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Sophie [7]
2 years ago
5

Can you solvefor x 3 (x+4)+5x=-20

Mathematics
1 answer:
inn [45]2 years ago
3 0
Solve for x:5 x + 3 (x + 4) = -20
3 (x + 4) = 3 x + 12:3 x + 12 + 5 x = -20
Grouping like terms, 5 x + 3 x + 12 = (5 x + 3 x) + 12:(5 x + 3 x) + 12 = -20
5 x + 3 x = 8 x:8 x + 12 = -20
Subtract 12 from both sides:8 x + (12 - 12) = -12 - 20
12 - 12 = 0:8 x = -20 - 12
-20 - 12 = -32:8 x = -32
Divide both sides of 8 x = -32 by 8:(8 x)/8 = (-32)/8
8/8 = 1:x = (-32)/8
The gcd of -32 and 8 is 8, so (-32)/8 = (8 (-4))/(8×1) = 8/8×-4 = -4:Answer: x = -4
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We know that the washer costs $51 more dollars than the dryer.

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So to simplify this we can do this equation:

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The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
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The equation of the parabola is y = -12\cdot x^{2}.

Step-by-step explanation:

Since the directrix is of the form y = a, the parabola is vertical. The vertex of the parabola (V(x,y)) is the midpoint between the focus (F(x,y)) and a point of the directrix (P(x,y)), that is to say:

V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y) (1)

If we know that F(x,y) = (0, -3) and P(x,y) = (0, 3), then the coordinates of the vertex of the parabola:

V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)

V(x,y) = (0, 0)

The vertex factor (p) is the distance of the focus with respect to the vertex:

p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]} (2)

If we know that F(x,y) = (0, -3) and V(x,y) = (0, 0), then the vertex factor is:

p = \sqrt{0^{2}+(-3)^{2}}

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The equation of the parabola in the vertex form is described below:

y - k = 4\cdot p \cdot (x-h)^{2} (3)

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x - Independent variable.

y - Dependent variable.

h, k - Coordinates of the vertex.

If we know that (h,k) = (0, 0) and p = -3, then the equation of the parabola is y = -12\cdot x^{2}.

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