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neonofarm [45]
2 years ago
6

Put the following equation in standard form and determine the quadratic, linear, and constant coefficients. -3x2 - 8 = 5x - 7

Mathematics
1 answer:
marusya05 [52]2 years ago
8 0

Answer:

  • -3x² -5x -1 = 0
  • -3 (quadratic)
  • -5 (linear)
  • -1 (constant)

Step-by-step explanation:

The equation will be in standard form when terms are listed in order of decreasing degree, and the right side of the equation is 0.

<h3>Standard form</h3>

We can subtract the right-side expression from both sides to get standard form.

  -3x² -8 -(5x -7) = 5x -7 -(5x -7)

  -3x² -8 -5x +7 = 0 . . . . . . . simplify a bit

  -3x² -5x -1 = 0 . . . . . . . . . collect terms

The standard form equation can be written ...

  -3x² -5x -1 = 0

<h3>Coefficients</h3>

The quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.

The linear coefficient is the coefficient of the term with degree 1. The linear coefficient is -5.

The constant coefficient is the coefficient of the term with no variables. The constant is -1.

__

<em>Additional comment</em>

We can make the leading coefficient positive by multiplying the equation by -1. This gives ...

  3x² +5x +1 = 0

with quadratic, linear, and constant coefficients 3, 5, 1.

This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.

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DanielleElmas [232]

Option A:

(x-5)^{2}+(y-3)^{2}=16

Solution:

Given data:

Center of the circle is (5, 3).

Radius of the circle = 4

To find the equation of the circle:

The general form of the equation of a circle in centre-radius format is

(x-h)^{2}+(y-k)^{2}=r^{2}

where (h, k) is the centre of the circle and r is the radius of the circle.

Substitute the given values in the equation of a circle formula:

(x-5)^{2}+(y-3)^{2}=4^{2}

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The equation of the given circle is (x-5)^{2}+(y-3)^{2}=16.

Hence Option A is the correct answer.

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3 years ago
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Step-by-step explanation:

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