9: Evaluate the following question for f(-2): ​ f(x)=3x+2

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

\( \displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }\)

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

\( \displaystyle \large{ {a}^{2} = a \times a = |b| }\)

Where b is the result from a×a. Let's see an example.

Examples

\( \displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}\)

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

\( \displaystyle \large{ {y}^{2} = - 1}\)

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

\( \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }\)

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

\( \displaystyle \large{ \sqrt{ {x}^{2} } = |x| }\)

Solving absolute value always gives the plus-minus. Therefore...

\( \displaystyle \large{ y = \pm \sqrt{ - 1} }\)

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

\( \displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }\)

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

Answer:

Therefore \(\sqrt{1} \neq -\sqrt{1}\)

Step-by-step explanation:

\(\sqrt{-1} \\\) cannot be calculated as no two identical numbers that are multiplid could give -1. However - \(\sqrt{1}\) means -1 x \(\sqrt{1}\) = -1 x 1 = -1 . Therefore \(\sqrt{1} \neq -\sqrt{1}\)

Answer:

Step-by-step explanation:

1. 3x + 2y - 2x + y + 12 is equivalent to x + 3y + 12

2. 4y + 3y + 3x - 6y - 10 - 2 is equivalent to 3x + y - 12

3. x + 3y + 2x - 3x + 7 + 5 is equivalent to 3y + 12

4. I do not know unfortunately

Answer:

See attached image

Step-by-step explanation:

To solve this, first simplify the compound expressions - the ones with multiple x, y terms and see which of the other expressions matches the simplified expression

I will tell you how to solve one of the more complex expressions; the technique is the same for the rest

Let's take the very last expression
4y + 3y + 3x - 6y -10 - 2

To simplify,

group like terms:

=(4y + 3y - 6y) + 3x +(-10 -2)

= y + 3x - 12

Rewriting with x before y gives
3x + y - 12

and there is a matching 3x + y - 12

4y + 3y + 3x - 6y -10 - 2   ⇔  3x + y - 12

The solution is in the attached image

Answer:

Tan 65=AB/9.5

Multiply both sides by 9.5

AB=20.372815

I don’t know what 3 SF means but you can round.

Step-by-step explanation: Also provided image of another answer!

13 1/4

4.5 into a fraction is 4 1/2. 4 1/2 + 8 3/4 is 13 1/4 feet.

Answer:

The answer is d. 13 1/4 feet PLEASE MARK BRAINLIEST

Step-by-step explanation:

the 8 feet plus the 4 feet from the 4.5 feet makes 12 feet plus the fractions so 8 inches is 1/4 feet and 8 inches plus 5 inches on the 4.5 feet makes 13 inches which is 13 1/4 feet so 8 3/4 feet + 4.5 feet = 13 1/4 feet

Answer:

B.

Step-by-step explanation:

When moving a decimal point 2 places to the right you are multiplying. When moving it to the left you are dividing. In this case we are moving 2 places to the left which the exponent 2 is representing. If you were to move 3 places to the right or left you would need to have a three as your exponent.

Answer:

4,200

Step-by-step explanation:

6.25 x 8 =50, 10.5 x 8 =84. 50 x 84 =4,200

Hope this helped! ;) Have a good day! :)

Answer:

The train travels 578 miles in total.

Step-by-step explanation:

Since the train travels 68 miles per hour and travels for 8.5 hours, 8.5x68 = 578

Answer:

Step-by-step explanation:well 1+1 equals 2 so figure it out yourself

(2/3)*75 = $50

I hope this is right! :)

Answer:

im not sure but i think the answer is The slope of the function A is greater than the slope of function B

Step-by-step explanation:

I did the calculations and what it would look like in my head and A came out greater than B. I hope this helps you :)

Answer: $638.40

Step-by-step explanation:

45% converted to a decimal is 0.45

0.45 of $1200 = 0.45* $1200 (of in this case means multiply)

0.45 * $1200= $440

Because they said 11% of remaining salary, we have to do:

$1200-$440=$760

Now 11% converted to a decimal is 0.11

5% converted to a decimal is 0.05

So 0.11+0.05

0.11+0.05= 0.16

Now 0.16 *$760=$121.60

Now we find the remaining amount so we subtract: $760-$121.60= $638.40

So our answer is $638.40 left

Step-by-step explanation:

-36.8 + 9.2(2). [as the value of x is 2]

-36.8 + 18.4

= - 18.4 [as the number with the

Negative sign is greater]

Answer:

-36.8+9.2x

-36.8+9.2(2)

-36.8+9.2×2

-36.8+18.4

= -18.4

By proportion that is:(54/150) * 8450= 54 * 56 1/3= 3042

Answer:

By proportion that is:(54/150) * 8450= 54 * 56 1/3= 3042

Step-by-step explanation:

Answer:

D (Alicia did 5 more jumping jacks per minute than Melissa.)

