which of the following systems of inequalities represents the graph? A solid line passes through the points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis 2 comma 8 right-parenthesis. The region above the line is shaded red. A dotted line passes through the points left-parenthesis 0 comma 2 right-parenthesis and left-parenthesis 2 comma 0 right-parenthesis. The region below the line is shaded blue. A region of the coordinate plane is shaded both red and blue. (1 point) Responses y ≤ 2x + 4 y ≥ –x + 2 y ≤ 2 x + 4 y ≥ –x + 2 2x – y ≥ 4 y < –x + 2 2 x – y ≥ 4 y < –x + 2 y ≥ 2x + 4 –x + y ≤ 2 y ≥ 2 x + 4 – x + y ≤ 2 –2x + y ≥ 4 x + y < 2
The correct system of inequalities that represents the graph described is:
y ≤ 2x + 4
y ≥ -x + 2
In the same graph, what is the approximate y-value of the point of intersection? A solid line passes through the points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis 2 comma 8 right-parenthesis. The region above the line is shaded red. A dotted line passes through the points left-parenthesis 0 comma 2 right-parenthesis and left-parenthesis 2 comma 0 right-parenthesis. The region below the line is shaded blue. A region of the coordinate plane is shaded both red and blue. (1 point) Responses –1 –1 4 4 3 3 2
The approximate y-value of the point of intersection of the two lines is 4.
A student spends no more than 2 hours on his math and English homework. If math takes about twice as long as English, what is the maximum time that the student can spend on English? (1 point) Responses hour Image with alt text: one-third hour hour Image with alt text: The fraction is 1 over 2. hour 1 hour 1 hour hour
If the student spends a maximum of 2 hours on math and English homework, and math takes about twice as long as English, then math will take x hours and English will take 2x hours. The total time spent on both subjects is 2 hours:
x (time spent on Math) + 2x (time spent on English) = 2
Solving for x:
x + 2x = 2
3x = 2
x = 2/3
Substitute the value of x back into the time spent on English equation:
2x = 2(2/3) = 4/3
Therefore, the maximum time that the student can spend on English is 4/3 or 1 and 1/3 hours. So, the answer is one-third hour.