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Korolek [52]
3 years ago
9

Mulitply the binomials and identify the value of "B" in the product. (−2x + 3)(x + 8) = −2x2 −Bx + 24 {"version":"1.1","math":"M

ulitply the binomials and identify the value of "B" in the product. (-2x + 3)(x + 8) = -2x2 -Bx + 24"}
Question 6 options:

7


16


19


13
Mathematics
1 answer:
RUDIKE [14]3 years ago
3 0
For
(c+d)(ex+f)
the expanded form is
dex^2+dex+cfx+df
(ce)x^2+(de+cf)x+(df)
ax^2+bx+c
the value of a is ce
the value of b is de+cf
the value of c is df


so

(-2x+3)(x+8)
(-2x+3)(1x+8)
b is 3*1+-2*8=3-16=-13

answer is -13
so pick 13 because we have -B, so B=13
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What is the value of the expression below when x<br> = 4 and y = 4?<br> 3x + 7y
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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.

4 0
4 years ago
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