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2 years ago

The amount a gardener gets paid is directly proportional to the number of hours it takes for him to complete the job.

Mathematics

1 answer:

astraxan [27]2 years ago

8 0

Answer:

£105

Step-by-step explanation:

The pay is proportional to the time, so working 18/12 = 3/2 times as long will gain the gardener 3/2 times the pay:

3/2 × £70 = £105

He would get paid £105 for an 18-hour job.

Here are a couple of other solution methods.

<h3>as a proportion</h3>

pay/hours = ?/(18 hours) = £70/(12 hours)

Multiplying by 18 hours, we get ...

? = £70×(18 hours)/(12 hours) = £70×(18/12)

? = £105 . . . . pay for 18 hours

He would get paid £105 for 18 hours.

<h3>as direct proportion equation</h3>

The equation for a directly proportional relationship is ...

y = kx

If we let y represent pay and x represent hours, then we have ...

70 = k(12) ⇒ k = 70/12 = 35/6

Then for 18 hours, the pay is ...

y = (35/6)x

y = (35/6)(18) = 35(3) = 105

He would get paid £105 for 18 hours.

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3 years ago

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HELP! I am confused since the -5 was added, so would it be the slope or would -7 be the slope?

In-s [12.5K]

Answer:

slope = 35; y-intercept = -45

Step-by-step explanation:

Function f(x) is written in the slope-intercept form, y = mx + b.

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You compare it with

f(x) = mx + b, and you see that m, the slope, is -7, and b, the y-intercept is 9.

Now we deal with function h(x).

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This is not written in the y = mx + b form, but we can put it in that form by distributing the -5.

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x lies in the III quadrant.

To find:

The values of $\sin 2x, \cos 2x, \tan 2x$ .

Solution:

It is given that x lies in the III quadrant. It means only tan and cot are positive and others are negative.

We know that,

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

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x lies in the III quadrant. So,

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And,

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We know that,

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$\tan 2x=\dfrac{240}{161}$

Therefore, the required values are $\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}$ .

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