Use the Commutative Property of Multiplication to rewrite the algebraic expression: j^37⋅h^24

Question

Use the Commutative Property of Multiplication to rewrite the algebraic expression: j^37⋅h^24
.

GPT-4o mini · Answer

The Commutative Property of Multiplication states that the order of multiplication does not affect the product. Therefore, you can rearrange the factors in the expression $ j^{37} \cdot h^{24} $.

Using the Commutative Property, the expression can be rewritten as:

\[ h^{24} \cdot j^{37} \]

Both forms represent the same value, but the order of the factors has changed.

adaleta · Answer

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8 of 408 of 40 Items
Question
Use the Distributive Property to rewrite the expression (2x−2)(x−6)
.(1 point)
Responses

2x2+10x−10
2 x squared plus 10 x minus 10

3x2−10x−8
3 x squared minus 10 x minus 8

x2−8x+12
x squared minus 8 x plus 12

2x2−14x+12

GPT-4o mini · Answer

To use the Distributive Property to rewrite the expression $(2x - 2)(x - 6)$, we will distribute each term in the first parentheses across each term in the second parentheses:

\[ (2x - 2)(x - 6) = 2x \cdot x + 2x \cdot (-6) - 2 \cdot x - 2 \cdot (-6) \]

Calculating each term:

$2x \cdot x = 2x^2$
$2x \cdot (-6) = -12x$
$-2 \cdot x = -2x$
$-2 \cdot (-6) = 12$

Now, combine these results:

\[ 2x^2 - 12x - 2x + 12 \]

Combine the like terms for $x$:

\[ 2x^2 - 14x + 12 \]

So, the expression $(2x - 2)(x - 6)$ can be rewritten as:

2x² - 14x + 12

Thus, the correct response from your provided options is:

2x² − 14x + 12.

adaleta · Answer

What is (a^2−11)+(3a^2−4a+6) ?(1 point) Responses −5 negative 5 −4a2+4a+5 negative 4 a squared plus 4 a plus 5 3a2−4a−5 3 a squared minus 4 a minus 5 4a2−4a−5

GPT-4o mini · Answer

To simplify the expression $(a^2 - 11) + (3a^2 - 4a + 6)$, we can combine like terms. 1. First, distribute the addition across the terms: $$ a^2 - 11 + 3a^2 - 4a + 6 $$ 2. Now, combine like terms: - For $a^2$ terms: $a^2 + 3a^2 = 4a^2$ - For $a$ terms: There is only one $-4a$ - For constant terms: $-11 + 6 = -5$ Putting it all together, we have: $$ 4a^2 - 4a - 5 $$ Thus, the correct response from your provided options is: **4a² − 4a − 5**.

adaleta · Answer

Multiply the polynomials (2r−5)(r+4) .(2 points) r^2+ r+

GPT-4o mini · Answer

To multiply the polynomials $(2r - 5)(r + 4)$, we can use the distributive property (often referred to as FOIL for binomials): 1. **First**: Multiply the first terms in each polynomial: $$ 2r \cdot r = 2r^2 $$ 2. **Outer**: Multiply the outer terms: $$ 2r \cdot 4 = 8r $$ 3. **Inner**: Multiply the inner terms: $$ -5 \cdot r = -5r $$ 4. **Last**: Multiply the last terms: $$ -5 \cdot 4 = -20 $$ Now, combine all these results: $$ 2r^2 + 8r - 5r - 20 $$ Combine like terms ($8r - 5r$): $$ 2r^2 + 3r - 20 $$ So, the final result of multiplying $(2r - 5)(r + 4)$ is: $$ 2r^2 + 3r - 20 $$ In the format you provided: - $r^2 + 3r - 20$

adaleta · Answer

? r^2+ ?r+?

GPT-4o mini · Answer

From the multiplication of the polynomials $(2r - 5)(r + 4)$, we derived the expanded form:

\[ 2r^2 + 3r - 20 \]

To fit it into the format you provided:

For $r^2$, the coefficient is 2.
For $r$, the coefficient is 3.
The constant term is −20, but since you are asking for $r^2 + ?r + ?$, it seems you want just the coefficients of $r^2$ and $r$.

Thus, the corresponding values would be:

$r^2 + 3r + (-20)$

So, you can fill in the blanks as follows:

First blank (coefficient of $r^2$): 2
Second blank (coefficient of $r$): 3
Third blank (constant term): -20

Putting it all together:

$2r^2 + 3r - 20$ corresponds to:
- 2 (for $r^2$)
- 3 (for $r$)
- −20 (constant term)

If you want it in the blanks format:
2, 3, -20.

adaleta · Answer

Which of the following values for n makes the inequality 2n−−√<5 true?(1 point) Responses 12.5 12.5 18 18 16 16 8

GPT-4o mini · Answer

To solve the inequality $ \sqrt{2n} < 5 $, we will isolate $ n $. 1. First, square both sides to eliminate the square root: $$ 2n < 5^2 $$ This simplifies to: $$ 2n < 25 $$ 2. Now, divide both sides by 2: $$ n < \frac{25}{2} $$ This simplifies to: $$ n < 12.5 $$ Now we can check the given values to see which ones satisfy the inequality $ n < 12.5 $: - **12.5**: Does not satisfy $ n < 12.5 $ (it is equal, not less than). - **18**: Does not satisfy $ n < 12.5 $. - **16**: Does not satisfy $ n < 12.5 $. - **8**: Satisfies $ n < 12.5 $ (8 is less than 12.5). Therefore, the value for $ n $ that makes the inequality true is: **8**.