What is the diameter of this circle? A) 2 cm B) 3.14 cm C) 4 cm D) 8 cm

QUESTION 1

SVEN [57.7K]

Answer:

1)

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

2)

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

Step-by-step explanation:

Question 1)

The given inequality is:

$\frac{5}{12}-\frac{x-3}{6} \leq \frac{x-2}{3}$

Step 1: Making the denominators common for all fractions

$\frac{5}{12}-\frac{2}{2} \times \frac{x-3}{6} \leq \frac{4}{4} \times \frac{x-2}{3}$

This step is done correctly in the given solution.

Step 2: Simplifying

$\frac{5}{12}-\frac{2x-6}{12}\leq \frac{4x-8}{12}$

This step is done correctly in the given solution

Step 3: Multiplying both sides by 12, and simplifying.

$5-(2x-6)\leq 4x-8\\\\ 5-2x+6\leq 4x-8$

First error is made in this step. While opening the brackets, the negative sign should be distributed inside the bracket, which will change the signs.

Step 4: Simplification:

$11-2x\leq 4x-8$

Step 5: Moving Common terms to one side and simplifying

$-2x-4x\leq -8-11\\\\ -6x\leq -19$

Error was made in this step. When a number is moved to other side, its sign will be changed.

Step 6: Dividing both sides by -6

$x\geq \frac{19}{6}$

Conclusion:

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

Question 2:

In the Equation 2: 12=-4(-6x-3), when -4 will be multiplied inside the brackets, the 12 on eft hand side will cancel the 12 that will appear on right hand side, giving a result that will lead to x = 0.

Same is the case with Equation 6: x+5=-5x+5, 5 on both sides will cancel out leaving x = 0.

So, 2nd and 6th equations will have the same solution.

In Equation 1, on expanding the bracket and moving 7 to other side, we get a relation: 4x = 16

In Equation 3, on simplifying the right hand side, and carrying common terms to one side, we get the relation: - 9x = -36

In Equation 5, on expanding the bracket and simplifying the relation is reduced to 4 = x

It can be observed that all these 3 equations have the same solution i.e. x = 4

So, the following set of Equations have the same solution:

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

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3 years ago

Read 2 more answers

What percent of 71 is 90? of 71 is 90.

sashaice [31]

Answer: 126.76056338%

Step-by-step explanation: To answer the question what percent of 71 is 90, we translate the question into an equation.

We have "what percent" which we can represent by the variable X. Next we have "of 71" which means "times 71" and "is 90" means "equals 90."

Now to solve for x, since x is being multiplied by 71, we need to divide by 71 on both sides of the equation.

On the left side of the equation the 71's cancel and we have x. On the right side of the equation we have 90 divided by 71 which is 1.2676056338.

Now, remember that we want to write our answer as a percent. To write 1.2676056338 as a percent, we move the decimal point two places to the right and we get 126.76056338%.