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3 years ago

(5m^3+7m-7m^2) + (4-7m^2-m^3)

Mathematics

1 answer:

ankoles [38]3 years ago

6 0

Answer:

4m3−14m2+7m+4

Step-by-step explanation:

so you do 5m3+7m−7m2+4−7m2−m3

=5m3+7m+−7m2+4+−7m2+−m3

Combine Like Terms:

=5m3+7m+−7m2+4+−7m2+−m3

=(5m3+−m3)+(−7m2+−7m2)+(7m)+(4)

=4m3+−14m2+7m+4

Hope this helps

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Find the determinant of the following matrix. [1 -2] [3 4]

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Answer:

Step-by-step explanation:

[1 -2]

[3 4]

We can obtain the determinant of the above matrix by doing the following:

Determinant =(1 × 4) – (3 × –2)

Determinant = 4 – – 6

Determinant = 4 + 6

Determinant = 10

Thus, the determinant of the above matrix is 10

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3 years ago

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3 years ago

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George is making a triangular enclosure in his yard. He plans on using two old fence posts as vertices, and will place a new

Genrish500 [490]

Answer:

The correct answers for the possible locations for the are;

(-9, 1)

(0, 0)

Step-by-step explanation:

The coordinates of two of the three posts are given in feet as (-5, 4) and (2, 6)

The length of the available fencing = 25 feet

The length, l, of the segment between the coordinates of the two old posts vertices of the fence is given by the following equation;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Where;

(x₁, y₁) = (-5, 4)

(x₂, y₂) = (2, 6)

$l = \sqrt{\left (6-4 \right )^{2}+\left (2-(-5) \right )^{2}} = \sqrt{53} \approx 7.25 \ feet$

Given the coordinates of the third point as (x₃, y₃), we have;

Therefore, we have;

$\sqrt{\left (y_{3}-4 \right )^{2}+\left (x_{3}-(-5) \right )^{2}} + \sqrt{\left (y_{3}-6 \right )^{2}+\left (x_{3}-(2) \right )^{2}} = 25 - \sqrt{53}$

For the point (2, 6), we have;

$\sqrt{\left ((-6)-4 \right )^{2}+\left (2-(-5) \right )^{2}} + \sqrt{\left ((-6)-6 \right )^{2}+\left (2-(2) \right )^{2}} = 24.2 > 25-\sqrt{53}$

For the point (-9, 1), we have;

$\sqrt{\left ((-6)-4 \right )^{2}+\left (2-(-5) \right )^{2}} + \sqrt{\left ((-6)-6 \right )^{2}+\left (2-(2) \right )^{2}} = 17.08 < 25-\sqrt{53}$

For the point (0, 0), we have;

$\sqrt{\left ((0)-4 \right )^{2}+\left (0-(-5) \right )^{2}} + \sqrt{\left ((0)-6 \right )^{2}+\left (0-(2) \right )^{2}} = 12.73 < 25-\sqrt{53}$

For the point (8, 8), we have;

$\sqrt{\left ((8)-4 \right )^{2}+\left (8-(-5) \right )^{2}} + \sqrt{\left ((8)-6 \right )^{2}+\left (8-(2) \right )^{2}} = 19.92 > 25-\sqrt{53}$

For the point (-4, -5), we have;

$\sqrt{\left ((-5)-4 \right )^{2}+\left ((-4)-(-5) \right )^{2}} + \sqrt{\left ((-5)-6 \right )^{2}+\left ((-4)-(2) \right )^{2}} = 22.04 > 25-\sqrt{53}$

Therefore, the correct answers for the possible locations for the are (-9, 1) and (0, 0).

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4 years ago