Step-by-step explanation:

Alicia's rate is 30 jumping jacks per minute. You can use the formula m=(y2-y1)/(x2-x1) to find the slope/rate. The two points in the table you can use are (1,30) and (2,60). You can plug those coordinates into the slope formula. (60-30)/(2-1)=30/1= 30 jumping jacks per minute.  To find the rate of change/slope for Melissa, you can use the same formula m=(y2-y1)/(x2-x1). The two points you could plug in are (0,0), and (4,100). (100-0)/(4-0)=100/4=25. Melissa does 25 jumping jacks per minute.

Answer:

2255÷86=26

4309÷43=100

7944÷15=529.6

Step-by-step explanation:

I dont have step by step srry

Answer:

6.05 feet

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

just convert it?

3/10

Step-by-step explanation:

60% is the same as 60/100

90% is the same as 90/100

90-60=30

30/100

30/100 is divided by 10 on each side to simplify it to 3/10

Answer:

The answer is choice D.

Answer:

Area of five squares = 1289.09 square units

Perimeter =  194.6 units

Step-by-step explanation:

Area of square and perimeter:

   First find the length of each square, then find the area of each square.

To find the area of five squares, add all the area of each square.

Side of square1 = 27 units

\(\sf Side \ of \ square2 = \dfrac{2}{3}*27=2*9 = 18 \ units\\\\Side \ of\ square3= \dfrac{2}{3}*18=2*6=12 \ units\\\\Side \ of \ square4=\dfrac{2}{3}*12=2*4=8 \ units\\\\Side \ of \ square5=\dfrac{2}{3}*8=\dfrac{16}{3}=5.3 \ units\)

Area of square1 = 27*27 = 729 square units

Area of square2 = 18*18 = 324 square units

Area of square3 = 12*12 = 144 square units

Area of square4 = 8*8 = 64 square units

Area of square5 = 5.3*5.3 = 28.09 square units

Area of five squares = 729 + 324 + 144 + 64 +28.09

                                  = 1289.09 square units

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Perimeter of the composite figure = (27 + 27+27+9) + (18+18+6) +(12+12+4) + (8+8+2.7)+ (5.3+5.3+5.3)

                                                         = 90 + 42 + 28 + 18.7 + 15.9

                                                          = 194.6 units

Answer:

-6.85

Step-by-step explanation:

Answer:

4 x 5 = 20 - 43 = 23

Step-by-step explanation:

Answer: 8

Step-by-step explanation: You can use division to solve.

Answer:

8 days

Step-by-step explanation:

1 day : -$1.26

? days : -$10.08

-10.08 ÷ -1.26 = 8

So ? = 8

Answer: 270

Step-by-step explanation: a. When x = 5 and y = 7,

x'y' = 5'7'

= 10110101 (in binary)

= 181 (in decimal)

b. x'y' can be written as (2^3+1)(2^2+1)(2^1+1)(2^0+1), where ^ denotes exponentiation.

c. When x = 5 and y = 7,

x'y' = (2^3+1)(2^2+1)(2^1+1)(2^0+1)

= (8+1)(4+1)(2+1)(1+1)

= 953*2

= 270

d. No, we did not get the same value for parts a and c. The reason for this is that in part a, we evaluated x'y' using binary arithmetic, while in part c, we evaluated it using decimal arithmetic. The two methods of arithmetic yield different results.

Answer:

A) The table shows a proportional relationship (as the number of pages increase the time is proportionally increasing as well)

D) The 11th page of notes takes longer than normal (too long time duration)           o((⊙﹏⊙))o.

Answer:

10 3/4

Step-by-step explanation:

\(x + \frac{7}{4} = - \frac{5}{2} \times - \frac{5}{1} \\ x = \frac{25}{2} - \frac{7}{4} \\ x = \frac{43}{4} \\ x = 10 + \frac{3}{4} \)

Answer:

8

Step-by-step explanation:

To find the area of a rectangle you have to multiply the base times the height. So you would do 4 x 2 to equal 8.

Hope this helps :)

Answer:  $1487.50

Step-by-step explanation:

hey there again!

Facts:

Principal (starting amount): $1,400

Annual interest rate: 12.5% of the principal. Whenever you get an annual interest rate as a percentage, its always that percentage of the starting amount.

Time given: 6 months, 1/2 a year

the question asks "total amount due' in 6 months. Basically, we want to know how much they will have in their account after 6 months.

Step 1: Find how much interest he will get in 6 months as a percentage.

6 months is 1/2 of a year, so find 1/2 of 12.5

1/2 of 12.5

1/2 x 12.5

0.5 x 12.5

6.25%

Step 2: Find how much interest he gets, but as a number.

Principal: $1400

6.25% of 1400= $87.50

Step 3: Find the total amount of money he will have after 6 months.

he starts with 1400, and gets an additional $87.50 added to his account after 6 months. How much does he have now?

To answer this, add to find the total:

87.50+1400= $1487.50