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Gekata [30.6K]
3 years ago
12

Animal Kingdom - You won the lottery and decided to buy all of the cats and dogs at a shelter and let them all roam free on a fa

rm. You forgot to ask exactly how many dogs and how many cats they were giving you, but you know that there are 152 animals altogether and there are 3 times as many dogs as there are cats. Write an equation to find out the number of dogs and cats and then solve it.​
Mathematics
1 answer:
zzz [600]3 years ago
5 0

Answer:

3x=152

Step-by-step explanation:

You know that there are 152 animals intotal so that goes at the end. if we say that the dogs are x because we dont know how many there are, then there are 3 times more cats then there are x.

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8. A right triangle has a perimeter of 60 cm. The legs have a ratio of 5:12. The hypotenuse is twice the
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Answer:

a=24

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Step-by-step explanation:

Perimeter is the sum of the sides (a+b+c=60)

The legs (a and b) have a ratio of 5:12, which means that 5a=12b, which can be simplified to \frac{5}{12} a=b, where b will be the smaller leg.

The hypotenuse will be double the smallest leg, 2b, increased by 6 meters, giving us an equation of c=2b+6

Let's plug these in to get one variable:

a+b+c=60\\a+b+2b+6=60\\a+\frac{5}{12}a+2(\frac{5}{12}a)+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a=54\\\frac{27a}{12}=54\\27a=648\\a=24

Now that we have a, we can plug it in to our previous equations to find our other sides:

5a=12b\\5(24)=12b\\120=12b\\10=b

c=2b+6\\c=2(10)+6\\c=20+6\\c=26

Double-checking:

a+b+c=60\\24+10+26=60\\60=60

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