Answer :
Let's solve each part of the question step-by-step:
The additive inverse of -15 is:
The additive inverse of a number is what you add to that number to get zero. Since -15 + 15 = 0, the additive inverse of -15 is [tex]\boxed{15}[/tex].The product of a negative integer and a positive integer is always:
When you multiply a negative integer by a positive integer, the result is always negative. This is because you are adding a negative value multiple times. Hence, the answer is [tex]\boxed{\text{Negative}}[/tex].(-8) + (-4) - (-2) =
Let's calculate step-by-step:
[tex](-8) + (-4) = -12[/tex]
[tex]-12 - (-2) = -12 + 2 = -10[/tex]
So, the answer is [tex]\boxed{-10}[/tex].18 ÷ (6 - 3) + 2 =
First, solve the expression in the brackets [tex](6 - 3) = 3[/tex].
Then perform the division:
[tex]18 ÷ 3 = 6[/tex]
Now add 2:
[tex]6 + 2 = 8[/tex]
The answer is [tex]\boxed{8}[/tex].24 + 3 + (12 - 4) × 3 =
First, calculate inside the parentheses [tex](12 - 4) = 8[/tex].
Multiply the result by 3:
[tex]8 \times 3 = 24[/tex]
Add the other terms:
[tex]24 + 3 + 24 = 51[/tex]
The correct calculation should show [tex]\boxed{51}[/tex]Which operation should be performed first in the expression 5 × (8 + 2) - 6 - 3?
According to the order of operations, operations inside parentheses are completed first. So, [tex]\boxed{\text{Addition}}[/tex] should be performed first.The standard form of -36/48 is:
To simplify the fraction, find the greatest common divisor of 36 and 48, which is 12:
[tex]-36/48 = -3/4[/tex] (after dividing each by 12). The answer is [tex]\boxed{-\frac{3}{4}}[/tex].Which of the following is an equivalent rational number to 9/4?
Rational numbers that are equivalent have the same value when simplified. [tex]9/4[/tex] is equivalent to [tex]\boxed{\frac{18}{8}}[/tex] when multiplied by 2. However, none of the given choices [tex]\left(\frac{12}{18}, \frac{16}{36}, \frac{4}{18}\right)[/tex] are equivalent. [tex]\frac{12}{18}[/tex] and [tex]\frac{4}{18}[/tex] are not equivalent due to incorrect simplification. So, [tex]\boxed{\text{None}}[/tex] of the given options are equivalent.The sum of 3x² + 5x - 2 and x² - 2x + 7 is:
[tex](3x^2 + 5x - 2) + (x^2 - 2x + 7)[/tex]
Combine like terms:
[tex]3x^2 + x^2 = 4x^2[/tex]
[tex]5x - 2x = 3x[/tex]
[tex]-2 + 7 = 5[/tex]
So, the sum is [tex]4x^2 + 3x + 5[/tex]
Hence, the answer is [tex]\boxed{4x^2 + 3x + 5}[/tex].Subtracting 2y - 3z from 5y + z gives:
Expression: [tex](5y + z) - (2y - 3z)[/tex]
Calculate each part:
[tex]5y - 2y = 3y[/tex]
[tex]z + 3z = 4z[/tex]
The result is [tex]3y + 4z[/tex]
So, the answer is [tex]\boxed{3y + 4z}[/tex].Dividing [tex]12b^3[/tex] by [tex]3b[/tex] gives:
When you divide terms with the same base, you subtract the exponents:
[tex]\frac{12b^3}{3b} = 4b^{3-1} = 4b^2[/tex]
The answer is [tex]\boxed{4b^2}[/tex].The solution of the equation [tex]x + 5 = 12[/tex] is:
To find [tex]x[/tex], subtract 5 from both sides:
[tex]x = 12 - 5[/tex]
[tex]x = 7[/tex]
Hence, the answer is [tex]\boxed{x = 7}[/tex].
