Which point lies on the line with point-slope equation y-2=5(x-6)

Mathematics

1 answer:

Leviafan [203]3 years ago

6 0

The numbers inside the brackets determine which point lies on the line.

The general formula is

y - h = m(x - k)

The point that lies on the line however is (h,k) both turn to the opposite sign.

So in your case the point is (6,2). I have made a graph to show you that this is true. No other point is possible.

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The sum of a number and 5 times a second number is represented by the equation a+5b=19 . The sum of half of the first number and

TiliK225 [7]

Here you have a system of 2 equations and 2 unknowns. An easy way to solve this type is to isolate one of the variables.

12a + 2b = 8
2b = 8 - 12a
b =
$b = \frac{8 - 12a }{2}$
b = 4 - 6a

Now plug 4 - 6a into equation 1 to solve for a.

a + 5(4 - 6a) = 19

a + 20 - 30a = 19

-29a = -1

a = 1/29 (answer)

Now plug a into the equation for b

b= 4 - 6(1/29)

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3 years ago

In the square pyramid shown below, the area of each triangle is 135 square meters and the area of the base is 324 square meters.

stepan [7]

Area of square base = 324 m²

Length of the square side = √324 = 18

The side of the square is the base of the triangle.

Area of triangle = (1/2)*base* height

135 = (1/2)*18* h

135 = 9h

135/9 = h

15 = h

height = 15 m

To get the height of the Pyramid, the height of the Triangle and half the length of the side of the square form a right angled triangle.

Hypotenus = 15
Half length of square = 18/2 = 9
Height of Pyramid = H

By Pythagoras' Theorem:

15² = H² + 9²

225 =H² + 81

H² + 81 = 225

H² = 225 - 81

H² = 144 Take square root of both sides

H = √144

H = 12

Height = 12 meters.

Option C.

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2 years ago

A boy who is flying a kite lets out 300 feet of string which makes an angle of 60o with the ground. Assuming that the string is

Aleks [24]

<h3>Answer :</h3>

See the attachment for better understanding.

Given : Length of string (AC) = 300ft

To Find : Height of the kite from ground (AB)

$:\implies\sf\:sin60^{\circ}=\dfrac{AB}{AC}$