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3 years ago

Three students used factoring to solve a quadratic equation.

Mathematics

1 answer:

DedPeter [7]3 years ago

3 0

Answer:

The solution was solved correctly by Keith

The solutions of the equation are x=-5,x=-12

Step-by-step explanation:

we have

$x^{2}+17x+72=12$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}+17x=12-72$

$x^{2}+17x=-60$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$x^{2}+17x+8.5^{2} =-60+8.5^{2}$

$x^{2}+17x+72.25 =12.25$

Rewrite as perfect squares

$(x+8.5)^{2}=12.25$

square root both sides

$(x+8.5)=(+/-)3.5$

$x=-8.5(+/-)3.5$

$x=-8.5(+)3.5=-5$

$x=-8.5(-)3.5=-12$

The solution was solved correctly by Keith

The solutions of the equation are x=-5,x=-12

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A sled is being held at rest on a slope that makes an angle theta with the horizontal. After the sled is released, it slides a d

Alenkasestr [34]

Answer:

μ = Sin θ * d₁ / (d₂ - Cos θ*d₁)

d₂ = (d₁*Sin θ) / μ

Step-by-step explanation:

a) We apply The work-energy theorem

W = ΔE

W = - Ff*d

Ff = μ*N = μ*m*g

Distance 1:

- Ff*d₁ = Ef - Ei

⇒ - (μ*m*g*Cos θ)*d₁ = (Kf+Uf) - (Ki+Ui) = (Kf+0) - (0+Ui) = Kf - Ui

Kf = 0.5*m*vf² = 0.5*m*v²

Ui = m*g*h = m*g*d₁*Sin θ

then

- (μ*m*g*Cos θ)*d₁ = 0.5*m*v² - m*g*d₁*Sin θ

⇒ - μ*g*Cos θ*d₁ = 0.5*v² - g*d₁*Sin θ (I)

Distance 2:

- Ff*d₂ = Ef - Ei

⇒ - (μ*m*g)*d₂ = (0+0) - (Ki+0) = - Ki

Ki = 0.5*m*vi² = 0.5*m*v²

then

- (μ*m*g)*d₂ = - 0.5*m*v²

⇒ μ*g*d₂ = 0.5*v² (II)

If we apply (I) + (II)

- μ*g*Cos θ*d₁ = 0.5*v² - g*d₁*Sin θ

μ*g*d₂ = 0.5*v²

⇒ μ*g (d₂ - Cos θ*d₁) = v² - g*d₁*Sin θ (III)

Applying the equation (for the distance 1) we get v:

vf² = vi² + 2*a*d = 0² + 2*(g*Sin θ)*d₁ ⇒ vf² = 2*g*Sin θ*d₁ = v²

then (from the equation III) we get

μ*g (d₂ - Cos θ*d₁) = 2*g*Sin θ*d₁ - g*d₁*Sin θ

⇒ μ (d₂ - Cos θ*d₁) = Sin θ * d₁

⇒ μ = Sin θ * d₁ / (d₂ - Cos θ*d₁)

If μ is a known value

d₂ = ?

We apply The work-energy theorem again

W = ΔK ⇒ - Ff*d₂ = Kf - Ki

Ff = μ*m*g

Kf = 0

Ki = 0.5*m*v² = 0.5*m*2*g*Sin θ*d₁ = m*g*Sin θ*d₁

Finally

- μ*m*g*d₂ = 0 - m*g*Sin θ*d₁ ⇒ d₂ = Sin θ*d₁ / μ

3 0

3 years ago

Polly bought a cracker for $7 and then bought a parrot for $2. By how much did Polly's account change after her transactions?

marysya [2.9K]

Answer:

$Changes = -\$9$

Step-by-step explanation:

Given

$Cracker = \$7$

$Parrot = \$2$

Required

Determine the changes in the account

First, we need to determine the total amount spent;

$Total = Cracker + Parrot$

$Total = \$7 + \$2$

$Total = \$9$

Hence, the changes in her account is a debit of $9 i.e. -$9

7 0

3 years ago

I need help!!!! Please lol

Dmitry_Shevchenko [17]

I hope this helps you

4 0

2 years ago

PLZ HELP ;-;

Vaselesa [24]

The answer is x=6 and y=4.

6+4=10

and 8 times 6 + 12 times 4 is 96.

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3 years ago

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We are given with three lengths of a triangle expressed in terms and variables: (3x – 4) feet, (x^2 – 1) feet, and (2x^2 – 15) feet. The perimeter of the triangle is equal to the sum of the three sides of the triangle. In this case, the sum is 3x^2 + 3x -20. When x is equal to 4, we substitute 3*16 + 3*4 -20 equal to 40 feet.

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