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Marina86 [1]
2 years ago
13

...

Mathematics
1 answer:
Kryger [21]2 years ago
5 0

Answer:

2nd option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

- 3x - 2y = 30 ( add 3x to both sides )

- 2y = 3x + 30 ( divide terms by - 2 )

y = - \frac{3}{2} x - 15 ← in slope- intercept form

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Find the equation of the line that passes through points (3,5) and (-6,2). Write the equation in slope intercept form.
andrezito [222]
1)  gradient of line = Δ y ÷ Δ x
                              = (5 -2) ÷ (3 - (-6))
                              = ¹/₃
   
     using the point-slope form (y-y₁) = m(x-x₁)
     using (3,5)
           (y - 5) = ¹/₃ (x -3)
             y - 5  = ¹/₃x - 1
        ⇒      <span>  y =   ¹/₃ x  + 4  [OPTION D]


</span>2)        y =  2x  +  5  .... (1)
<span>           </span>y = ¹/₂ x  + 6  .... (2)
       
         by substituting y in (1) for y in (2)

           2x  +  5 = ¹/₂ x  + 6 
                 ³/₂ x = 1
                      x = ²/₃

        by substituting found x (2)

            y = ¹/₂ (²/₃)  + 6
            y = ¹⁹/₃

∴ common point is (²/₃ , ¹⁹/₃)  thus answer is FALSE [OPTION B]


3) Yes [OPTION A]
     This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.

4) No [OPTION B]
       Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other.  Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.

6 0
3 years ago
Write the equation in standard form for the circle with center (5,0) passing through (-1, 9/2)
andreev551 [17]

Answer:

(x - 5)^2 + y^2 = 225/4,

or you could write it as (x - 5)^2 + y^2 = 56.25.

Step-by-step explanation:

The factor form is

(x - h)^2 + (y - k)^2 = r^2  where the center is (h, k) and r = the radius.

So we have:

(x - 5)^2 + (y - 0)^2 = r^2

As the point  (-1, 9/2) is on the line:

(-1 - 5)^2 +  (9/2)^2 = r^2

r^2 =  36 +  81/4

r^2 = 225/4.

So  substituting for r^2:

(x - 5)^2 + (y - 0)^2 = 225/4

(x - 5)^2 + y^2 = 225/4 is the standard form.

3 0
3 years ago
A can is 7 inches high and has a radius of 2 inches,
Yuliya22 [10]

Answer:

87.92 cubic inches

Step-by-step explanation:

to find the volume of a cylinder the formula is V = \pir^{2}h

so first i squared 2

2x2= 4

i then multiplied 4 by the height (7)

4x7 = 28

then times 28 by pi (3.14)

28x 3.14 = 87.92

4 0
2 years ago
Are short-term investments less prone to price validity than long-term investments true or false
gizmo_the_mogwai [7]

Answer:

yes its true

Step-by-step explanation

its true

5 0
2 years ago
The side length of an equilateral triangle is 6 cm. What is the height of the triangle? StartFraction 3 Over StartRoot 3 EndRoot
iren2701 [21]

Answer:

C: 3 root 3

Step-by-step explanation:

got it right on edge

8 0
3 years ago
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