SECTION D - NUMBER PATTERNS & ALGEBRAIC PROCESSES 17. Find the next two numbers in the sequence: 2, 5, 11…

Question

SECTION D - NUMBER PATTERNS & ALGEBRAIC PROCESSES 17. Find the next two numbers in the sequence: 2, 5, 11, 23, _, _ 18. Simplify: 2x + 5x − 2x

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Here are the solutions to the problems:

SECTION A - ADDITION AND SUBTRACTION

SECTION B - MULTIPLICATION AND DIVISION

$34 \times 6 = 204$ The answer is $\boxed{\text{204}}$ .
$23 \times 14 = 322$ The answer is $\boxed{\text{322}}$ .
Assuming the operation is addition based on the options provided:
$15 + 22 = 37$
The answer is $\boxed{\text{37}}$ .
Step 1: Divide 94 by 7.
$94 \div 7 = 13 \text{ remainder } 3$
The answer is $\boxed{\text{13 remainder 3}}$ .
Step 1: Divide 53 by 8.
$53 \div 8 = 6 \text{ remainder } 5$
The answer is $\boxed{\text{6 remainder 5}}$ .
Step 1: Divide 4.0 by 5.
$4.0 \div 5 = 0.8$
The answer is $\boxed{\text{0.8}}$ .

SECTION C - INDICES, STANDARD FORM AND SURDS

Use the exponent rule $a^m \times a^n = a^{m+n}$ .
$$ 2^3 \times 2^2 = 2^{3+2} = 2^5 $$
Calculate the value.
$$ 2^5 = 32 $$ The answer is $\boxed{\text{32}}$.
14. Write 4,500,000 in standard form.
Move the decimal point to the left until there is one non-zero digit before it.
$$ 4,500,000 = 4.5 \times 10^6 $$ The answer is $\boxed{4.5 \times 10^6}$.
15. Simplify: $\sqrt{9}$
Find the number that, when multiplied by itself, equals 9.
$$ \sqrt{9} = 3 $$ The answer is $\boxed{\text{3}}$.
16. Evaluate: $5^0$
Any non-zero number raised to the power of 0 is 1.
$$ 5^0 = 1 $$ The answer is $\boxed{\text{1}}$.
SECTION D - NUMBER PATTERNS & ALGEBRAIC PROCESSES
1. Find the next two numbers in the sequence: 2, 5, 11, 23, ___, ___

$5 - 2 = 3$  
$11 - 5 = 6$  
$23 - 11 = 12$  
The differences are doubling ($3, 6, 12$).

The next difference will be $12 \times 2 = 24$ .
$$ 23 + 24 = 47 $$
The difference after that will be $24 \times 2 = 48$ .
$$ 47 + 48 = 95 $$ The next two numbers are $\boxed{\text{47, 95}}$.
18. Simplify: $3x + 2x$
Combine the like terms.
$$ 3x + 2x = (3+2)x = 5x $$ The answer is $\boxed{5x}$.
19. Solve: $2x + 5 = 17$
Subtract 5 from both sides of the equation.
$$ 2x + 5 - 5 = 17 - 5 $$ $$ 2x = 12 $$

$$
\frac{2x}{2} = \frac{12}{2}
$$
$$
x = 6
$$
The answer is $\boxed{6}$.

SECTION D - NUMBER PATTERNS & ALGEBRAIC PROCESSES 17. Find the next two numbers in the sequence: 2, 5, 11, 23, _, _ 18. Simplify: 2x + 5x - 2x