Annie earns $7.50 per hour working after school. She needs at least $185 for a stereo system. Write an inequality that describes
2 answers:
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Let x = the shorter leg
2x + 6 is the longer leg
2x + 9 is the hypotenuse
We now do the Pythagorean Theorem of
Multiply out to get:
The
will cancel out each other when you combine like terms to get all the terms on one side of the equal sign.
Combine like terms with the rest to end with
Factor this to get
then set each factor equal to zero.
You end up with two solutions, x = 15 and x = - 3 HOWEVER distance cannot be measure in negatives so that answer will not work so x = 15. Now plug into our given information.
The short leg is 15 cm long.
The longer leg of 2(15) + 6 = 36 cm long
The hypotenuse of 2(15) + 9 = 39 cm long.
You can check your answers by plugging them into the Pythagorean Theorem again.
2x + 6 is the longer leg
2x + 9 is the hypotenuse
We now do the Pythagorean Theorem of
Multiply out to get:
The
Combine like terms with the rest to end with
Factor this to get
You end up with two solutions, x = 15 and x = - 3 HOWEVER distance cannot be measure in negatives so that answer will not work so x = 15. Now plug into our given information.
The short leg is 15 cm long.
The longer leg of 2(15) + 6 = 36 cm long
The hypotenuse of 2(15) + 9 = 39 cm long.
You can check your answers by plugging them into the Pythagorean Theorem again.
.0029 see picture below for step by step explanation.
The values that correctly models the scenario of the rollercoaster graph will be:
- Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6
- Green (x) = -2.5 × cos(π(x - 6)/4) + 4.5
- Purple (x) = 3.5 - 3.5 × sin(π(x - 12.5)/5)
From the complete question,
For Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6
where at x = 0, Red(x) = 10,
at x = 5, Red(x) = 2.5
For Green (x) = -2.5 × cos(π(x - 6)/4) + 4.5 if 6 ≤ x < 10
where at x = 10, Green (x) = 7,
at x = 6, Green (x) = 2.0
For Purple (x) = 3.5 - 3.5 × sin(π(x - 12.5)/5) if 10 ≤ x ≤ 15
where at x = 10, Purple (x) = 7,
at x = 15, Purple (x) = 0
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