Think about the examples of how the federal government took actions to extend or protect the civil rights of marginalized groups. Identify the action that is matched with the correct marginalized group.(1 point)
Responses
The Twenty-sixth Amendment protects women’s rights.
The Twenty-sixth Amendment protects women’s rights.
A Supreme Court ruling creates Title IX to protect the rights of female college students.
A Supreme Court ruling creates Title IX to protect the rights of female college students.
A Supreme Court ruling protects LGBTQ+ rights in Obergefell v. Hodges.
A Supreme Court ruling protects LGBTQ+ rights in Obergefell v. Hodges.
An executive order creates the ADA.
An executive order creates the ADA.
Which of the following is the foundation of modern civil rights law?(1 point)
Responses
the Americans with Disabilities Act
the Americans with Disabilities Act
Section 504
Section 504
the Civil Rights Act of 1964
the Civil Rights Act of 1964
Title IX
Title IX
the Civil Rights Act of 1964
Which of these best explains why the 1924 Immigration Act favored immigrants from northern and western Europe?(1 point)
Responses
The act required all immigrants to be Protestants.
The act required all immigrants to be Protestants.
The act used the 1890 census to determine national quotas.
The act used the 1890 census to determine national quotas.
The act required all immigrants to be fluent in English.
The act required all immigrants to be fluent in English.
The act used the 1920 census to determine national quotas
The act used the 1890 census to determine national quotas.
Current policy on Deferred Action for Childhood Arrivals (DACA) is the result of what type of federal action?(1 point)
Responses
act of Congress
act of Congress
presidential veto
presidential veto
constitutional amendment
constitutional amendment
executive order
executive order
Solve the system by substitution.
y equals negative x squared plus 2 x plus 10
y equals x plus 4
(1 point)
Responses
left-parenthesis 3 comma 7 right-parenthesis comma left-parenthesis negative 2 comma 2 right-parenthesis
Image with alt text: left-parenthesis 3 comma 7 right-parenthesis comma left-parenthesis negative 2 comma 2 right-parenthesis
left-parenthesis negative 1 comma 3 right-parenthesis comma left-parenthesis 2 comma 6 right-parenthesis
Image with alt text: left-parenthesis negative 1 comma 3 right-parenthesis comma left-parenthesis 2 comma 6 right-parenthesis
left-parenthesis 0 comma 4 right-parenthesis comma left-parenthesis 4 comma 8 right-parenthesis
Image with alt text: left-parenthesis 0 comma 4 right-parenthesis comma left-parenthesis 4 comma 8 right-parenthesis
left-parenthesis 1 comma 5 right-parenthesis comma left-parenthesis 5 comma 9 right-parenthesis
To solve the system by substitution, we can substitute the value of y from the second equation into the first equation:
x + 4 = -x^2 + 2x + 10
Rearranging the equation:
x^2 - x - 6 = 0
Factoring the quadratic equation:
(x - 3)(x + 2) = 0
Setting each factor equal to zero:
x - 3 = 0 --> x = 3
x + 2 = 0 --> x = -2
Now, we can substitute these x-values back into the second equation to find the corresponding y-values:
For x = 3:
y = x + 4 = 3 + 4 = 7
For x = -2:
y = x + 4 = -2 + 4 = 2
Therefore, the solution to the system of equations is:
(3, 7) and (-2, 2)
In which of the following ways are linear systems similar to quadratic systems? Select all that apply.
(2 points)
Responses
Both can be solved by graphing.
Both can be solved by graphing.
Both can have two solutions.
Both can have two solutions.
Both can be solved by substitution.
Both can be solved by substitution.
Both have solutions at the points of intersection
Both can be solved by graphing.
Both can have two solutions.
Both have solutions at the points of intersection.
olve the system by substitution.
