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3 years ago

Which equation represents the perpendicular

Mathematics

1 answer:

Brrunno [24]3 years ago

4 0

Answer:

y = ½x + 2

Step-by-step explanation:

We are given the coordinates of the endpoint as;A(8,2) and

B(0,6)

The midpoint coordinates will be;

((8 + 0)/2, (2 + 6)/2) = (4, 4)

The slope of the midpoint using gradient formula will be;

m = (6 - 2)/(0 - 8)

m = 4/-8

m = -2

Thus, slope of a line perpendicular to the midpoint is;

m_p = -1/m

m_p = -1/-2

m_p = 1/2

Thus, using slope intercept concept, the equation to represent the perpendicular bisector is;

y - 4 = ½(x - 4)

Multiply both sides by 2 to get;

2y - 8 = x - 4

Add 8 to both sides to get;

2y - 8 + 8 = x - 4 + 8

2y = x + 4

Divide through by 2 to get;

y = ½(x + 4)

y = ½x + 2

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3 years ago

Tom has 120 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house

mezya [45]

Answer:

a) Function A(x) = (60*x - 1/2*x²)

b)Side length x = 60 m the other side y = 30 m

c) A (max) = 1800 m²

Step-by-step explanation:

Area of rectangular garden with length " x " and wide "y"

A = x*y

Perimeter of rectangular area ( only three sides 2*y and 1*x)

P(r) = 2*y + x

P(r) = 120 = 2*y + x

y = ( 120 - x ) /2

Area of the garden as function of x is

A(x) = [( 120 - x ) /2]*x ⇒ A(x) = (60*x - 1/2*x²)

Taking derivatives on both sides of the equation:

A´(x) = 60 - x

A´(x) = 0 60 - x = 0

x = 60 m

Then

y = ( 120 - x ) / 2 ⇒ y = (120 - 60 )/2

y = 30 m

A(max) = 30 * 60

A(max) = 1800 m²

8 0

4 years ago

If a truck weighs 3 1/2 tons, how many pounds does it weigh?

Gennadij [26K]

1 ton is 2000 pounds your answer is 7000 pounds

Hope this helps

4 0

3 years ago

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Nat2105 [25]

I don't know but I think it is (3.5,6.7) and the nature I haven't learned that yet

7 0

3 years ago

The terminal ray of angle β , drawn in standard position, passes through the point (−5, 2√7) . What is the value of cos β ? Ente

Alexxx [7]

Step-by-step explanation:

Draw the triangle formed by the ray.

The hypotenuse of the triangle is:

c² = a² + b²

c² = (-5)² + (2√7)²

c² = 25 + 28

c = √53

Therefore:

cos β = -5 / √53

Or, as a proper fraction:

cos β = -5√53 / 53

7 0

3 years ago