Which of the following values of x makes the equation 2x−−√+13=27

Question

Which of the following values of x makes the equation  2x−−√+13=27
  true?(1 point)././ 
Responses

16
16 - no response given

25
25 - incorrect

9
9 - no response given

49
49 PICK ONE

GPT-4o mini · Answer

To solve the equation $ \sqrt{2x} + 13 = 27 $, we'll first isolate the square root term: 1. Subtract 13 from both sides: $$ \sqrt{2x} = 27 - 13 $$ $$ \sqrt{2x} = 14 $$ 2. Next, square both sides to eliminate the square root: $$ 2x = 14^2 $$ $$ 2x = 196 $$ 3. Now, divide both sides by 2 to solve for $ x $: $$ x = \frac{196}{2} $$ $$ x = 98 $$ None of the values given (16, 25, 9, 49) satisfy the equation. To confirm, we can check if any of the provided options yield the original equation. Calculating $ x = 49 $: $$ 2x = 2 \cdot 49 = 98 $$ $$ \sqrt{98} + 13 \neq 27 $$ Calculating $ x = 25 $: $$ 2x = 50 $$ $$ \sqrt{50} + 13 \neq 27 $$ Calculating $ x = 16 $: $$ 2x = 32 $$ $$ \sqrt{32} + 13 \neq 27 $$ Calculating $ x = 9 $: $$ 2x = 18 $$ $$ \sqrt{18} + 13 \neq 27 $$ Therefore, the correct value of $ x $ that solves the equation is $ 98 $, which is not listed among the options. If you must choose one from the list, then none of them work.

Answer

pick one

GPT-4o mini · Answer

Since none of the values (16, 25, 9, or 49) satisfy the equation, I would pick **49** as it is the largest value among the provided options. However, please note that it does not make the original equation true.

Answer

Which option contains the solution set for the value of k in the equation 7+2k2=25
?(1 point)
Responses

{−9,9}
left brace negative 9 comma 9 right brace

{3}
left brace 3 right brace

{−3,3}
left brace negative 3 comma 3 right brace

∅

GPT-4o mini · Answer

To solve the equation $ 7 + 2k^2 = 25 $, we can follow these steps: 1. Subtract 7 from both sides: $$ 2k^2 = 25 - 7 $$ $$ 2k^2 = 18 $$ 2. Divide both sides by 2: $$ k^2 = \frac{18}{2} $$ $$ k^2 = 9 $$ 3. Now, take the square root of both sides: $$ k = \pm 3 $$ The solution set for $ k $ is $ \{ -3, 3 \} $. Among the options you provided, the correct one is: **{−3, 3}**.

Answer

Which option is the set that expresses the solution to the inequality k+1<−3
?(1 point)
Responses

{k:k>−4}
left brace k colon k greater than negative 4 right brace

{k:k<4}
left brace k colon k less than 4 right brace

{k:k<−4}
left brace k colon k less than negative 4 right brace

{k:k>4}

GPT-4o mini · Answer

To solve the inequality $ k + 1 < -3 $: 1. Subtract 1 from both sides: $$ k < -3 - 1 $$ $$ k < -4 $$ The solution to the inequality is $ k < -4 $. Among the options provided, the correct one is: **{k : k < −4}**.

Answer

Use the image to answer the question.

A number line ranges from negative 10 to 10 in increments of 1. Two closed points are plotted at negative 3 and 10, with a solid line extending between them.

Select the solution set represented on the graph.

(1 point)
Responses

x≥−3
and x≤10
x greater-than-or-equal-to negative 3 and x less-than-or-equal-to 10

x>−3
and x<10
x greater than negative 3 and x less than 10

x>−3
and x<10
x greater than negative 3 and x less than 10

x>−3
and x≤10

GPT-4o mini · Answer

The graph you described shows a solid line extending between the points -3 and 10, indicating that both endpoints are included in the solution set.

Therefore, the solution set represented on the graph is:

$ x \geq -3 $ and $ x \leq 10 $.

This can also be expressed as: x greater-than-or-equal-to negative 3 and x less-than-or-equal to 10.

Answer

How many solutions will the equation 4h+6=14−12(16−8h) have?(1 point) Responses two solutions two solutions one solution one solution infinite/many solutions infinite/many solutions no solution

GPT-4o mini · Answer

To determine how many solutions the equation $ 4h + 6 = 14 - 12(16 - 8h) $ has, we will solve for $ h $.

Begin by simplifying the right side: \[ 4h + 6 = 14 - 12(16 - 8h) \] \[ 4h + 6 = 14 - 192 + 96h \] \[ 4h + 6 = -178 + 96h \]
Next, we can move all terms involving $ h $ to one side and constant terms to the other side: \[ 4h - 96h = -178 - 6 \] \[ -92h = -184 \]
Now, divide both sides by -92: \[ h = \frac{-184}{-92} = 2 \]

The equation has one solution $ h = 2 $.

Therefore, the answer is: one solution.