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grigory [225]
2 years ago
12

4m-2(3+5m) in standard form

Mathematics
1 answer:
NNADVOKAT [17]2 years ago
3 0
Simplified: -6m-6
Factored: 6(m+1)
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Answer:

all u have to do is dvide

4 0
3 years ago
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Write the polar equation in rectangular form.
zhuklara [117]

Answer:

Step-by-step explanation:

The identities you need here are:

r=\sqrt{x^2+y^2}  and   r^2=x^2+y^2

You also need to know that

x = rcosθ  and

y = rsinθ

to get this done.

We have

r = 6 sin θ

Let's first multiply both sides by r (you'll always begin these this way; you'll see why in a second):

r² = 6r sin θ

Now let's replace r² with what it's equal to:

x² + y² = 6r sin θ

Now let's replace r sin θ with what it's equal to:

x² + y² = 6y

That looks like the beginnings of a circle.  Let's get everything on one side because I have a feeling we will be completing the square on this:

x^2+y^2-6y=0

Complete the square on the y-terms by taking half its linear term, squaring it and adding it to both sides.

The y linear term is 6.  Half of 6 is 3, and 3 squared is 9, so we add 9 in on both sides:

x^2+(y^2-6y+9)=9

In the process of completing the square, we created within that set of parenthesis a perfect square binomial:

x^2+(y-3)^2=9

And there's your circle!  Third choice down is the one you want.

Fun, huh?

5 0
3 years ago
What is the equation of the quadratic graph with a focus of (4,3) and a directrix of y=-6
Rufina [12.5K]

Answer:

f(x) = (1/18)x^2 - (4/9)x - 65/18

Step-by-step explanation:

Since the focus (4,3) is higher up than is the directrix y = -6, the vertex is between y = -6 and y = 3, halfway between these values, to be exact:  y = -3/2.  Thus, the y-coordinate of the vertex is (-6 + 3/2), or -4.5.  The x-coordinate of the vertex is 4, which comes from that 4 in (4,3).  Thus, the vertex is (4, -4.5) or (4, -4 1/2).

The standard equation for a vertical parabola with vertex at (h,k) is:

4p(y-k) = (x-h)^2, where p is the distance between vertex and focus or between vertex and directrix.  In this case p = 4.5.  Thus, the equation of this quadratic is 4(4.5)(y - [-4.5]) = (x - 4)^2, or

18(y+4.5) = (x-4)^2, or y+4.5 = (1/18)(x-4)^2.

Let's expand this and rewrite the result as a quadratic equation in standard form y = ax^2 + bx + c:

y + 4.5 = (1/18)(x^2 - 8x + 16).  Multiplying all terms by 18 to remove both fractions, we get:

18y + 81 = x^2 - 8x + 16.  Rearranging these terms, we get:

18y = x^2 - 8x + 16 - 81, or

18y = x^2 - 8x - 65, or

y = f(x) = (1/18)x^2 - (4/9)x - 65/18.

5 0
3 years ago
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Mr. Scott’s workroom is a rectangle that measures 25 feet by 27 feet. His woodworking equipment takes up an area of 300 ft squar
Mashutka [201]
375 because if you do 27x25=675 then I did 675-300=375.
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7 0
3 years ago
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A rectangle has an area of 96 sq ft if the width of the yard is 4 ft less than the length, what is the perimeter in ft of the ya
Veronika [31]
The area of a rectangle is obtained through the equation,
  
                                  A = L x W 

The width of the yard is 4 ft less than the length and may be expressed as L - 4. Length may be solved through the following steps,
   
                               A = (L)(L-4)   ; 96 = L(L - 4)    ; L = 12 ft

The length and width are 12 ft and 8 ft, respectively. Perimeter may be solved through the equation,
 
                                           P = 2 x (L + W)

Substituting the values of L and W
 
                                           P = 2 x ( 12 ft + 8 ft) = 40 ft

Therefore, the perimeter of the yard is 40 ft. 




6 0
3 years ago
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