Answer:
15.
x = 40/9 = 4 4/9
z = 24/5 = 4 4/5
17.
x = 50
y ≈ 11.5
Step-by-step explanation:
15. Corresponding segments are proportional:
top right side / whole right side = x / 8
5/(5+4) = x/8
x = 8(5/9) = 40/9
x = 4 4/9
__
right side bottom / right side top = z / 6
z = 6(4/5) = 24/5
z = 4 4/5
____
17. The acute angles are complementary:
x = 90 -40 = 50
__
From the Pythagorean theorem:
y = √(15² -9.6²) = √132.84
y ≈ 11.5
Answer:
![\displaystyle x \approx 37.4^\circ](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%5Capprox%2037.4%5E%5Ccirc)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] cosθ = adjacent over hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
Angle θ = <em>x</em>
Adjacent Leg = 5.8
Hypotenuse = 7.3
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [Cosine]:
![\displaystyle cosx^\circ = \frac{5.8}{7.3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cosx%5E%5Ccirc%20%3D%20%5Cfrac%7B5.8%7D%7B7.3%7D)
- [Fraction] Divide:
![\displaystyle cosx^\circ = 0.794521](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cosx%5E%5Ccirc%20%3D%200.794521)
- [Equality Property] Trig inverse:
![\displaystyle x^\circ = cos^{-1}(0.794521)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E%5Ccirc%20%3D%20cos%5E%7B-1%7D%280.794521%29)
- Evaluate trig inverse:
![\displaystyle x = 37.39^\circ](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%2037.39%5E%5Ccirc)
- Round:
![\displaystyle x \approx 37.4^\circ](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%5Capprox%2037.4%5E%5Ccirc)
Kaleerain5,
In order to get your answer you must remember that if the exponent is negative move to the left and if the exponent is positive you have to move to the right.
![8.57 \times 10^{-4}](https://tex.z-dn.net/?f=8.57%20%5Ctimes%2010%5E%7B-4%7D)
- The exponent is negative so move to the left:
![8. = .8 = .08 = .008 = .0008](https://tex.z-dn.net/?f=8.%20%3D%20.8%20%3D%20.08%20%3D%20.008%20%3D%20.0008)
![= .000857](https://tex.z-dn.net/?f=%3D%20.000857)
Therefore your answer is ".000857."
Hope this helps!
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