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3 years ago

Helppppppppppppppppppp

Mathematics

1 answer:

Alex Ar [27]3 years ago

7 0

Answer:

Step-by-step explanation:

Remote interior angle is an interior angle that is not adjacent to the exterior angle of interest.

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HELP PICS INCLUDED! WILL GIVE BRAINLIEST! SHOW WORK AND EXPLAIN

Naddik [55]

I assume you know about the dot product, and that for two vectors $\mathbf a$ and $\mathbf b$ , the angle between them $\theta$ satisfies

$\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta\iff\cos\theta=\dfrac{\mathbf a\cdot\mathbf b}{\|\mathbf a\|\|\mathbf b\|}$

Then the vectors are parallel if the angle between them is 0 or 180 degrees (0 or pi radians), which would make $\cos\theta=1$ or $\cos\theta=-1$ , respectively.

Part A)

$\vec v_1=\langle\sqrt3,1\rangle\implies\|\vec v_1\|=\sqrt{(\sqrt3)^2+1^2}=\sqrt4=2$

$\vec v_2=\langle-\sqrt3,-1\rangle=-\vec v_1\implies\|\vec v_2\|=\|\vec v_1\|=2$

$\vec v_1\cdot\vec v_2=(\sqrt3)(-\sqrt3)+(1)(-1)=-4$

Then the angle between $\vec v_1,\vec v_2$ is such that

$\cos\theta=\dfrac{-4}{(2)(2)}=-1\implies\theta=\pi\,\mathrm{rad}$

so these vectors are parallel ("antiparallel", more specifically, which means they are parallel but point in opposite directions).

Part B) involves the same computations:

$\vec u_1=\langle2,3\rangle\implies\|\vec u_1\|=\sqrt{2^2+3^2}=\sqrt{13}$

$\vec u_2$ has the same components but differing by sign and order, as $\vec u_1$ ; its magnitude remains the same, though:

$\vec u_2=\langle-3,-2\rangle\implies\|\vec u_2\|=\sqrt{(-3)^2+(-2)^2}=\sqrt{13}$

$\vec u_1\cdot\vec u_2=(2)(-3)+(3)(-2)=-12$

$\implies\cos\theta=\dfrac{-12}{(\sqrt{13})(\sqrt{13})}=-\dfrac{12}{13}\implies\theta=\cos^{-1}\left(-\dfrac{12}{13}\right)$

which is neither 0 nor pi, which means these vectors are not parallel.

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4 years ago

I could really use your help

nydimaria [60]

Answer:

x = $\frac{c-a}{5y}$

Step-by-step explanation:

Given

5xy + a = c ( isolate 5xy by subtracting a from both sides )

5xy = c - a ( isolate x by dividing both sides by 5y )

x = $\frac{c-a}{5y}$

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4 years ago

There are 18 pieces of chalk. The ratio if chalk that is yellow to chalk that is not yellow is 1:2. How many more pieces of whit

katen-ka-za [31]

The amount of chalk are equal

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4 years ago

What fraction of the months in the year have 30 days?

weeeeeb [17]

Answer:

4/12 which reduces to 1/3

Step-by-step explanation:

4 out of 12 months have 30 days.

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3 years ago

The equation y=3x+2 represents a line on a graph. If, (x,5) are the coordinates of a point on the line, what is the value of x?

vovangra [49]

Step-by-step explanation:

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