Write f(x) = 2x2 44x + 185 in vertex form. to write f(x) = 2x2 44x + 185, factor out from the first two terms. next, form a perf

Answer:

The term 6x should actually be 6x²

Step-by-step-explanation:

The illustration referenced, which depicts the multiplication of the trinomial with the binomial, is provided in the image below.

To identify where Chin's multiplication went wrong and to establish the correct expression, we'll analyze each multiplication performed. Therefore, we have:

3x*x² = 3x³

3x*2x = 6x² (the mistake occurred here, as Chin recorded it as 6x in the chart)

3x*4 = 12x

2*x²=2x²

2*2x = 4x

2*4 = 8

Thus, the term 6x should indeed be corrected to 6x²

Answer: $35

Step-by-step explanation:

The question states that the individual's current bill is $140.00 per month and they wish to reduce this amount by 25%.

To determine how much needs to be subtracted, we calculate 25% of $140.00, as follows:

= 25% of $140

= 25/100 × $140

= 1/4 × $140

= 0.25 × $140

= $35

The individual must cut $35 from the bill, resulting in a new monthly payment of ($140 - $35) = $105.

The measurement of arc DB equals 74.57°. Step-by-step explanation: To clarify the resolution method: A secant intersects a circle in precisely two points, while a tangent intersects at just one point. When a tangent and a secant intersect outside of a circle, the formed angle's measurement is precisely half of the positive difference between the measures of the intercepted arcs. Now, applying this to the issue where secant CE intersects circle A at points D and E, while tangent CB touches circle A at B, forming angle ECB. As such, m∠ECB = 1/2 (m arc EB - m arc DB). Given m arc EB as 96° and m arc DB given as 25x + 21, along with m∠ECB as 5x, we establish the equation 5x = 1/2[96 - (25x + 21)]. After rearranging and solving, we find x = 75/35, simplifying to 15/7. Next, substituting x back into the arc DB formula gives m arc DB = 25(15/7) + 21 = 522/7 yields approximately 74.57°.

Step-by-step explanation of the answer:

Sam allocated $48,000 with 6% interest and the remainder at 10%. He earned a total of $4,000 in interest over the course of one year, and now we need to determine the amount invested at each rate.

Let us denote the amount invested at 6% as .

This results in the 6% investment being $20,000 and the 10% investment totaling = (48000 - 20000) = $28,000

A) The speed of pedestrian BC is 5 km/h

    The speed of pedestrian CD is 0 km/h

    The speed of pedestrian DE is 5 km/h

B) He reached E since the stop after 6 hours

C) The formula for section BC is d(t) = 40 - 5t

    The formula for section CD is d(t) = 20

    The formula for section DE is d(t) = 50 - 5t

Step-by-step breakdown:

A)

In the time-distance graph, speed represents the change in distance with respect to time

this means speed = Δd/Δt ⇒ (slope of the line)

For line BC:

1. Δd = 40 - 20 = 20 km

2. Δt = 4 - 0 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed of pedestrian BC stands at 5 km/h

For line CD:

1. Δd = 20 - 20 = 0 km

2. Δt = 6 - 4 = 2 hours

3. The speed = 0 ÷ 2 = 0 km/h

The speed of pedestrian CD is 0 km/h

For line DE:

1. Δd = 20 - 0 = 20 km

2. Δt = 10 - 6 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed for pedestrian DE is 5 km/h

B)

∵ He stopped at t = 4 hours

∵ He reached point E at t = 10 hours

∵ 10 - 4 = 6 hours

He arrived at E since the stop took 6 hours

C)

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1. f(x) is referenced as d(t)

2. m is the speed

3. x corresponds to t

4. You can calculate c by substituting any coordinates of a point along the line into the formula

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Line BC has a negative slope because d decreases as t increases

∵ m = -5 and c = 40

Thus, d(t) = 40 - 5t

The equation for section BC is d(t) = 40 - 5t

Line CD

Line CD is a horizontal line (which follows the form of any horizontal line represented as y = c)

Thus, m = 0 and c = 20

Therefore, d(t) = 20

The equation for section CD is d(t) = 20

Line DE

Line DE features a negative slope as d decreases along with an increase in t

∵ m = -5

Thus, d(t) = -5t + c

The value of c can be determined by substituting point D's coordinates into the equation

∵ D's coordinates are (6, 20)

Thus, 20 = -5(6) + c

So, 20 = -30 + c

Adding 30 to both sides yields

∴ c = 50

Thus, d(t) = 50 - 5t

The equation for section DE is d(t) = 50 - 5t

Further Learning:

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