y equals negative x squared plus x minus 1
y equals negative x minus 1
(1 point)
Responses
left-parenthesis 3 comma negative 4 right-parenthesis comma left-parenthesis negative 1 comma 0 right-parenthesis
Image with alt text: left-parenthesis 3 comma negative 4 right-parenthesis comma left-parenthesis negative 1 comma 0 right-parenthesis
left-parenthesis negative 1 comma 0 right-parenthesis comma left-parenthesis 2 comma negative 3 right-parenthesis
Image with alt text: left-parenthesis negative 1 comma 0 right-parenthesis comma left-parenthesis 2 comma negative 3 right-parenthesis
left-parenthesis 4 comma negative 5 right-parenthesis comma left-parenthesis 1 comma negative 1 right-parenthesis
Image with alt text: left-parenthesis 4 comma negative 5 right-parenthesis comma left-parenthesis 1 comma negative 1 right-parenthesis
left-parenthesis 0 comma negative 1 right-parenthesis comma left-parenthesis 2 comma negative 3 right-parenthesis
To solve the system by substitution, we can substitute the value of y from the second equation into the first equation:
y = -x - 1
Substituting this into the first equation:
-x^2 + x - 1 = -x - 1
Simplifying the equation:
-x^2 + x = 0
Factoring out x:
x(-x + 1) = 0
Setting each factor equal to zero:
x = 0
-x + 1 = 0 --> x = 1
Now, we can substitute these x-values back into the second equation to find the corresponding y-values:
For x = 0:
y = -x - 1 = -0 - 1 = -1
For x = 1:
y = -x - 1 = -1 - 1 = -2
Therefore, the solution to the system of equations is:
(0, -1) and (1, -2)
Solve the system by substitution.
y equals 2 x squared minus 3 x minus 1
y equals x minus 3
(1 point)
Responses
left-parenthesis 3 comma 0 right-parenthesis comma left-parenthesis 5 comma 2 right-parenthesis
Image with alt text: left-parenthesis 3 comma 0 right-parenthesis comma left-parenthesis 5 comma 2 right-parenthesis
left-parenthesis 1 comma negative 2 right-parenthesis
Image with alt text: left-parenthesis 1 comma negative 2 right-parenthesis
left-parenthesis 4 comma 1 right-parenthesis
Image with alt text: left-parenthesis 4 comma 1 right-parenthesis
no solution
To solve the system by substitution, we can substitute the value of y from the second equation into the first equation:
y = x - 3
Substituting this into the first equation:
2x^2 - 3x - 1 = x - 3
Simplifying the equation:
2x^2 - 4x + 2 = 0
Now we can solve this quadratic equation. However, upon factoring, we can see that it cannot be factored nicely. Therefore, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For this equation a = 2, b = -4, and c = 2. Plugging these values into the quadratic formula:
x = (-(-4) ± √((-4)^2 - 4(2)(2))) / (2(2))
x = (4 ± √(16 - 16)) / 4
x = (4 ± √0) / 4
We can see that the discriminant is 0, which means there is only one real solution for x:
x = 4/4
x = 1
Now, we can substitute this x-value back into the second equation to find the corresponding y-value:
For x = 1:
y = x - 3 = 1 - 3 = -2
Therefore, the solution to the system of equations is:
(1, -2)
olve the system by substitution.
y equals negative x squared plus x minus 5
y equals x minus 5
(1 point)
Responses
no solution
no solution
left-parenthesis 1 comma negative 4 right-parenthesis
Image with alt text: left-parenthesis 1 comma negative 4 right-parenthesis
left-parenthesis 0 comma negative 5 right-parenthesis
Image with alt text: left-parenthesis 0 comma negative 5 right-parenthesis
left-parenthesis 2 comma negative 3 right-parenthesis comma left-parenthesis 1 comma negative 4 right-parenthesis
To solve the system by substitution, we can substitute the value of y from the second equation into the first equation:
y = x - 5
Substituting this into the first equation:
-x^2 + x - 5 = x - 5
Simplifying the equation:
-x^2 = 0
We can see that the equation simplifies to 0, which means there are no x-values that satisfy the equation. Therefore, there is no solution to the system of equations.
Multiple Choice
Solve by graphing.
x2 + 2x – 3 = 0
(1 point)
Responses
graph aThe function has a maximum at left-parenthesis negative 1 comma 4 right-parenthesis and passes through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis 1 comma 0 right-parenthesis.
x = 1, –3
Image with alt text: graph a The function has a maximum at left-parenthesis negative 1 comma 4 right-parenthesis and passes through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis 1 comma 0 right-parenthesis. x = 1, –3
graph bThe function has a minimum at left-parenthesis 1 comma negative 4 right-parenthesis and passes through the points left-parenthesis negative 1 comma 0 right-parenthesis and left-parenthesis 3 comma 0 right-parenthesis.
x = –1, 3
Image with alt text: graph b The function has a minimum at left-parenthesis 1 comma negative 4 right-parenthesis and passes through the points left-parenthesis negative 1 comma 0 right-parenthesis and left-parenthesis 3 comma 0 right-parenthesis. x = –1, 3
graph cThe function has a minimum at left-parenthesis negative 1 comma negative 4 right-parenthesis and passes through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis 1 comma 0 right-parenthesis.
x = 1, –3
Image with alt text: graph c The function has a minimum at left-parenthesis negative 1 comma negative 4 right-parenthesis and passes through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis 1 comma 0 right-parenthesis. x = 1, –3
graph dThe function has a maximum at left-parenthesis 1 comma 4 right-parenthesis and passes through the points left-parenthesis negative 1 comma 0 right-parenthesis and left-parenthesis 3 comma 0 right-parenthesis.
x = –1, 3
To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.
