3. Which two expressions are equivalent for any value of y? *

Mathematics

1 answer:

-Dominant- [34]3 years ago

5 0

Given:

The pair of expressions in the options.

To find:

The two expressions are equivalent for any value of y.

Solution:

Two expressions are equivalent for any value of y, iff they are equivalent.

$3(3y+3)=3(3y)+3(3)$

$3(3y+3)=9y+9$

Clearly, $3(3y+3)$ is not equivalent to $6y+6$ or $9y+6$ . So, options A and B are incorrect.

$9(y+3)=9(y)+9(3)$

$9(y+3)=9y+27$

$9(y+3)=27+9y$

The expression $9(y+3)$ is not equivalent to $12+9y$ . So, option C is incorrect.

The expression $9(y+3)$ is equivalent to $27+9y$ .

Therefore, the correct option is D.

You might be interested in

Alybia was making 115 cookies for a Valentine’s Day party. They were each either red or purple. Forty percent of the cookies wer

NeTakaya

Answer:

69 purple cookies!

Step-by-step explanation:

7 0

3 years ago

I think I know this much so far for A (but I could be wrong):

Eduardwww [97]

Part A. You have the correct first and second derivative.

---------------------------------------------------------------------

Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.

-------------------------------------------------------------

Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out

To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0.
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well.

6 0

3 years ago

Find x please so difficult

Colt1911 [192]

Answer:

120 degrees

Step-by-step explanation:

Attached is a screenshot.

y = 180 - 50 - 70 = 60.

x + y = 180, so x = 120

Remember to try to use parallel lines when you can

The second uses the same method, just the opposite side.