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Jobisdone [24]
3 years ago
11

Math help plss !! uwu im stuck.

Mathematics
1 answer:
Alexxx [7]3 years ago
6 0

Step-by-step explanation:

1) The four points are:

(x₁, y₁) = (-2, -1)

(x₂, y₂) = (3, 13)

(x₃, y₃) = (15, 5)

(x₄, y₄) = (13, -11)

Using the distanced formula the four side lengths are:

d₁₂ = √((13−-1)² + (3−-2)²) = √221

d₂₃ = √((5−13)² + (15−3)²) = √208

d₃₄ = √((-11−5)² + (13−15)²) = √260

d₄₁ = √((-1−-11)² + (-2−13)²) = √325

None of the lengths are equal, so we know this isn't a rhombus, parallelogram, or kite.  Is it a trapezoid?  To find out, let's find the slopes between the two lines that look like they might be parallel.

m₂₃ = (5 - 13) / (15 - 3) = -2/3

m₄₁ = (-1−-11) / (-2−13) = -2/3

They are indeed parallel.  So this is a trapezoid.

2) Given:

PS ≅ QR

m∠P + m∠Q = 180

m∠R + m∠S = 180

∠P ≅ ∠S

By converse of Alternate Interior Angles Theorem, since ∠P and ∠Q are supplementary, line PS and QR must be parallel.

If a quadrilateral has one pair of opposite sides that are both parallel and congruent, then it is a parallelogram.

Adjacent angles of a parallelogram are supplementary, so m∠P + m∠S = 180.

Since ∠P ≅ ∠S, then by definition of congruent angles, m∠P = m∠S.

Substitution:

m∠P + m∠P = 180

m∠P = 90

Substitution:

m∠S = 90

Opposite angles of a parallelogram are congruent, so m∠Q = m∠S = 90 and m∠R = m∠P = 90.

A parallelogram with four right angles is a rectangle.

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Answer:

m=\frac{9}{13} and b=\frac{40}{13}

Step-by-step explanation:

The equation of curve is

2(x^2+y^2)^2=25(x^2-y^2)

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Differentiate with respect to x.

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130\frac{dy}{dx}=90

Divide both sides by 130.

\frac{dy}{dx}=\frac{9}{13}

If a line passes through a points (x_1,y_1) with slope m, then the point slope form of the line is

y-y_1=m(x-x_1)

The slope of tangent line is \frac{9}{13} and it passes through the point (-3,1). So, the equation of tangent is

y-1=\frac{9}{13}(x-(-3))

y-1=\frac{9}{13}(x)+\frac{27}{13}

Add 1 on both sides.

y=\frac{9}{13}(x)+\frac{27}{13}+1

y=\frac{9}{13}(x)+\frac{40}{13}

Therefore, m=\frac{9}{13} and b=\frac{40}{13}.

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I hope you understand! If not, i'll try to elaborate more

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