first and then Adjacent. This is because you're going to write a fraction with those two numbers, and since Opposite is first, it's the numerator. That means that Adjacent is the denominator. We don't know the value of the opposite side, so it'll be represented by x, and we do know the value of the adjacent side, 41.5. This means the fraction is $\frac{x}{41.5}$ .

This isn't the number to input into the calculator -- you need to isolate the variable:

The original equation is:

tan 70 = x/41.5

Multiply both sides by 41.5 (To cancel out the denominator and isolate x)

tan 70 (41.5) = x

Now you've got the equation for x, you're ready to put this in your calculator.

What appeared on your calculator was:

tan(__)

Input like follows:

(tan(70))41.5

The brackets are needed like that so the calculator knows to multiply the entire thing by 41.5. You might get a wrong answer otherwise.

Hit enter, and you'l get the height of the tree:

114.02 meters

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