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3 years ago

6

Tourists covered 640 km for a 4 hour ride by car and a 7 hour ride by train. What is the speed of the train, if it is 5 km/h gre

ater than the speed of the car?

2 answers:

anzhelika [568]3 years ago

6 0

670 Is the answer.

I hope this helps. :)

marissa [1.9K]3 years ago

4 0

670 km i hoped that helped

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Find the area of the triangle

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Answer:

180

Step-by-step explanation:

A=1/2*b*h

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kolbaska11 [484]

Answer:

24: x = 31

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Step-by-step explanation:

Remark

24 is supplementary which means that the two angles add to 180o which is on the right hand side of the equation

25 is complementary which means that the two angles add to 90o which is on the left hand side of the equation

Twenty Four

3x + 31 +2x - 6 = 180 Collect the like terms

3x +2x + 31 - 6 = 180 Do the adding and subtracting.

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5x + 25 - 25 = 180 - 25

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2 years ago

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Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

$\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta$

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

$\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta$

Simplify. The denominator uses the difference of two squares pattern:

$\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta$

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

$\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta$

Split into two separate fractions:

$\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta$

Rewrite the two fractions:

$\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta$

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

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2 years ago

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