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denpristay [2]
2 years ago
13

What is the simplified form of the following expression?

Mathematics
2 answers:
Zigmanuir [339]2 years ago
7 0
2 \sqrt{18} +3 \sqrt{2} + \sqrt{168} =25.558
A. 8.485
B. 25.558
C. 42.426
D. 50.911

B. 18 \sqrt{2} is your answer
Dahasolnce [82]2 years ago
5 0

Answer:

Option B is correct.

The simplified form of the given expression is, 18\sqrt{2}.

Explanation:

Given the expression:  2\sqrt{18} +3 \sqrt{2} +\sqrt{162}

Square root of a number is a value that when multiplied by itself, gives the number.

\sqrt{a^2}=\sqrt{a \times a}= a

we can write the given expression as;

2\sqrt{9 \times 2} +3\sqrt{2} +\sqrt{2 \times 81} or

2\sqrt{3^2 \times 2}+3 \sqrt{2} +\sqrt{9^2 \times 2}

Then by definition of square root,

2 \cdot 3 \sqrt{2} +3\sqrt{2}+9 \sqrt{2} or

6\sqrt{2} +3\sqrt{2} +9\sqrt{2} = 18\sqrt{2}

Therefore, the simplified form of the given expression is, 18\sqrt{2} .




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1.59

Step-by-step explanation:

Divide 2,787 by 1,750

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A famous Premier-league footballer was quoted on Match of the Day to have a goal-scoring statistic of 0.36
stepan [7]

Answer:

13a.\  The \ probability\ of \ scoring\ a\  goal\  in\  a\  game\  is\  0.36\\\\b. 3 \ games

14.

a. \ \£90\\b. \ 26 \ weeks\\c. \ \£4,860

15. This is not possible since p(yellow)=0.10 which is less than the stated 0.35

Step-by-step explanation:

13 a. -A goal-scoring statistic is the probability of a player scoring one goal in any given game played.

-A 0.36 goal scoring statistic means that the player has a 0.36 or 36% chance of scoring a goal in any game that he is involved in.

b. To determine the number of games it takes to score a whole goal, we divide the probability by 1 goal:

Games=\frac{1 \ game}{p(goal)}\\\\=\frac{1}{0.36}\\\\=2.778\approx 3

Hence, it takes approximately 3 games to score a full goal.

14.-The cost of a GCSE retake is £600 and attracts a 15% deposit

#The 15% equivalent in actual pounds is calculated by multiplying the percentage by the total cost as:

C_g=0.15\times 600\\\\=\£90

Hence, the 15%  deposit amount equals £90

b.#The student pays the balance in a £20 per week scheme,the total number of weeks is calculated as:

t=\frac{Balance}{Rate}\\\\=\frac{600-90}{20}\\\\=\frac{510}{20}\\\\=25.5\approx 26

Hence, it takes 26 weeks to clear the balance.

c. Given that 10% is the equivalent of £450

-We divide this amount by 10% to get the 100% equivalent

#We know that 10%=0.10

100\%=\frac{540}{0.1}\\\\=\£5400

#Alternatively, 100% divided by 10% is 10. Multiply this value by £540:

=540\times 10\\\\=\£5400

We subtract the discount amount for the per-discount price:

Cost=Total -discount\\\\=5400-540\\\\=\£4860

Hence, it will cost £4,860 without the discount.

15. Since we are not given the proportion of colors in the bag, we assume that all the 10 beads have different colors.

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P(Each \ Color)=P(Yellow)=\frac{1}{10}\\\\\therefore P(Yellow)

Hence, this is impossible since 0.10<0.35

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