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Here are the solutions to the questions:

23. The value of x in the equation $2x - 3 = 5$ is

Add 3 to both sides of the equation.
$2x - 3 + 3 = 5 + 3$ $2x = 8$
Divide both sides by 2.
$\frac{2x}{2} = \frac{8}{2}$ $x = 4$
The correct option is C. 4.

24. The value of x in the equation $x^2 = 16$ is
Take the square root of both sides of the equation.
$\sqrt{x^2} = \sqrt{16}$ $x = \pm 4$
The correct option is D. $\pm 4$ .

25. The value of x in the equation $2x + 3 = 3x - 5$ is
Subtract $2x$ from both sides of the equation.
$2x + 3 - 2x = 3x - 5 - 2x$ $3 = x - 5$
Add 5 to both sides of the equation.
$3 + 5 = x - 5 + 5$ $8 = x$
The correct option is A. 8.

26. The value of x in the inequality $2x - 1 < 5$ is
Add 1 to both sides of the inequality.
$2x - 1 + 1 < 5 + 1$ $2x < 6$
Divide both sides by 2.
$\frac{2x}{2} < \frac{6}{2}$ $x < 3$
The correct option is B. $x < 3$ .

27. The solution to the simultaneous equations: $x + y = 5$ and $x - y = 1$ is
Add the two equations together to eliminate $y$ .
$(x + y) + (x - y) = 5 + 1$ $2x = 6$
Solve for $x$ .
$x = \frac{6}{2}$ $x = 3$
Substitute the value of $x$ into the first equation ( $x + y = 5$ ).
$3 + y = 5$
Solve for $y$ .
$y = 5 - 3$ $y = 2$
The solution is $x=3, y=2$ .
The correct option is A. $x=3, y=2$ .

28. The value of x in the sequence $1, 3, 5, x, 9$ is
Determine the common difference between consecutive terms.
$3 - 1 = 2$ $5 - 3 = 2$
This is an arithmetic sequence with a common difference $d=2$ .
Find the value of $x$ by adding the common difference to the preceding term.
$x = 5 + 2$ $x = 7$
The correct option is B. 7.

29. The 10th term of the sequence $2, 4, 6, 8, \dots$ is
Identify the first term ( $a$ ) and the common difference ( $d$ ).
The first term $a = 2$ .
The common difference $d = 4 - 2 = 2$ .
Use the formula for the $n$ -th term of an arithmetic sequence, $T_n = a + (n-1)d$ , with $n=10$ .
$T_{10} = 2 + (10-1)2$ $T_{10} = 2 + (9)2$ $T_{10} = 2 + 18$ $T_{10} = 20$
The correct option is C. 20.

30. The sum of the first 10 terms of the sequence $2, 4, 6, 8, \dots$ is
Identify the first term ( $a$ ), the common difference ( $d$ ), and the number of terms ( $n$ ).
From question 29, $a = 2$ , $d = 2$ , and $n = 10$ .
Use the formula for the sum of the first $n$ terms of an arithmetic sequence, $S_n = \frac{n}{2}(2a + (n-1)d)$ .
$S_{10} = \frac{10}{2}(2(2) + (10-1)2)$ $S_{10} = 5(4 + (9)2)$ $S_{10} = 5(4 + 18)$ $S_{10} = 5(22)$ $S_{10} = 110$
The correct option is D. 110.

31. The common ratio of the sequence $2, 4, 8, 16, \dots$ is
Calculate the ratio of any term to its preceding term.
$\frac{4}{2} = 2$ $\frac{8}{4} = 2$ $\frac{16}{8} = 2$
The common ratio $r = 2$ .
The correct option is A. 2.

32. The 5th term of the sequence $2, 4, 8, 16, \dots$ is
Identify the first term ( $a$ ) and the common ratio ( $r$ ).
The first term $a = 2$ .
From question 31, the common ratio $r = 2$ .
Use the formula for the $n$ -th term of a geometric sequence, $T_n = ar^{n-1}$ , with $n=5$ .
$T_5 = 2 \times 2^{5-1}$ $T_5 = 2 \times 2^4$ $T_5 = 2 \times 16$ $T_5 = 32$
The correct option is B. 32.

33. The sum to infinity of the sequence $1, \frac{1}{2}, \frac{1}{4}, \dots$ is
Identify the first term ( $a$ ) and the common ratio ( $r$ ).
The first term $a = 1$ .
The common ratio $r = \frac{1/2}{1} = \frac{1}{2}$ .
Use the formula for the sum to infinity of a geometric sequence, $S_\infty = \frac{a}{1-r}$ , since $|r| < 1$ .
$S_\infty = \frac{1}{1 - \frac{1}{2}}$ $S_\infty = \frac{1}{\frac{1}{2}}$ $S_\infty = 1 \times 2$ $S_\infty = 2$
The correct option is A. 2.

