Question

Line joins ordered pairs negative 4, 3, 2, negative 3. Second joins negative 4, negative 3, 2, 3. A shaded above first second line. B shaded below first, above second line. C shaded below first second lines. D shaded above first line below second. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1? (5 points) Part D Part A Part B Part C

Answer 1

Answer:

Part B represents the solution set to the system of inequalities.

Step-by-step explanation:

Line joins ordered pairs (-4, 3) and (2, -3). Second joins (-4, -3) and (2, 3).

If a line passing through two points then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of first line is

$y-3=\frac{-3-3}{2+4}(x+4)$

$y-3=-1(x+4)$

$y-3=-x-4$

$y+x=-4+3$

$y+x=-1$

The equation of second line is

$y+3=\frac{3+3}{2+4}(x+4)$

$y+3=1(x+4)$

$y+3=x+4$

$y=x+4-3$

$y=x+1$

Plot the inequalities given inequalities on the coordinate plane.

$y+x\leq-1$

The related equation of this inequality is same as the equation of first line. The sign of inequality is ≤, therefore the shaded region is below the first line.

$y\geq x+1$

The related equation of this inequality is same as the equation of second line. The sign of inequality is ≥, therefore the shaded region is above the second line.

Therefore part B represents the solution set to the system of inequalities.

Answer 2

Answer

That should be it!

Step-by-step explanation:

Question 1 (Multiple Choice Worth 1 points) (04.03) The expression below shows the population of foxes in a forest after 12x years: f(x) = 50(1.05)12x Which of the following is an equivalent function? f(x) = 50(1.7959)x f(x) = 50(12.6000)x f(x) = 600(1.05)x f(x) = 4.2(1.05)x Question 2 (Multiple Choice Worth 1 points) (04.01) Which of the following best defines 3 to the power of 2 over 3? Square root of 9 Cube root of 9 Cube root of 3 Square root of 3 Question 3 (Multiple Choice Worth 1 points) (04.06) A sequence has its first term equal to 4, and each term of the sequence is obtained by adding 2 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence? f(1) = 2 and f(n) = f(n − 1) + 4; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2n; n > 1 f(1) = 2 and f(n) = f(n − 1) + 4n; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2; n > 1 Question 4 (Multiple Choice Worth 1 points) (05.05) Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≤ x + 1 and y + x ≤ −1? Part A Part B Part C Part D Question 5 (Multiple Choice Worth 1 points) (04.03) The number of bacteria in a sample increased by a factor of 2 every minute from 9:05 AM to 9:55 a.m.. The function below shows the number of bacteria in the sample f(x) after x minutes from 9:05 a.m.: f(x) = 10(2)x Which of the following is a reasonable domain for the function? 0 ≤ x ≤ 10 5 ≤ x ≤ 55 0 ≤ x ≤ 50 All positive integers Question 6 (Multiple Choice Worth 1 points) (03.05) The graph below shows the velocity f(t) of a runner during a certain time interval: graph of line going through ordered pairs 0, 2 and 6, 8. Graph of another line through ordered pairs 6, 8 and 8, 0. Label on the x axis is time in second and label on the y axis is velocity in meters per second Which of the following describes the intercepts on the graph? The initial velocity of the runner was 8 m/s, and the runner stopped after 2 seconds. The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds. The initial acceleration of the runner was 8 m/s2, and the runner stopped after 2 seconds. The initial acceleration of the runner was 2 m/s2, and the runner stopped after 8 seconds. Question 7 (Multiple Choice Worth 1 points) (03.03) Choose the equation that represents the graph below: Graph of a line passing through points negative 3 comma 0 and 0 comma 3 y = x − 3 y = −x + 3 y = −x − 3 y = x + 3 Question 8 (Multiple Choice Worth 1 points) (04.03) Jake forgot to replace the cap on a bottle of cologne. The cologne began to evaporate at the rate of 18% per day. If the original amount of cologne in the bottle was 50 grams, which of the following graphs best represents the amount of cologne f(x) remaining in the bottle after x days? graph of function f of x equals 30 multiplied by 0.88 to the power of x graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis graph of function f of x equals 50 multiplied by 0.82 to the power of x graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis