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Dahasolnce [82]
3 years ago
9

8. Albert's father is 24 years older than Albert is. In 8 years, his father will be twice as old as Albert. How old is Albert no

w? How old is his father?

Mathematics
1 answer:
Hunter-Best [27]3 years ago
4 0
Albert´s ftather age=x
Albert age=y

We suggest this system of equations:
y=x-24
x+8=2(y+8)

we solve this system of equation by substitution method.

x+8=2[(x-24)+8]
x+8=2(x-16)
x+8=2x-32
x-2x=-32-8
-x=-40
x=40

y=x-24
y=40-24
y=16

Answer: Albert´s father is 40 years old, and Albert is 16 years old.


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6. Benny earns $12.00 per hour as a lifeguard. He earns a bonus of $75.00
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Answer:

75+12h ≥ 399

He must work at least 27 hours

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d1i1m1o1n [39]
<h2>Hello!</h2>

The answer is:

The interval notation will be:  (-∞,-1.59) and (-4.41,∞+)

<h2>Why?</h2>

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Using the quadratic equation, we have:

\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}

We are given the quadratic expression:

x^{2} +6x+7

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a=1\\b=6\\c=7

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\frac{-6+-\sqrt{6^{2}-4*1*7 } }{2*1}=\frac{-6+-\sqrt{36-28 } }{2}\\\\\frac{-6+-\sqrt{36-28}}{2}=\frac{-6+-\sqrt{8}}{2}\\\\x_{1}=\frac{-6+\sqrt{8}}{2}=\frac{-6+2.82}{2}=-1.59\\\\x_{2}=\frac{-6-\sqrt{8}}{2}=\frac{-6-2.82}{2}=-4.41

- Inequality interpretation:

Now that we already know the roots of the quadratic expression, and we can see that the parabola open upwards (positive quadratic coefficient), we can conclude that the function is less than 0 between the numbers -4.41. and -1.59

The interval notation will be:and  (-∞,-1.59) and (-4.41,∞+)

Have a nice day!

Note: I have attached a picture for better understanding.

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