At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take German each year, and be

Answer:

b = 5√3

b = -5√3

Step-by-step explanation:

We have

Keep in mind, the root of a function corresponds to the value of x at which the function's output is zero.

In this case

The roots of the equation are the b values for which f(b) equals zero.

Thus

For f(b)=0

Take the square root of both sides

Now simplify

 and

So we find that

b = 5√3

b = -5√3

Response:

Synthetic division involves dividing a polynomial exclusively by a linear factor.

Elaboration:

The valid points are:

1. The division must occur involving a polynomial and a linear expression.

3. If the last term in the quotient contains a number, a remainder will exist. After performing the division, if a number other than zero remains in the final term of the quotient, it is classified as the remainder.

4. The resulting quotient is represented as a polynomial with a degree one higher than that of the original dividend.

Response: 8n

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Clarification:

The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n

That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11

Side 1 = 4n + 5

Side 2 = 5n + 6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n + 5) + (5n + 6) + (8n)

Perimeter = 4n + 5 + 5n + 6 + 8n

Perimeter = (4n + 5n + 8n) + (5 + 6)

Perimeter = 17n + 11

So this confirms we possess the correct expression for the third side that is missing.

for a width of 7.5 cm

3x^2 + 15x = 3*(7.5)^2 + 15*7.5 = 281.25 cm3

<span>281.25 > 252 </span><span> </span>

<span>Thus, a width of 7.5 cm is not possible.</span>