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3 years ago

Find the distance from the point (6,10) to the line y=-x to the nearest tenth

1 answer:

4 0

<span>points (6,10)
</span>y = -x
x + y = 0

distance = lax1 + by1 + cl/√(a^2 + b^2)
= l1(6) + 1(10) + 0l/√(1^2 + 1^2)
= l6 + 10 + 0l/√(1 + 1)
= l16l/√2
= 16/√2
= 8 .2/√2
= 8 . √2.√2/√2
= 8√2

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What is the value of cosθ given that (−2, −3) is a point on the terminal side of θ ?

snow_tiger [21]

Answer:

-0.555

Step-by-step explanation:

The terminal point of the vector in this problem is

(-2,-3)

So, it is in the 3rd quadrant.

We want to find the angle $\theta$ that gives the direction of this vector.

We can write the components of the vector along the x- and y- direction as:

$v_x = -2\\v_y = -3$

The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:

$tan \theta = \frac{v_y}{v_x}=\frac{-3}{-2}=1.5\\\theta=tan^{-1}(1.5)=56.3^{\circ}$

However, since we are in the 3rd quadrant, the actual angle is:

$\theta=180^{\circ} + 56.3^{\circ} = 236.3^{\circ}$

So now we can find the cosine of the angle, which will be negative:

$cos \theta = cos(236.3^{\circ})=-0.555$

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2 years ago

The matrix equation below represents a two variable linear system. Are there solutions? Explain.

almond37 [142]

Answer:

The coefficient matrix is singular, so there are no solutions or infinite solutions.

The two equations in the linear system are the same, so there are infinite solutions.

Yes, there are solutions

Step-by-step explanation:

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3 years ago

Read 2 more answers

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Answer:

Step-by-step explanation: c

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3 years ago

A laundry bag contains 7 brown socks and 2 black socks. Find the probability of picking a brown sock first,

PilotLPTM [1.2K]

Answer

7/9 chance to pick a brown sock first and 1/4 chance to get a black sock after

Step-by-step explanation:

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3 years ago

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7/3 IS an improper fraction 2 1/3 is a mixed number

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