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vredina [299]
3 years ago
8

2 At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three

more of each, the ratio
of cats to dogs will be – Write an equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop. Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning. Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.​
Mathematics
1 answer:
KatRina [158]3 years ago
6 0

Let D be dogs and C be cats

<em>dogs, d, is initially five less than twice the number of cats, c</em>

D + 5 = 2C

<em>If she decides to add three more of each, the ratio  of cats to dogs will be</em>

D + 8 = 2C + 3

<em>Could Bea's Pet Shop initially have 15 cats and 20 dogs?</em>

Simply plug in the numbers

20 + 5 = 2(15)

This is clearly not true: 25 does not equal 30

<em />

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CONVERSIONS, PHYSICAL CONSTANTS, AND UNITS

Length:
1 inch (in) =  2.54 centimeters (cm) exactly
1 foot (ft) =  0.305 meters (m)
1 yard (yd)  = 0.914 meters (m)
1 mile (mi) = 5280 feet (ft)  =  1.61 kilometers (km)
1 centimeter (cm)  = 0.394 inches (in)
1 meter (m)  = 100 centimeters (cm)  =  39.4 inches (in) = 3.28 feet (ft)  =  1.09 yards (yd)
1 kilometer (km) = 1000 meters (m)  = 0.621 miles (mi)
1 rod =  16.5 feet (ft) = 5.5 yards (yd) =  5.03 meters (m)
1 astronomical unit (AU) = 1.50 x 108 kilometers (km)  = 9.29 x 107 miles (mi)  
1 light year (LY) = 9.461 x 1012 kilometers ( km) = 5.88 x 1012 miles (mi)  = 0.307 parsec
1 parsec =  approximately 3.26 light years (LY)

Area  =  length  x  width
1 square inch (in2) =  0.00694 square feet (ft2  =  6.45 square centimeters, cm2
1 square foot, (ft2) =  144 square inches (in2  =  0.0929 square meters, m2
1 square yard (yd2  =  1296 square inches (in2  =  9 square feet (ft2  =  0.836 square meters (m2
1 square mile (mi2  =  640 acres  =  2.59 square kilometers (km2 
1 acre  = 160 square rods  =  43,560 square feet (ft2) =  0.405 hectares
1 hectare  =  10,000 square meters (m2  =  100 ares  =  2.47 acres
1 square rod  =  30,25 square yards (yd2  =  25.29 square meters (m2
1 are  =  100 square meters (m2  =  0.01 hetares  =  119.6 square yards (yd2   

Volume =  length  x  width  x  height
1 cubic inch (in3) =  0.000579 cubic feet (ft3) =  16.4 cubic centimeters (cm3)
1 cubic foot (ft3) =  1728 cubic inch (in3) =  0.0283 cubic meters (m3)
1 cubic yard (yd3) =  27 cubic feet (ft3) =  4.65 x 104 cubic inch (in3) =  0.765 cubic meters (m3)
1 cubic meters (m3) =  106 cubic centimeters (cm3) =  1,000 liters (L)  =  35.3 cubic feet (ft3)
1 quart (qt)  =  2 pints (pt) = 946 milliliters (mL) = 0.946 liters (L)
1 gallon (gal) = 4 quarts  = 231 cubic inch (in3) =  3.79 liters (L)
1 liter (L) =  1000 cubic centimeters (cm3) = 1.06 quarts (qt) = 0.265 gallons (gal)

Mass
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1 kilogram (kg) =  1,000 grams  = 0.0685 slugs 
1 atomic mass unit (u)  =  1.66 x 10-27 kilogram (kg) =1.66 x 10-24
1 electron mass  = 9.11 x 10-31 kilogram (kg) =  9.11 x 10-28 grams (g)  =  5.46 x 10-4 atomic mass unit (u) 
1 proton mass =  1.00728 atomic mass unit (u)
1 neutron mass =  1.00866 atomic mass unit (u)

Conversion Between Weight and Mass on Earth
A slug is the mass unit in the British system and is equal to 32.2 pounds (lb) 
A kilogram weighs 9.81 newtons (N) or 2.21 pounds (lb) 
A mass of one (1) gram (g) weighs 981 dynes or 0.0353 ounces (oz) 
A one (1) ounce weight has a mass 28.4 grams (g) or 0.0284 kilograms (kg) 
A one (1) pound weight has a mass of 454 grams (g) or 0.454 kilograms (kg) 
A metric ton has a mass of 1,000 kilograms (kg) 
A one (1) ton (regular) weight has a mass of 2,000 pounds (lb)

Velocity and Speed  =  distance/time
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Force  = mass x acceleration
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Normal Body Temperature  =  98.6 oF

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Air pressure at sea level is approximately  =  1 atm  =  1 bar  =  105 N/m2  (or Pa)   =  14.50 lb/in2
Water pressure increases 9810 N/m2  for each meter of depth or 0.433 lb/in2 for each foot of depth

Work and Energy or Heat Work  =  Force  x  parallel distance
1 joule, J  =  0.738 ft . lb  =  107 ergs
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1 electron Volt, eV  =   1.602 x 10-19 J
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Power  =  Work/time
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Radioactivity
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