use the pythagorean theorem to find the distance between $(3, 4)$ and $(-2, 1)$.

* $\sqrt{8}$
* $\sqrt{34}$
* $34$
* $5.2$

7 multiple choice 1 point
what is the following in exponential form:
$12 \times 12 \times 12 \times 12 \times 12 =$

* $248,832$
* $5^{12}$
* $60$
* $12^5$

8 true or false 1 point
the distance between $(-3, 7)$ and $(4, 1)$ is $9.21$ or $\sqrt{85}$

* true
* false

Question

use the pythagorean theorem to find the distance between $(3, 4)$ and $(-2, 1)$.

* $\sqrt{8}$
* $\sqrt{34}$
* $34$
* $5.2$

7 multiple choice 1 point
what is the following in exponential form:
$12 \times 12 \times 12 \times 12 \times 12 =$

* $248,832$
* $5^{12}$
* $60$
* $12^5$

8 true or false 1 point
the distance between $(-3, 7)$ and $(4, 1)$ is $9.21$ or $\sqrt{85}$

* true
* false

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem Coordinate Geometry", "Exponents" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem Coordinate Geometry", "Exponents", "Distance Formula" ] } ## Find horizontal and vertical distances for the first question $$ \begin{aligned} a &= |3 - (-2)| = 5 \ b &= |4 - 1| = 3 \end{aligned} $$ ## Apply the Pythagorean theorem $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 5^2 + 3^2 = 25 + 9 = 34 \ c &= \sqrt{34} \end{aligned} $$ ## Write the repeated multiplication in exponential form for Question 7 $$ 12 \times 12 \times 12 \times 12 \times 12 = 12^5 $$ ## Calculate the distance for Question 8 $$ \begin{aligned} d &= \sqrt{(4 - (-3))^2 + (1 - 7)^2} \ d &= \sqrt{7^2 + (-6)^2} = \sqrt{49 + 36} = \sqrt{85} \approx 9.2195 \end{aligned} $$ Since $\sqrt{85} \approx 9.22$, the statement "9.21 or $\sqrt{85}$" is true (using standard rounding to two decimal places, $9.2195 \approx 9.22$, but $9.21$ is a common truncation or close approximation). Thus, the statement is True. ## Question 1 (A) $\sqrt{8}$

(B) $\sqrt{34}$

(C) 34

(D) 5.2 ## Question 7 (A) 248,832

(B) $5^{12}$

(C) 60

(D) $12^5$ ## Question 8 (A) True

(B) False

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QUESTION IMAGE

Question

Explanation:

Find horizontal and vertical distances for the first question

Apply the Pythagorean theorem

Write the repeated multiplication in exponential form for Question 7

Calculate the distance for Question 8

Answer:

Question 1

Question 7

Question 8