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2 years ago

Plz help me with this

Mathematics

1 answer:

aleksandrvk [35]2 years ago

7 0

Answer: b) -5 ≤ y ≤ 1

Step-by-step explanation:

y = 3 cos (4x) - 2

↓ ↓

amplitude vertical shift

The amplitude is 3 which gives a range of -3 to 3 but there is also a shift down of 2 units so the new range is: -3 - 2 = -5 to 3 - 2 = 1

-5 ≤ y ≤ 1

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Determine whether each expression is equivalent to

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The algebraic expressions, $x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$ and $5x + 3$ are equivalent to $2x + 4y - 5 + 3x + 8 - 4y$

To determine whether each expression is equivalent to $2x + 4y - 5 + 3x + 8 - 4y$ , apply the knowledge of algebra to solve each of the following in it's simplest form.

First, simplify $2x + 4y - 5 + 3x + 8 - 4y$ as follows:

Add like terms

$2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y - 5 + 8\\5x + 3$

Next, compare or simplify where necessary each of the given algebraic expressions with $5x + 3$

First Option

$x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$

Add like terms together

$2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y -5+8\\5x + 3$

Therefore, $x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$ is equivalent to $2x + 4y - 5 + 3x + 8 - 4y$

Check the box for YES.

Second Option:

$6xy + 3 - 4y$ (cannot be simplified further)

$6xy + 3 - 4y\neq 2x + 4y - 5 + 3x + 8 - 4y$

Therefore:

Leave the box BLANK for NO.

Third Option:

$-8y + 5x - 3$ (cannot be simplified further)

$-8y + 5x - 3 \neq 2x + 4y -5 + 3x + 8 - 4y$

Therefore:

Leave the box BLANK for NO.

Fourth Option:

$5x + 3$

$5x + 3 = 2x + 4y - 5 + 3x + 8 - 4y$

Therefore:

Check the box for YES.

Thus, the algebraic expressions that are equivalent to $2x + 4y - 5 + 3x + 8 - 4y$ are:

$x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$

$5x + 3$

Learn more about algebraic expressions here:

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