34. The value of x in the equation $\log_2 x = 3$ is
Convert the logarithmic equation to its equivalent exponential form.
The definition of logarithm states that $\log_b a = c$ is equivalent to $b^c = a$ .
Here, $b=2$ , $a=x$ , and $c=3$ .
$2^3 = x$
Calculate the value of $2^3$ .
$x = 2 \times 2 \times 2$ $x = 8$
The correct option is D. 8.

English please not french

Answer

Step-by-step solution

Add 3 to both sides of the equation.

Divide both sides by 2.

Take the square root of both sides of the equation.

Subtract $2x$ from both sides of the equation.

Add 5 to both sides of the equation.

Add 1 to both sides of the inequality.

Divide both sides by 2.

Add the two equations together to eliminate $y$ .

Solve for $x$ .

Substitute the value of $x$ into the first equation ( $x + y = 5$ ).

Solve for $y$ .

Determine the common difference between consecutive terms.

Find the value of $x$ by adding the common difference to the preceding term.

Identify the first term ( $a$ ) and the common difference ( $d$ ).

Use the formula for the $n$ -th term of an arithmetic sequence, $T_n = a + (n-1)d$ , with $n=10$ .

Identify the first term ( $a$ ), the common difference ( $d$ ), and the number of terms ( $n$ ).

Use the formula for the sum of the first $n$ terms of an arithmetic sequence, $S_n = \frac{n}{2}(2a + (n-1)d)$ .

Calculate the ratio of any term to its preceding term.

Identify the first term ( $a$ ) and the common ratio ( $r$ ).

Use the formula for the $n$ -th term of a geometric sequence, $T_n = ar^{n-1}$ , with $n=5$ .

Identify the first term ( $a$ ) and the common ratio ( $r$ ).

Use the formula for the sum to infinity of a geometric sequence, $S_\infty = \frac{a}{1-r}$ , since $|r| < 1$ .

Convert the logarithmic equation to its equivalent exponential form.

Calculate the value of $2^3$ .

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English please not french

Answer

Step-by-step solution

Add 3 to both sides of the equation.

Divide both sides by 2.

Take the square root of both sides of the equation.

Subtract $2x$ from both sides of the equation.

Add 5 to both sides of the equation.

Add 1 to both sides of the inequality.

Divide both sides by 2.

Add the two equations together to eliminate yyy.

Solve for xxx.

Substitute the value of xxx into the first equation (x+y=5x + y = 5x+y=5).

Solve for yyy.

Determine the common difference between consecutive terms.

Find the value of xxx by adding the common difference to the preceding term.

Identify the first term (aaa) and the common difference (ddd).

Use the formula for the nnn-th term of an arithmetic sequence, Tn=a+(n−1)dT_n = a + (n-1)dTn​=a+(n−1)d, with n=10n=10n=10.

Identify the first term (aaa), the common difference (ddd), and the number of terms (nnn).

Use the formula for the sum of the first nnn terms of an arithmetic sequence, Sn=n2(2a+(n−1)d)S_n = \frac{n}{2}(2a + (n-1)d)Sn​=2n​(2a+(n−1)d).

Calculate the ratio of any term to its preceding term.

Identify the first term (aaa) and the common ratio (rrr).

Use the formula for the nnn-th term of a geometric sequence, Tn=arn−1T_n = ar^{n-1}Tn​=arn−1, with n=5n=5n=5.

Identify the first term (aaa) and the common ratio (rrr).

Use the formula for the sum to infinity of a geometric sequence, S∞=a1−rS_\infty = \frac{a}{1-r}S∞​=1−ra​, since ∣r∣<1|r| < 1∣r∣<1.

Convert the logarithmic equation to its equivalent exponential form.

Calculate the value of 232^323.

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More Languages Questions

Add the two equations together to eliminate $y$ .

Solve for $x$ .

Substitute the value of $x$ into the first equation ( $x + y = 5$ ).

Solve for $y$ .

Find the value of $x$ by adding the common difference to the preceding term.

Identify the first term ( $a$ ) and the common difference ( $d$ ).

Use the formula for the $n$ -th term of an arithmetic sequence, $T_n = a + (n-1)d$ , with $n=10$ .

Identify the first term ( $a$ ), the common difference ( $d$ ), and the number of terms ( $n$ ).

Use the formula for the sum of the first $n$ terms of an arithmetic sequence, $S_n = \frac{n}{2}(2a + (n-1)d)$ .

Identify the first term ( $a$ ) and the common ratio ( $r$ ).

Use the formula for the $n$ -th term of a geometric sequence, $T_n = ar^{n-1}$ , with $n=5$ .

Identify the first term ( $a$ ) and the common ratio ( $r$ ).

Use the formula for the sum to infinity of a geometric sequence, $S_\infty = \frac{a}{1-r}$ , since $|r| < 1$ .

Calculate the value of $2^3$ .