Angle ABD and angle DBC are linear pairs, and angle ABD and angle EDC are vertical angles. If the measure of angle ABD=5(2x+1),

Answer: £164.50

Reducing 175 by 6% results in 164.5.

The absolute change is:

164.5 - 175 = -10.5

Step-by-step explanation:

The calculation is as follows:

175 - Percentage decrease =

175 - (6% × 175) =

175 - 6% of 175 =

(1 - 0.06) × 175 =

0.94 × 175 =

94 ÷ 100 × 175 =

94 × 175 divided by 100 =

16,450 ÷ 100 =

164.5

So, the final amount is £164.50

To determine this, we will apply the simple interest formula:
where
signifies the total amount.
indicates the principal amount.
represents the interest rate in decimal.
denotes the time period in years.

Investment A. The initial investment amount is $10,000, so . The investment period is 5 years, meaning . To express the interest rate in decimal, divide it by 100%

Now, we can substitute these values into our formula to find :




Investment B. , , and .




In conclusion, investment A will yield a greater value than investment B at the investment period's conclusion.

The tension does not approach infinity.
<span>Let's analyze free body diagrams (FBDs) for each mass, considering the direction of motion of m₁ as positive.

For m₁: m₁*g - T = m₁*a

For m₂: T - m₂*g = m₂*a

Assuming a massless cord and pulley without friction, the accelerations are the same.

From the second equation: a = (T - m₂*g) / m₂

Substitute into the first:
m₁*g - T = m₁ * [(T - m₂*g) / m₂]
Rearranging:
m₁*g - T = (m₁*T)/m₂ - m₁*g
2*m₁*g = T * (1 + m₁/m₂)
2*m₁*m₂*g = T * (m₂ + m₁)
T = (2*m₁*m₂*g) / (m₂ + m₁)
Taking the limit as m₁ approaches infinity:
T = 2*m₂*g

This aligns with intuition since the greatest acceleration m₁ can have is -g. The cord then accelerates m₂ upward at g while gravity acts downward, leading to a maximum upward acceleration of 2*g for m₁.</span>

9. Observing the pattern, the decimal digit at position n is 9 when n is even and 0 when n is odd. Because 44 is an even number, the 44th digit after the decimal point is 9.

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