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2 years ago

8

How many square floor tiles of side 1/2m are needed to cover the school hall, excluding the room, shown in the diagram below. Pl

ease show ALL working.

1 answer:

iren [92.7K]2 years ago

8 0

Answer:

Step-by-step explanation:

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Apply division algorithm to find the quotient and remainder on dividing the polynomial 3 x^ + 4 x^ square + 6 x + 9 by x^ + 3x +

Ulleksa [173]

I suppose you mean

$\dfrac{3x^3+4x^2+6x+9}{x^2+3x+7}$

$3x^3=3x\cdot x^2$ , and if we multiply $x^2+3x+7$ by $3x$ we get $3x^3+9x^2+21x$ . Subtracting this from the numerator gives a remainder of $-5x^2-15x+9$ .

$-5x^2=-5\cdot x^2$ , and multiplying $x^2+3x+7$ by $-5$ gives $-5x^2-15x-35$ . Subtracting this from the previous remainder gives a new remainder of $44$ .

$44$ has no remaining factors of $x^2$ in it, so we're done, and

$\dfrac{3x^3+4x^2+6x+9}{x^2+3x+7}=\underbrace{3x-5}_{\rm quotient}+\dfrac{\overbrace{44}^{\rm remainder}}{x^2+3x+7}$

4 0

4 years ago

2x^2+5x+3/x^2-3x-4 divided by 4x^2+2x-6/x^2-8x+16

Masja [62]

Answer: $\frac{x-4}{2x-2}$

Step-by-step explanation:

$\frac{2x^2+5x+3}{x^2-3x-4}$ divided by $\frac{4x^2+2x-6}{x^2-8x+16}$ is the same thing as multiplying $\frac{2x^2+5x+3}{x^2-3x-4}$ by $\frac{x^2-8x+16}{4x^2+2x-6}$ .

The equation we get is:

$\frac{2x^2+5x+3}{x^2-3x-4}*\frac{x^2-8x+16}{4x^2+2x-6}$

With this equation, we can factor each equation:

$\frac{(x+1)(2x+3)}{(x+1)(x-4)} *\frac{(x-4)(x-4)}{2(x-1)(2x+3)}$

We can cancel out like terms since they would be dividing each other:

$\frac{x-4}{2x-2}$

8 0

3 years ago

You invest $1,050.00, buying stock in a company at $10.00/share. The shares increase in value by 13% the first year and decrease

allochka39001 [22]

Number of shares
1050/10=105
After one year share value
10×(1+0.13)=11.3
After the second year share value
11.3×(1−0.05)=10.735
Total
10.735×105=1,127.175

3 0

3 years ago

Read 2 more answers

13(6x – 5) – x = 13 – 2(x + 1

elena-s [515]

Answer:

Step-by-step explanation:

$13(6x-5)-x=13-2(x+1)\\78x-65-x=13-2x-2\\77x-65=11-2x\\77x+2x=11+65\\x=76/79\\x=0.9620$

6 0

3 years ago

what is the base of the exponent in the function f(x)=3(3\8)^2x when the function is written using only rational numbers and is

NeX [460]

The answer:

by definition, an exponential function with base c is defined by <span>h (x) = ac^x</span><span>
where a ≠0, c > 0 , b ≠1, and x is any real number.</span>
The base, c, is a constant and the exponent, x<span>, is a variable.
</span>so if we have f(x)=3(3\8)^2x, this equivalent to f(x)=3(3\8)^y(x),
where y (x)=2x, <span>
therefore, the base is 3/8, and the variable is the function </span>y (x)=2x,

5 0

3 years ago

Read 2 more answers