5x + 10x −2x+4 Convert 21 from base 10 to base 2 Without using calculator, solve 12.5×0.4

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your problems:

: Simplify the expression

Combine the terms with $x$ .
$5x + 10x - 2x + 4 = (5 + 10 - 2)x + 4$
Perform the arithmetic within the parentheses.
$(5 + 10 - 2)x + 4 = (15 - 2)x + 4$ $= 13x + 4$
The simplified expression is:
$\boxed{13x + 4}$
: Convert 21 from base 10 to base 2
Divide 21 by 2 and record the remainder.
$21 \div 2 = 10 \text{ remainder } 1$
Divide the quotient (10) by 2 and record the remainder.
$10 \div 2 = 5 \text{ remainder } 0$
Divide the quotient (5) by 2 and record the remainder.
$5 \div 2 = 2 \text{ remainder } 1$
Divide the quotient (2) by 2 and record the remainder.
$2 \div 2 = 1 \text{ remainder } 0$
Divide the quotient (1) by 2 and record the remainder.
$1 \div 2 = 0 \text{ remainder } 1$
Read the remainders from bottom to top to get the base 2 number.
The remainders are $1, 0, 1, 0, 1$ .
So, $21_{10}$ in base 2 is:
$\boxed{10101_2}$
: Solve $12.5 \times 0.4$ without using a calculator
Multiply the numbers as if they were whole numbers, ignoring the decimal points for now.
$125 \times 4$
Perform the multiplication.
$125 \times 4 = 500$
Count the total number of decimal places in the original numbers.
12.5 has one decimal place.

0.4 has one decimal place.
Total decimal places = $1 + 1 = 2$ .
Place the decimal point in the product (500) two places from the right.
$5.00$ $5.00 = 5$
The product is:
$\boxed{5}$

5x + 10x -2x+4 Convert 21 from base 10 to base 2 Without using calculator, solve 12.5×0.4