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3 years ago

12

How can you write and solve equations involving rational number.

1 answer:

Viefleur [7K]3 years ago

5 0

Answer:turn them into a fraction or decimal

Step-by-step explanation:

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What is the volume of a box measuring 8mm×10cm×5cm

notka56 [123]

The answer is 400 because u multiply 8 x 10= 80 x 5=400

8 0

3 years ago

Read 2 more answers

Please help me for the love of God if i fail I have to repeat the class

Elena-2011 [213]

$\theta$ is in quadrant I, so $\cos\theta>0$ .

$x$ is in quadrant II, so $\sin x>0$ .

Recall that for any angle $\alpha$ ,

$\sin^2\alpha+\cos^2\alpha=1$

Then with the conditions determined above, we get

$\cos\theta=\sqrt{1-\left(\dfrac45\right)^2}=\dfrac35$

and

$\sin x=\sqrt{1-\left(-\dfrac5{13}\right)^2}=\dfrac{12}{13}$

Now recall the compound angle formulas:

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

$\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta$

$\sin2\alpha=2\sin\alpha\cos\alpha$

$\cos2\alpha=\cos^2\alpha-\sin^2\alpha$

as well as the definition of tangent:

$\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}$

Then

1. $\sin(\theta+x)=\sin\theta\cos x+\cos\theta\sin x=\dfrac{16}{65}$

2. $\cos(\theta-x)=\cos\theta\cos x+\sin\theta\sin x=\dfrac{33}{65}$

3. $\tan(\theta+x)=\dfrac{\sin(\theta+x)}{\cos(\theta+x)}=-\dfrac{16}{63}$

4. $\sin2\theta=2\sin\theta\cos\theta=\dfrac{24}{25}$

5. $\cos2x=\cos^2x-\sin^2x=-\dfrac{119}{169}$

6. $\tan2\theta=\dfrac{\sin2\theta}{\cos2\theta}=-\dfrac{24}7$

7. A bit more work required here. Recall the half-angle identities:

$\cos^2\dfrac\alpha2=\dfrac{1+\cos\alpha}2$

$\sin^2\dfrac\alpha2=\dfrac{1-\cos\alpha}2$

$\implies\tan^2\dfrac\alpha2=\dfrac{1-\cos\alpha}{1+\cos\alpha}$

Because $x$ is in quadrant II, we know that $\dfrac x2$ is in quadrant I. Specifically, we know $\dfrac\pi2$ , so $\dfrac\pi4$ . In this quadrant, we have $\tan\dfrac x2>0$ , so

$\tan\dfrac x2=\sqrt{\dfrac{1-\cos x}{1+\cos x}}=\dfrac32$

8. $\sin3\theta=\sin(\theta+2\theta)=\dfrac{44}{125}$

6 0

3 years ago

What is the slope-intercept form of this equation?

kirill [66]

Answer:

y = -8x + 12

Step-by-step explanation:

Slope intercept form: y = mx + b

m ---> Slope & b ----> y-intercept

8x + y = 12

Subtract 8x from both sides

y = -8x + 12

5 0

3 years ago

Find x and y…………….????????

emmasim [6.3K]

Answer:

$let \: \alpha \: be \: the \: 45 \\ \tan( \alpha ) = \frac{p}{b} \\ \tan(45) = \frac{x}{3 \sqrt{2} } \\ 1 = \frac{x}{3 \sqrt{2} } \\ x = 3 \sqrt{2} \\ by \: using \: pythagoras \: therom \\ {y}^{2} = {3 \sqrt{2} }^{2} + {3 \sqrt{2} }^{2} \\ {y}^{2} = 18 + 18 \\ y = \sqrt{36} \\ y = 6$

Step-by-step explanation:

hope this will help you

8 0

2 years ago

Can someone please help me, I'm stuck

mylen [45]

Continue the slop until it hits the y axis and that point will be your y intercept

4 0

3 years ago