I see the solution in three steps.
1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS<span>≅RS | Reflexive Property
3.) </span><span>△RST ≅ △RSQ | AAS Triangle Congruence Property</span>
The solution to the problem is as follows:
We have 2+.8(2) + .8(.8(2)) + .8(.8(.8(2))) + ... =
2( .8^0 + .8^1 + .8^2 + .8^3 + ... ) =
2(.8^n -1) / (.8-1) . As n-->infinity, .8^n-->0 giving us
<span>2(-1)/(-.2) = 2(5) = 10 meters.
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M∠X = 54.3°.
Using the Law of Sines, we have:
Cross multiplying gives us
61(sin 34) = 42(sin X)
Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X
Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X
From the given data, we can generate two equations with two unknowns.
We let x = number of loaves of bread
y = number of batches of muffins
For the equation of the flour requirement:
17 = 3.5x + 2.5y
<span>For the equation of the sugar requirement:
</span>4.5 = 0.75x + 0.75y
We evaluate the solutions by manipulating one of the equations into terms of the other. We use the first equation.We write x in terms of y.
x = (4.5/0.75) - y
Substitute the third equation to the second equation.
17 = (3.5((4.5/0.75)-y)) + 2.5y
Evaluating y and x, we have,
y = 4 and x = 2
Thus, from the amounts she has in hand, she can make 4 loaves of bread and 2 batches of muffins.
