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3 years ago

Below are two parallel lines with a third line intersecting them.

Mathematics

2 answers:

Andreyy893 years ago

5 0

Answer:

I think x= 84

if the lines are parallel then the angle should be the same. Because one angle =48° the other side is likely to equal the same. Add 48+48, subtract 180 from your answer and that's how you get 84°. hope this helps

andrew-mc [135]3 years ago

4 0

Answer:

132 degrees

Step-by-step explanation:

One sit of the 48 degrees is 48 degrees, so that opposite will be the same. Add them up, get 96. There is a full 360 degrees circle, so get 360 and subtract 96 from it, to get 264 degrees. That is the top and bottom angle of the right side, so just divide it in two

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The following list shows the colours of a random selection of sweets.

Westkost [7]

Answer:

Categorical or Continuous.

Step-by-step explanation:

Because the red appears in each colours (continuous)

6 0

3 years ago

X divided by 1/4 equals 3/4 how do you do it?

Alexus [3.1K]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

$\frac{1}{4} divide \frac{3}{4}$

5 0

3 years ago

in the table are shown the number of hours. Wendy works an amount of pay she receives. Dose this table show direct variation? if

ankoles [38]

Yes, it does because all of those can be multiplied by 9. So, H*9=P. And It means for every hour of work she gets paid 9 dollars. Or 9 dollars an hour.

5 0

3 years ago

A lighthouse is located on a small island 5 km away from the nearest point P on a straight shoreline and its light makes seven r

Vaselesa [24]

Answer:

Light is moving at the speed = 77.78 km/min

Step-by-step explanation:

Given:

Distance between island and point P = 5 km

Moving along the the shoreline when it is 1 km from P.

So, x = 1

From the above statement light makes seven revolutions per minute.

Therefore,

$\frac{d\theta}{dt}=\frac{7\times 2\pi\ rad}{1\ min} = 14\pi\ rad/min$

Solution:

From the given figure.

$tan\theta=\frac{x}{5}$

Substitute x = 1

$tan\theta=\frac{1}{5}$ -------------------(1)

Now, first we differentiate both side with respect to t.

$\frac{d(tan\theta)}{dt} = \frac{d}{dt}.(\frac{x}{3})$

Using chain rule.

$\frac{d(tan\theta)}{dt}.\frac{d\theta}{dt} = (\frac{1}{5})\frac{dx}{dt}$

$sec^{2} \theta.\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

$(1+tan^{2} \theta).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

Substitute $tan\theta=\frac{1}{5}$ from equation 1.

$(1+(\frac{1}{3})^{2} ).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

$(1+\frac{1}{9}).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

Substitute $\frac{d\theta}{dt}=14\pi$

$\frac{10}{9}.14\pi = \frac{1}{5}.\frac{dx}{dt}$

Applying cross multiplication rule.

$\frac{dx}{dt}= \frac{700\pi }{9}$

$\frac{dx}{dt}= 77.78\pi$

Therefore, light is moving along the shore at the speed of 77.78 km/min

6 0

3 years ago

A car cost $20,000 when it was purchased. The value of the car decreases by 8% each year. Find the rate of decay each month and

Lorico [155]

Answer:

The rate of decay each month is -0.006924%

Step-by-step explanation:

The cost of a car after 1 year at a 8% decreased

Decreased price = Sale price - (Sale price x porcentage of decreased/100%)

Decreased price = $20,000 - ($20,000 x 8%/100%)

Decreased price = $20,000 - ($20,000 x 0.08)

Decreased price = $20,000 - $1,600 = $18,400

So, the value of the car decreased by 8% in a year is $18,400.

The general equation for exponential decay is:

$y=C(1-r)^{t}$

Where

y = final amount

C = Sale price

r = rate of decay

t = time

We know that the sale price was $20,000. After a year the decreased price is $18,400.

From the general equation for exponential decay, our sale price is $20,000 decreased over a time of 12 months resulting the final amount of $18,400.

substituting the values

$18,400=20,000(1-r)^{12}$