A Grade 9 teacher had flash cards containing questions on indices. Kirui picked a flash card containing the…

Question

A Grade 9 teacher had flash cards containing questions on indices. Kirui picked a flash card containing the question 2^x = 2² . 32. What is the value of x in the equation?

ScanSolve AI Tutor · Accepted Answer

here are the solutions for these questions.

5. Value of $x$ in the equation
The equation given is $2^x \times 2^1 = 32$ .
Assumption: Based on the provided options, it is highly probable that the question intended to be $2^x \times 2^3 = 32$ , as $2^1$ would lead to $x=4$ , which is not among the choices. We will solve assuming the exponent was meant to be 3.

Apply the rule of indices $a^m \times a^n = a^{m+n}$ .
$2^x \times 2^3 = 32$ $2^{x+3} = 32$
Express the right side of the equation as a power of 2.
$32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5$
Equate the powers since the bases are the same.
$2^{x+3} = 2^5$ $x+3 = 5$
Solve for $x$ .
$x = 5 - 3$ $x = 2$
The correct option is C.
$\boxed{\text{C}}$
6. Number of sheep in the farm
Identify the number of each type of animal.
- Total animals = 26
- Donkeys = $x$
- Goats = $2 \times (\text{number of donkeys}) = 2x$
Calculate the total number of donkeys and goats.
$\text{Donkeys} + \text{Goats} = x + 2x = 3x$
Calculate the number of sheep by subtracting the total of donkeys and goats from the total number of animals.
$\text{Number of sheep} = \text{Total animals} - (\text{Donkeys} + \text{Goats})$ $\text{Number of sheep} = 26 - 3x$
The correct option is A.
$\boxed{\text{A}}$
7. Inequality representing the information
Translate "at least 30 learners" into an inequality.
If $x$ is the number of learners, "at least 30" means $x$ must be greater than or equal to 30.
$x \ge 30$
Translate "but less than 50 learners" into an inequality.
"Less than 50" means $x$ must be strictly less than 50.
$x < 50$
Combine the two inequalities.
The number of learners $x$ must satisfy both conditions simultaneously.
$30 \le x < 50$
The correct option is D.
$\boxed{\text{D}}$

A Grade 9 teacher had flash cards containing questions on indices. Kirui picked a flash card containing the question 2^x = 2² . 32. What is the value of x in the equation?

Answer

Step-by-step solution

Apply the rule of indices $a^m \times a^n = a^{m+n}$ .

Express the right side of the equation as a power of 2.

Equate the powers since the bases are the same.

Solve for $x$ .

Identify the number of each type of animal.

Calculate the total number of donkeys and goats.

Calculate the number of sheep by subtracting the total of donkeys and goats from the total number of animals.

Translate "at least 30 learners" into an inequality.

Translate "but less than 50 learners" into an inequality.

Combine the two inequalities.

Try one yourself

Still stuck on this one?

More Mathematics Questions

A Grade 9 teacher had flash cards containing questions on indices. Kirui picked a flash card containing the question 2^x = 2² . 32. What is the value of x in the equation?

Answer

Step-by-step solution

Apply the rule of indices am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Express the right side of the equation as a power of 2.

Equate the powers since the bases are the same.

Solve for xxx.

Identify the number of each type of animal.

Calculate the total number of donkeys and goats.

Calculate the number of sheep by subtracting the total of donkeys and goats from the total number of animals.

Translate "at least 30 learners" into an inequality.

Translate "but less than 50 learners" into an inequality.

Combine the two inequalities.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Apply the rule of indices $a^m \times a^n = a^{m+n}$ .

Solve for $x$ .