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2 years ago

What are the coordinates of the roots of the equation x^2+4x+3=0.

SAT

1 answer:

aleksklad [387]2 years ago

5 0

Answer:Solving the quadratic equation, the coordinates of the roots are: (-1,0) and (-3,0)

The quadratic equation given is:

Which has coefficients .

Now, we find the solutions:

The coordinates of the roots are and , as a root is a value of x when y = 0, thus, in the problem, (-1,0) and (-3,0).

A similar problem is given at brainly.com/question/13729358

Explanation:

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Based on the calculations, we have the following:

The area of the sheet of paper is 96 square inches.
The combined area of the triangle cutouts is equal to 36 square inches.
The area of the parallelogram is equal to 60 square inches.
The altitude of the parallelogram is equal to 6.51 square inches.

<u>Given the following data:</u>

Dimension of paper = 12-inch by 8-inch.

<h3>How to calculate the paper's area.</h3>

Mathematically, the area of the paper is given by this formula:

$Area = length \times breadth\\\\Area = 12 \times 8$

Area = 96 square inches.

<u>For the four (4) right triangles:</u>

Dimension 1 = 2 inches by 9 inches.

Dimension 2 = 3 inches by 6 inches.

Therefore, the combined area of the triangle cutouts is given by:

$A_2= (2 \times \frac{1}{2} \times 2 \times 9) + 2 \times \frac{1}{2} \times 3 \times 6\\\\A_2=18+18\\\\A_2=36\;in^2$

<h3>The area of the parallelogram.</h3>

This would be determined by subtracting the area of the four (4) right triangles from the areas of the paper as follows:

$P = A_p -A_2\\\\P=96-36$

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<h3>The altitude of the parallelogram.</h3>

$P = base \times altitude\\\\Altitude =\frac{P}{base} \\\\Altitude =\frac{60}{9.22}$

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<u>Complete Question:</u>

A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. The resulting parallelogram has a base of approximately 9.22 inches.

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