Item 20 Factor 42x+28yusing the GCF.

Mathematics

1 answer:

Yanka [14]3 years ago

4 0

So 7×6=42 and 7×4=28 GCF is 7 so 7x(6x+4)

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Will give brainiest and extra points if the answer is correct

Setler79 [48]

Answer:

The range in the average rate of change in temperature of the substance is from a low temperature of $-22^{\circ}$ to a high of $16^{\circ}$ .

Step-by-step explanation:

In the sinusoidal function $y=a\sin(b(x-c))+d$ , $|a|$ represents the amplitude and $y=d$ represents the equation of the midline.

By definition sinusoidal functions ebb and flow with respect to this midline. Therefore, the minimums must occur at $y=d-|a|$ and the maximums must occur at $y=d+|a|$ .

Thus, the minimum, or low, occurs at $y=-3-|-19|=-3-19=\boxed{-22}$ and the maximum, or high, occurs at $y=-3+|-19|=-3+19=\boxed{16}$ .

3 0

3 years ago

what set of transformations could be applied to rectangle abcd to create a'b'c'd'? a. reflected over the x-axis and reflected ov

eduard

It's impossible to give exact answer as you've not attached the image. But I think I can help you by giving some rulles about rotation. 180° rotation is (x;y) change to (-x;-y); 90° counterclockwise (x,y) change to (-y, x); then clockwise <span>90° (x,y), cange to (y, -x). Hope it will help.
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8 0

3 years ago

Cos^2 x+4sin^2 x/2=1

lana [24]

$Let\ \dfrac{x}{2}=a,\ therefore\ x=2a.\\\\\cos^2x+4\sin^2\dfrac{x}{2}=\cos^22a+4\sin^2a\\\\\text{use}\ \cos2x=\sin^2x-\cos^2x\\\\=(\sin^2a-\cos^2a)^2+4\sin^2a\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(\sin^2a)^2-2(\sin^2a)(\cos^2a)+(\cos^2a)^2+4\sin^2a\\\\=\sin^4a-2\sin^2a\cos^2a+\cos^4a+4\sin^2a\\\\=\underbrace{\sin^4a+2\sin^2a\cos^2a+\cos^4a}_{(*)}-4\sin^2a\cos^2a+4\sin^2a\\\\\text{use}\ (*)\qquad(a+b)^2=a^2+2ab+b^2$

$=\underbrace{(\sin^2a)^2+2\sin^2a\cos^2a+(\cos^2a)^2}_{(*)}-4\sin^2a(\cos^2a-1)\\\\=(\sin^2a+\cos^2a)^2-4\sin^2a(\cos^2a-1)\\\\\text{use}\ \sin^2a+\cos^2a=1\to\sin^2a=\cos^2a-1\\\\=1^2-4\sin^2a(\sin^2a)=1-4\sin^4a=1-(2\sin^2a)^2$

$\cos^22a+4\sin^2a=1\\\\1-(2\sin^2a)^2=1\qquad\text{subtract 1 from both sides}\\\\-(2\sin^2a)^2=0\to2\sin^2a=0\qquad\text{divide both sides by 2}\\\\\sin^2a=0\to\sin a=0\\\\a=k\pi\ for\ k\in\mathbb{Z}\\\\\dfrac{x}{2}=k\pi\qquad\text{multiply both sides by 2}\\\\\boxed{x=2k\pi\ for\ k\in\mathbb{Z}}$