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3 years ago

Simplify to create an equivalent equation 6(7-3y)+(6y+1)

Mathematics

1 answer:

garri49 [273]3 years ago

4 0

Answer:

43 - 12y

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

6 • (7 - 3y) + (6y + 1)

Step 2 :

Final result :

43 - 12y

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suppose the population of a certain city has been doubling every 30 years and the population was 48,000 in 1900. what will the p

Brilliant_brown [7]

Answer:

768000

Step-by-step explanation:

From 1900 to 2020 = 120 means that it doubles 4 times ( once every 30 years)

=> 48000 * 2 ^ 4 = 768000

3 0

2 years ago

(a) 4x²y + 4xy – 12y

lana [24]

Answer:

4y(x^2+x−3)

Step-by-step explanation:

Hope this helps

8 0

3 years ago

Read 2 more answers

Find the value of x for which ABCD must be a parallelogram

Tamiku [17]

They are equal so...

15x+2 = 9x+20

15x-9x = 20-2

6x =18

x = 18/6 = 3

x = 3

6 0

3 years ago

Identify the standard form of the equation by completing the square.

OLEGan [10]

Answer:

$\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Step-by-step explanation:

<u>Given equation</u>:

$4x^2-9y^2-8x+36y-68=0$

This is an equation for a horizontal hyperbola.

<u>To complete the square for a hyperbola</u>

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

$\implies 4x^2-8x-9y^2+36y=68$

Factor out the coefficient of the x² term and the y² term.

$\implies 4(x^2-2x)-9(y^2-4y)=68$

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

$\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2$

$\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36$

Factor the two perfect trinomials on the left side:

$\implies 4(x-1)^2-9(y-2)^2=36$

Divide both sides by the number of the right side so the right side equals 1:

$\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}$

Simplify:

$\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Therefore, this is the standard equation for a horizontal hyperbola with:

center = (1, 2)
vertices = (-2, 2) and (4, 2)
co-vertices = (1, 0) and (1, 4)
$\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}$
$\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)$