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saul85 [17]
2 years ago
7

What is the slope of the following 12x - 6y = 30

Mathematics
2 answers:
blagie [28]2 years ago
6 0

Answer:

slope = m = 2

olga_2 [115]2 years ago
6 0

Answer:

2

Step-by-step explanation:

The slope intercept form is

y = mx+b where m is the slope

Solve for y

12x - 6y = 30

Subtract 12x from each side

-6y =-12x+30

Divide by -6

y = -12x/-6 +30/-6

y = 2x -5

The slope is 2

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Expand (3 - 2x)6. What is the coefficient of the sixth term?
stich3 [128]
To expand (3 - 2x)^6 use the binomial theorem:

(x + y)^ n = C(n,0) x^ny^0 + C(n,1)x^(n-1) y + C(n,2)x^(n-2) y^2 + ...+ C(n,n+1)xy^(n-1) + C(n,n)x^0y^n


So, for x = 3, y = -2x , and n = 6 you get:

(3 - 2x) ^6 = C(6,0)(3)^6 + C(6,1)(3)^5 (-2x) + C(6,2) (3)^4 (-2x)^3 + C(6,3) (3^3) (-2x)^4 + C(6,4)(3)^2 (-2x)^4 + C(6,5) (3) (-2x)^5 + C(6,6) (-2x)^6

So, the sixth term is C(6,5)(3)(-2x)^5 =  6! / [5! (6-5)! ] * 3 * (-2)^5 x^5 = - 6*3*32 = - 576 x^5.

The coefficient of that term is - 576.

Answer: - 576
5 0
2 years ago
A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.
Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 cm^{3}

The function that represents the area of the cardboard without a lid is given by

f (x,y,z) = xy + 2xz + 2yz ------  (1)

Volume of the cardboard with sides x, y & z is

xyz = 16384

z =  \frac{16384}{xy}

Put this value of z in equation (1) we get

f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )

f (x,y,z) = xy + \frac{32768}{y}  + 2y(\frac{32768}{x} )

Differentiate above equation with respect to x & y we get

f_{x}  = y - \frac{32768}{x^{2} }

f_{y}  = x - \frac{32768}{y^{2} }

Take f_{x}  = 0 \ and  \ f_{y} = 0

y - \frac{32768}{x^{2} } = 0

y = 32768 \ x^{-2}  ------ (2)

x - \frac{32768}{y^{2} } = 0

x = 32768 \ y^{-2}  ------- (3)

By solving equation (2) & (3) we get

x^{3} = 32768

x = 31 cm

From equation 2

y = 32768 \ x^{-2}

y = 32768 (31^{-2})

y = 34 cm

z =  \frac{16384}{xy}

z =  \frac{16384}{(34)(31)}

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

6 0
2 years ago
The center of a hyperbola is (−2,4) , and one vertex is (−2,7) . The slope of one of the asymptotes is 1/2 .
maxonik [38]

Answer:

<h2>The equation is \frac{(y - 4)^{2} }{9 } - \frac{(x + 2)^{2} }{36 } = 1.</h2>

Step-by-step explanation:

The equation of a hyperbola is represented by \frac{(y - k)^{2} }{b^{2} } - \frac{(x - h)^{2} }{a^{2} } = 1, where (h, k) is the center of the hyperbola.

As per the given condition, h = -2 and k = 4.

Thus, the equation becomes \frac{(y - 4)^{2} }{b^{2} } - \frac{(x + 2)^{2} }{a^{2} } = 1.

One vertex is (-2, 7).

Hence, putting x = -2 and y = 7, we get b^{2} = 9.

The slope of the asymptote is \frac{b}{a}.

Hence, \frac{b^{2} }{a^{2} } = \frac{1}{4} \\a^{2} = 36.

Thus, the equation is \frac{(y - 4)^{2} }{9 } - \frac{(x + 2)^{2} }{36 } = 1.

7 0
2 years ago
If f(x)=sinx−1/cos2x, then limx→π2f(x) is equivalent to which of the following?
Harrizon [31]

Answer:

2

Step-by-step explanation:

Given g(x) = sin(x)-1/cos2(x), we are to find the limit if the function g(x) as g(x) tends to π/2

Substituting π/2 into the function

lim x-->π/2 sin(x)-1/cos 2(x)

= sin(π/2) - 1/cos(2)(π/2)

= 1 - 1/cosπ

= 1- 1/-1

= 1 -(-1)

= 1+1

= 2

Hence the limit of the function h(x) = sin(x)-1/cos2(x) as x--> π/2 is 2

8 0
2 years ago
If you vertically stretch the exponential function f(x) = 2X by a factor of 5, what
Aleksandr [31]
The answer to your question is A
8 0
2 years ago
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