Esme says the two expressions 4x - 5.2y + 6y + 7.9x - 8x and 19.9x + 11.2y are equivalent. Is she correct? Explain how you know.
1 answer:
Answer:
No, she's incorrect. 4x - 5.2y + 6y + 7.9x - 8x = 3.9x + 0.8y
Step-by-step explanation:
To find out if Esme is correct, we have to group the like terms and simplify.
As you can see, 3.9x + 0.8y is the correct simplified expression, thus making Esme incorrect.
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Refer to the diagram shown below.
The vector has a magnitude of a and a direction of θ degrees south of west.
Use the Pythagorean Theorem to calculate a.
a² = (-530)² + (-200)² = 320900
a = √(320900) = 566.48 mi ≈ 566.5 mi
By definition,
tan θ = (-200)/(-530) = 0.3774
θ = tan⁻¹ 0.3774 = 20.68° ≈ 21°
Answer: about 566.5 mi; 21° south of west.
The vector has a magnitude of a and a direction of θ degrees south of west.
Use the Pythagorean Theorem to calculate a.
a² = (-530)² + (-200)² = 320900
a = √(320900) = 566.48 mi ≈ 566.5 mi
By definition,
tan θ = (-200)/(-530) = 0.3774
θ = tan⁻¹ 0.3774 = 20.68° ≈ 21°
Answer: about 566.5 mi; 21° south of west.