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3 years ago

8

Which is the graph of the system of equations? x + 2y = 2 4x - y = 4

1 answer:

Sladkaya [172]3 years ago

4 0

Solve for x for x: x+2y=2
x+2y +-2y=2+-2y (add -2y on both sides.)
x=-2y+2
Substitute : -2y+2 for x in
4x-y=4:
4(-2y+2)-y=4
-9y+8=4 Simplify both sides of the equation.
-9y+8+-8=4+-8 Add -8 to both sides.
-9y=-4
-9/-9=-4-9 Divide both sides by -9
y=4/9
Substitute 4/9 for y in
x=-2y+2
x=-2(4/9)+2
x=10/9
y=4/9,x=10/9

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

<em><u>Solution:</u></em>

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

2 years ago

Answer to this please ?

stepan [7]

Answer:

(-a,b)

Step-by-step explanation:

You use midpoint formula which is (x1+x2/2),(y1+y2/2)

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3 years ago

Matthew visited the fruits garden last weekend and helped farmers count the fruits. There were 10% more dragon fruits than passi

lara31 [8.8K]

Answer:

Step-by-step explanation:

let number of passion fruits=x

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=x+0.1 x=(1+0.1)x=1.1 x

total number of fruits=x+1.1 x=(1+1.1)x=2.1 x

1.1x+60% of 1.1x+x+9% of x=2.1x+75

1.1 x+0.6 of 1.1 x+x+0.09 of x=2.1x+75

1.1x+0.66 x+x+0.09 of x =2.1x+75

2.1 x+0.75x-2.1 x=75

0.75 x=75

$\frac{75}{100}x =75\\x=75 \times \frac{100}{75} =100\\Originally ~total ~number~ of~ fruits=2.1x=2.1 \times100=210$

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