A. 4 dimes and 1 penny because it equal 41 cents, 7 nickels and 6 pennies equal 41 cents too
I suppose you just have to simplify this expression.
(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)
Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :
… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)
Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have
… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)
… = (2¹ - 2²) / (2⁰ - 2¹)
… = (2 - 4) / (1 - 2)
… = (-2) / (-1)
… = 2
Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :
… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)
… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)
… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)
… = (-4<em>y</em>) / (-2<em>y</em>)
… = 2
Here it is given that AB || CD
< EIA = <GJB
Now
∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)
∠EIA ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)
∠IKL + ∠IKC 180° and ∠DLH + ∠JLD =180° (Linear Pair Theorem)
So
m∠IKL + m∠IKC = 180° ....(1)
But ∠IKC ≅ ∠JLD
m∠IKC = m∠JLD (SUBTRACTION PROPERTY OF CONGRUENCY)
So we have
m∠IKL + m∠JLD = 180°
∠IKL and ∠JLD are supplementary angles.
But ∠DLH and ∠JLD are supplementary angles.
∠IKL ≅ ∠DLH (CONGRUENT SUPPLEMENTS THEOREM)
Answer:
y-intercept = (0,-21)
vertex = (2,-25)
Step-by-step explanation:
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