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Cerrena [4.2K]
2 years ago
9

Simplify 4(x - 3) - 2x + 9. O A. -4x + 24 O B. 6x + 3 O C. 2x-3 О D. 2x + 6

Mathematics
1 answer:
QveST [7]2 years ago
8 0

Answer:

c. 2x-3

Step-by-step explanation:

factor the 4 into the parenthesis. To do this you multiply 4 by x and then -3. This will give you 4x-12-2x+9. combine like terms and you get 2x-3

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The figure below shows a shaded rectangular region inside a large rectangle:
SSSSS [86.1K]

Answer:

Step-by-step explanation:

The formula for determining the length of a rectangle is expressed as

Area = length × width

The large rectangle has a length of 10 units and width 5 units. The area of the large rectangle would be

10 × 5 = 50 units²

Inside this rectangle is a smaller rectangle of length 4 units and width 2 units. The area of the smaller rectangle would be

4 × 2 = 8 units²

Probability is expressed as favorable outcome/total number of possible outcomes

The region that is not shaded grey is

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The probability that a point chosen inside the large rectangle is not in the shaded region is

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3 years ago
Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$
horrorfan [7]

Answer:

A +B+C+D  = 3 is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

A+B+C+D = ? if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under \sqrt (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \   (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, A +B+C+D = 5+6-10+2 = \bold3

5 0
3 years ago
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