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aleksley [76]
3 years ago
9

Callie has a new kitten. The kitten weighs 3 pounds less than half the weight of Callie’s cat. Together, the cat and the kitten

weigh 18 pounds. Which system of equations could be used to find the weight of each animal?
Mathematics
1 answer:
Ronch [10]3 years ago
4 0

Answer:

y = \frac{1}{2} x - 3

x + y = 18

Step-by-step explanation:

Let the kitten's weight be y and the cat's weight be x

<u><em>Condition # 1: </em></u>

y = \frac{1}{2} x - 3

<u><em>Condition # 2:</em></u>

x + y = 18

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If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2<br> Express answer as a common fraction.<br> Thanks!!
timama [110]

x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0

By the quadratic formula,

x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2

Then

(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2

\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}

Multiply numerator and denominator by the denominator's conjugate:

\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15

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3 years ago
a woman is 10 times as old as her daughter. In 8 years she will be 4 times as old as her daughter. How okd is her mother now?
Bond [772]

Answer:

48 yr. old

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Assume daughter is 4 and mom is 10 times her age,  so mom is 40.

10 (woman) * 4 (daughter's age) = 40 yr. old mom

Present day...

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4 (yr old daughter) + 8 (yrs later) = 12 yr. old daughter today

So, if mom is 4 times as her daughter's age today...

48 (yr. old mom) / 12 (yr. old daughter) = 4

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How to model the problem
Ilia_Sergeevich [38]
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Cerrena [4.2K]
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I need help with this question ASAP
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Answer:

A, D, and I think E

I hope this helps :)

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