Answer :
Let's go through each of the given expressions step-by-step and simplify them.
### a. [tex]\(-42 + (-17)\)[/tex]
To add two negative numbers, you add their absolute values and then make the result negative:
[tex]\[ -42 + (-17) = -(42 + 17) \][/tex]
[tex]\[ 42 + 17 = 59 \][/tex]
[tex]\[ -42 + (-17) = -59 \][/tex]
So, the result is [tex]\(-59\)[/tex].
### b. [tex]\(8 - (-9)\)[/tex]
Subtracting a negative number is the same as adding the positive version of that number:
[tex]\[ 8 - (-9) = 8 + 9 \][/tex]
[tex]\[ 8 + 9 = 17 \][/tex]
So, the result is [tex]\(17\)[/tex].
### c. [tex]\(8(-9)\)[/tex]
To multiply a positive number and a negative number, multiply their absolute values and the result will be negative:
[tex]\[ 8 \times (-9) = -(8 \times 9) \][/tex]
[tex]\[ 8 \times 9 = 72 \][/tex]
[tex]\[ 8 \times (-9) = -72 \][/tex]
So, the result is [tex]\(-72\)[/tex].
### d. [tex]\(-42 \div (-7)\)[/tex]
To divide two negative numbers, divide their absolute values. The result will be positive:
[tex]\[ -42 \div (-7) = \frac{42}{7} \][/tex]
[tex]\[ 42 \div 7 = 6 \][/tex]
So, the result is [tex]\(6.0\)[/tex].
### e. [tex]\(-2(-3)(-4)\)[/tex]
Multiply three numbers by their absolute values, keeping the negative sign in mind:
[tex]\[
-2 \times (-3) = 6 \quad (\text{because } - \times - = +)\\
6 \times (-4) = -24 \quad (\text{because } + \times - = -)
\][/tex]
So, the result is [tex]\(-24\)[/tex].
### f. [tex]\(-18 - 7\)[/tex]
Subtracting a positive number from a negative number is the same as adding their absolute values, but the result is negative:
[tex]\[ -18 - 7 = -(18 + 7) \][/tex]
[tex]\[ 18 + 7 = 25 \][/tex]
[tex]\[ -18 - 7 = -25 \][/tex]
So, the result is [tex]\(-25\)[/tex].
### g. [tex]\((-5)^2\)[/tex]
Squaring a negative number results in a positive number:
[tex]\[ (-5)^2 = (-5) \times (-5) \][/tex]
[tex]\[ (-5) \times (-5) = 25 \][/tex]
So, the result is [tex]\(25\)[/tex].
### h. [tex]\(-5^2\)[/tex]
According to the order of operations, you should square 5 first and then apply the negative sign:
[tex]\[ -5^2 = -(5^2) \][/tex]
[tex]\[ 5^2 = 25 \][/tex]
[tex]\[ -5^2 = -25 \][/tex]
So, the result is [tex]\(-25\)[/tex].
### i. [tex]\(\sqrt{49}\)[/tex]
The square root of 49 is the number which when multiplied by itself gives 49:
[tex]\[ \sqrt{49} = 7 \][/tex]
So, the result is [tex]\(7.0\)[/tex].
In summary, the simplified expressions are:
a. [tex]\(-59\)[/tex]
b. [tex]\(17\)[/tex]
c. [tex]\(-72\)[/tex]
d. [tex]\(6.0\)[/tex]
e. [tex]\(-24\)[/tex]
f. [tex]\(-25\)[/tex]
g. [tex]\(25\)[/tex]
h. [tex]\(-25\)[/tex]
i. [tex]\(7.0\)[/tex]
### a. [tex]\(-42 + (-17)\)[/tex]
To add two negative numbers, you add their absolute values and then make the result negative:
[tex]\[ -42 + (-17) = -(42 + 17) \][/tex]
[tex]\[ 42 + 17 = 59 \][/tex]
[tex]\[ -42 + (-17) = -59 \][/tex]
So, the result is [tex]\(-59\)[/tex].
### b. [tex]\(8 - (-9)\)[/tex]
Subtracting a negative number is the same as adding the positive version of that number:
[tex]\[ 8 - (-9) = 8 + 9 \][/tex]
[tex]\[ 8 + 9 = 17 \][/tex]
So, the result is [tex]\(17\)[/tex].
### c. [tex]\(8(-9)\)[/tex]
To multiply a positive number and a negative number, multiply their absolute values and the result will be negative:
[tex]\[ 8 \times (-9) = -(8 \times 9) \][/tex]
[tex]\[ 8 \times 9 = 72 \][/tex]
[tex]\[ 8 \times (-9) = -72 \][/tex]
So, the result is [tex]\(-72\)[/tex].
### d. [tex]\(-42 \div (-7)\)[/tex]
To divide two negative numbers, divide their absolute values. The result will be positive:
[tex]\[ -42 \div (-7) = \frac{42}{7} \][/tex]
[tex]\[ 42 \div 7 = 6 \][/tex]
So, the result is [tex]\(6.0\)[/tex].
### e. [tex]\(-2(-3)(-4)\)[/tex]
Multiply three numbers by their absolute values, keeping the negative sign in mind:
[tex]\[
-2 \times (-3) = 6 \quad (\text{because } - \times - = +)\\
6 \times (-4) = -24 \quad (\text{because } + \times - = -)
\][/tex]
So, the result is [tex]\(-24\)[/tex].
### f. [tex]\(-18 - 7\)[/tex]
Subtracting a positive number from a negative number is the same as adding their absolute values, but the result is negative:
[tex]\[ -18 - 7 = -(18 + 7) \][/tex]
[tex]\[ 18 + 7 = 25 \][/tex]
[tex]\[ -18 - 7 = -25 \][/tex]
So, the result is [tex]\(-25\)[/tex].
### g. [tex]\((-5)^2\)[/tex]
Squaring a negative number results in a positive number:
[tex]\[ (-5)^2 = (-5) \times (-5) \][/tex]
[tex]\[ (-5) \times (-5) = 25 \][/tex]
So, the result is [tex]\(25\)[/tex].
### h. [tex]\(-5^2\)[/tex]
According to the order of operations, you should square 5 first and then apply the negative sign:
[tex]\[ -5^2 = -(5^2) \][/tex]
[tex]\[ 5^2 = 25 \][/tex]
[tex]\[ -5^2 = -25 \][/tex]
So, the result is [tex]\(-25\)[/tex].
### i. [tex]\(\sqrt{49}\)[/tex]
The square root of 49 is the number which when multiplied by itself gives 49:
[tex]\[ \sqrt{49} = 7 \][/tex]
So, the result is [tex]\(7.0\)[/tex].
In summary, the simplified expressions are:
a. [tex]\(-59\)[/tex]
b. [tex]\(17\)[/tex]
c. [tex]\(-72\)[/tex]
d. [tex]\(6.0\)[/tex]
e. [tex]\(-24\)[/tex]
f. [tex]\(-25\)[/tex]
g. [tex]\(25\)[/tex]
h. [tex]\(-25\)[/tex]
i. [tex]\(7.0\)[/tex]
