Question 5 Six pairs of shoes cost as much as 1 coat, 2 pairs of jeans cost as much as 3 pairs of shoes, and 4 pairs of socks co

Answer:

m = - 3

Step-by-step explanation:

a³ + 27 can be recognized as a sum of cubes, which factors generally as

a³ + b³ = (a + b)(a² - ab + b²). Therefore:

a³ + 27

= a³ + 3³

= (a + 3)(a² - 3a + 9).

By comparing a² - 3a + 9 to a² + ma + 9, we find that

m = - 3.

Jay's bread has risen to 220% of its initial size. The question, as it stands, is incomplete. What is missing would clarify: Jay's bread increases to 11/5 of its original size after three hours. To determine the percentage of its original size: New bread size = units when dough is at 11/5 of its original size.

Answer:

The exact population of Vermont in 2008 could have been around 618,000

Step-by-step explanation:

* Here's how rounding to the nearest ten thousand works:

- Numbers ending with the last four digits between 0001 and 4999 are rounded down to the nearest lower multiple of ten thousand

- Example: 83,525 rounds down to 80,000.

- If the last four digits are 5000 or above, round up to the next higher ten thousand

- Example: 58,988 rounds up to 60,000

* Applying this rule to the problem given:

Since the rounded population is 620,000 to the nearest ten thousand, the actual population could be any value with the last four digits from 0001 to 4999 (like 618,000) or from 5000 upwards (like 624,000).

Therefore, 618,000 might represent the actual population of Vermont in 2008

The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.

Answer:

Step-by-step explanation:

We are provided with the information that

Function f is decreasing as it moves from quadrant 2 to quadrant 1, tending towards y=0

It intersects the y-axis at the point (0,6) and goes through (1,2).

Function g(x) also approaches y=0 in quadrant 2, but increases in quadrant 1.

It passes through (-1,2) and crosses the y-axis at (0,6).

Reflection across y-axis:

The transformation rule is identified as

Applying this rule, we derive

Then, by substituting

for x=-1

for x=0

Consequently, holds true.