Answer:
see explanation
Step-by-step explanation:
Using the exact values of the trigonometric ratios
sin60° =
, cos60° = 
sin45° = cos45° = 
Using the sine ratio on the right triangle on the left
sin60° =
=
= 
Cross- multiply
2a = 4
×
= 12 ( divide both sides by 2 )
a = 6
Using the cosine ratio on the same right triangle
cos60° =
=
= 
Cross- multiply
2c = 4
( divide both sides by 2 )
c = 2
------------------------------------------------------------------------------------------
Using the sine/cosine ratios on the right triangle on the right
sin45° =
=
= 
Cross- multiply
b = 6
cos45° =
=
= 
Cross- multiply
d = 6
( divide both sides by
)
d = 6
------------------------------------------------------------------------------------------------
a = 6, b = 6
, c = 2
, d = 6
Answer:
your friend has 6 more marbles
Step-by-step explanation:
7×2=14
10×2=20
20-14=6
Answer:
(-1, 4)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define systems</u>
10x + 6y = 14
-x - 6y = -23
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Elimination</em>
- Add 2 equations together: 9x = -9
- Divide 9 on both sides: x = -1
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: -x - 6y = -23
- Substitute in <em>x</em>: -(-1) - 6y = -23
- Multiply: 1 - 6y = -23
- Subtract 1 on both sides: -6y = -24
- Divide -6 on both sides: y = 4
Answer:
√11
Step-by-step explanation:
4 = x^2 -7
Add 7 to both sides
11 = x^2
Square root both sides
√11 = x