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2 years ago

How do you know when an expression is its simplest form

Mathematics

2 answers:

marishachu [46]2 years ago

5 0

Answer:

you know it is when you can't solve it any further. If the numbers cannot be divided by a common number. there is no possible way to make it any more compacted.

Step-by-step explanation:

kramer2 years ago

5 0

Answer: You know when an expression is in it's simplest form when you can't do anything to it.

Step-by-step explanation:

Example: -3x + 100 > -50

You can break this equation down into tinier pieces and make it easier to understand.

-3x > -150

This is a simpler inequality than the first one but, not in simplest form.

Now, x<50 is -3x+100>-50 in it's simplest form. You can't do anything to x>50 anymore. It's in simplest form.

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A square mosaic is made of small glass squares. If there are 196 small squares in the mosaic, how many are along an edge?

alexandr402 [8]

There would be 14 small glass squares along the edges of the square mosaic.

This is because 14 * 14 = 196, which means that if each side length was 14 squares, that the area of the square would contain 196 squares.

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2 years ago

Please Help???!!! I'm a 7th grader and need help! will give 20 points!

Ganezh [65]

Answer:

3. d= 20mm

4. r= 8 in

5. d= 14 mi

6. r= 11 yd

Step-by-step explanation:

Radius is half of diameter.

Example:

What is the diameter of a circle with a radius of 4?

If r = 4, d = 8

Do radius times 2.

Example 2:

What is the radius of a circle with a diameter of 10?

D = 10, so r = 5

Do diameter divided by 2.

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3 years ago

A room has the area of 60 square meters and perimeter of 32 meters .What are the length and width of the room?

ad-work [718]

I am sorry but i don't no

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2 years ago

Please help with any of this Im stuck and having trouble with pre calc is it basic triogmetric identities using quotient and rec

german

How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.

Let's start with sin here. $\frac{2\sqrt{5}}{5} = \frac{2}{\sqrt{5}}$ Therefore, because sin is y/r, r = $\sqrt{5}$ and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.

cos = $\frac{-1}{\sqrt{5}} = \frac{-\sqrt{5}}{5}$

Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = $4\sqrt{2}$ . Now, to find csc, we have to do r/y.

csc = $\frac{9}{4\sqrt{2}} = \frac{9\sqrt{2}}{8}$

The pythagorean identities are

sin^2 + cos^2 = 1,

1 + cot^2 = csc^2,

tan^2 + 1 = sec^2.

Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.

sin^2 + (-3/4)^2 = 1

sin^2 + 9/16 = 1

sin^2 = 7/16

sin = $\sqrt{7/16}$ = $\frac{\sqrt{7}}{4}$

Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.

tan^2 + 1 = (-4/3)^2

tan^2 + 1 = 16/9

tan^2 = 7/9

tan = - $\sqrt{7/9} = \frac{-\sqrt{7}}{3}$

Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.

1 + cot^2 = $(\frac{-\sqrt{6}}{2})^{2}$

1 + cot^2 = 6/4

cot^2 = 2/4

cot = $\frac{\sqrt{2}}{2}$

tan = $\sqrt{2}$

Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.

$(\frac{2}{\sqrt{2}})^2$ + 1 = sec^2