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3 years ago

What is the equation of the line that passes through the point (9, 6) and is perpendicular to the line y = 3x - 5?

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

5 0

Answer:

Step-by-step explanation:

y = 3x - 5

m₁ = 3

The required line is perpendicular to y = 3x - 5. Let the required line's slope be m₂

m₂ = -1/m₁

m₂ = -1/3

Point (9,6)

Equation of line: y - y₁ = m(x - x₁)

y - 6 = (-1/3)(x - 9)

$y-6=\frac{-1}{3})x+\frac{1}{3}*9\\\\y-6=\frac{-1}{3}x+3\\\\y=\frac{-1}{3}x+3+6\\\\y=\frac{-1}{3}x+9\\$

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Is negative 1/3 less than 1/5

nika2105 [10]

Negatives are always smaller then positives because negatives are less then 0. So, yes, -1/3 is less then 1/5

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3 years ago

A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

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3 years ago

A stretched spring has a length of 12 inches when a weight of 2 lbs is attached to the spring. The same spring has a length of 1

Advocard [28]

The way I figured this one out was saying that if it takes 2lbs to stretch it to 12 inches and 5lbs to stretch to 18 inches that means that 3 additional pounds = 6 inches. Therefore, each additional pound is 2 inches. We know already that with 2 lbs it was 12 inches in length and we can also say that 2 lbs = 4 inches. So subtract 4 from 12 and you end up with the answer of 8 inches.

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3 years ago

A rectangle is 2/5 inches long and 1/3 inches wide what is the area of the rectangle

Agata [3.3K]

2/5 x 1/3 = 2/15 square inches

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4 years ago

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What scale factor was used in going from the grey triangle to the yellow triangle?

Lena [83]

Answer:

Step-by-step explanation:

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3 years ago