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3 years ago

32.443 rounded to the nearest hundredth

Mathematics

2 answers:

Naddik [55]3 years ago

5 0

The answer would be 32.44 because the 3 is smaller than 5, therefore closer to 40 than 50.

Roman55 [17]3 years ago

5 0

The digit place to the right of the hundredths digit is the thousandths place. The digit in that place is less than 5, so that digit and all to its right can be dropped. Your rounded number is

... 32.44

_____

Had the thousanths place digit been 5 or greater, you would have increased the hundredths-place digit by 1 before dropping digits to its right.

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A rectangle has a height of t^2+7t+6t

jek_recluse [69]

Answer:

$2t^3+15t^2+19t+6$

Step-by-step explanation:

Height of the Rectangle $=t^2+7t+6$

Width of the Rectangle $=2t+1$

Area of the Rectangle = Height X Width

$=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\$

The area of the rectangle is $2t^3+15t^2+19t+6$

4 0

3 years ago

What is the answer to this question?

melisa1 [442]

Answer: I think it is negative.

Step-by-step explanation: When you add a negative to a negative you still have a negative.

7 0

3 years ago

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

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.

5 0

2 years ago

Read 2 more answers

Write the equation of the circle graphed below.

Darina [25.2K]

Answer:

Your equation is $(x - 1)^2 + (y +1)^2 = (\frac{1}{2} )^2$

Step-by-step explanation:

Well, the center origin of the circle is given (h,k) = (1,-1).

We have to find our radius as they gave us a point. from origin to the edge of the circle.

Using the formula: (x - h)^2 + (y - k)^2 = r^2

Plug in our (h,k) = (1,-1) and (x,y) = (0.5,-1) to solve for radius.

(x - h)^2 + (y - k)^2 = r^2

(0.5 - (1))^2 + (-1 - (-1))^2 = r^2

(-0.5)^2 + (0)^2 = r^2

1/4= r^2

r^2 = 1/4

r = 1/2

6 0

2 years ago

Triangle abc has vertices A (4,3) B(1,4) and c (2,1) . What are the vertices of the image after the reflection across the line y

andre [41]

Answer:

A'(4,-5), B'(1,-6), C'(2,-3)

Step-by-step explanation:

Reflect across the line y = -1 to get these points. You can count how many points it takes to get to that line and then add the same amount of points to the other side.

8 0

3 years ago