The class party started with five chocolate cakes cut in fourths as shown below in the example.

Mathematics

1 answer:

professor190 [17]3 years ago

5 0

<h3>Answer: 7/20</h3>

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Explanation:

One large square cake cuts into 4 smaller slices

Since we have 5 such cakes that are cut like this, we have 5*4 = 20 slices all together.

Count the number of dark shaded slices that are shown in the lower diagram. We have 4+3+4+2 = 7+6 = 13 slices of cake that are left over. This must mean the class ate 20-13 = 7 slices.

The fraction of the cakes eaten is 7/20

Notes:

7/20 = 35/100 = 0.35 = 35%
The fraction 7/20 cannot be reduced further because 7 and 20 have no common factors other than 1.

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A ladder that is 13 meters long is leaning against a wall. The distance between the foot of the ladder and the wall is 7 meters

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<h2>Answer:</h2>

The equation that is used to model the length of ladder in terms of x is:

$x^2-7x-60=0$

<h2>Step-by-step explanation:</h2>

We can model this problem with the help of a right angled triangle whose hypotenuse is 13 meters and the other two legs are x meters and (x-7) meters.

where x is the distance between the top of the ladder and the ground.

and (x-7) is the distance between the foot of the ladder and the wall.

Hence, using Pythagorean Theorem we have:

$13^2=x^2+(x-7)^2\\\\i.e.\\\\169=x^2+x^2+49-14x\\\\i.e.\\\\169=2x^2-14x+49\\\\i.e.\\\\2x^2-14x+49-169=0\\\\i.e.\\\\2x^2-14x-120=0\\\\i.e.\\\\x^2-7x-60=0$