Based on the provided options, the correct answer is:
graph b The function has a minimum at (1, -4) and passes through the points (-1, 0) and (3, 0).
x = -1, 3
The function y equals negative 0.296 x squared plus 2.7 x models the length x and height y that your sister's pet rabbit can jump, in centimeters. What is the maximum height that the rabbit can reach during its jump? Once the rabbit reaches the ground, what is the total length of its jump?
(1 point)
Responses
2.7 cm high; 0.296 cm long
2.7 cm high; 0.296 cm long
6.2 cm high; 9.1 cm long
6.2 cm high; 9.1 cm long
4.6 cm high; 6.2 cm long
4.6 cm high; 6.2 cm long
9.1 cm high; 6.2 cm long
9.1 cm high; 6.2 cm long
To find the maximum height that the rabbit can reach during its jump, we need to find the y-coordinate of the vertex of the quadratic function y = -0.296x^2 + 2.7x. The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b / 2a.
In this case, a = -0.296 and b = 2.7. Let's calculate the x-coordinate of the vertex:
x = -2.7 / (2 * -0.296)
x ≈ 4.566
Now, let's substitute this value of x back into the quadratic function to find the maximum height (y-coordinate) of the rabbit's jump:
y = -0.296 * (4.566)^2 + 2.7 * 4.566
y ≈ 6.1876
Therefore, the maximum height that the rabbit can reach during its jump is approximately 6.2 cm.
To find the total length of the rabbit's jump, we need to find the x-intercepts of the quadratic function. These are the points where the function intersects the x-axis (i.e., where y = 0).
Let's solve the quadratic equation -0.296x^2 + 2.7x = 0:
x(-0.296x + 2.7) = 0
Setting each factor equal to zero:
x = 0 (This represents the starting point of the jump)
-0.296x + 2.7 = 0
x ≈ 9.1216
Therefore, the total length of the rabbit's jump is approximately 9.1 cm.
The correct answer is:
6.2 cm high; 9.1 cm long
Simplify the expression.
(3 – i) – (2 + 6i)
(1 point)
Responses
1 – 7i
1 – 7 i
–1 + 7i
–1 + 7 i
–6i
–6 i
5 + 5i
To simplify the expression (3 - i) - (2 + 6i), we can distribute the negative sign to each term in the second parentheses:
3 - i - 2 - 6i
Next, we can combine like terms:
(3 - 2) + (-1 - 6i)
1 - 7i
Therefore, the simplified expression is 1 - 7i.
What is the number of real solutions?
–11x2 = x + 11
(1 point)
Responses
cannot be determined
cannot be determined
one solution
one solution
two solutions
two solutions
no real solutions
To find the number of real solutions for the equation -11x^2 = x + 11, we can start by rearranging the equation to make it equal to zero:
-11x^2 - x - 11 = 0
This is a quadratic equation in standard form, where a = -11, b = -1, and c = -11.
Using the discriminant, which is given by D = b^2 - 4ac, we can determine the number of real solutions:
D = (-1)^2 - 4(-11)(-11)
D = 1 - 484
D = -483
Since the discriminant is negative (D < 0), there are no real solutions for the equation.
Therefore, the correct answer is no real solutions.
Identify the graph of 3i.
(1 point)
Responses
graph a
Image with alt text: graph a
graph b
Image with alt text: graph b
graph c
Image with alt text: graph c
graph d
To identify the graph of 3i, we need to remember that the number i represents the imaginary unit, which is defined as the square root of -1.
Since 3i has no real component, it lies entirely on the imaginary axis. The value 3 corresponds to the distance from the origin (0,0) on the vertical axis.
Looking at the provided options, the correct answer would be:
graph a
What are the solutions?
16x2 + 9 = 0
(1 point)
Responses
–3 over 4i, 3 over 4i
– Image with alt text: 3 over 4 i, Image with alt text: 3 over 4 i
–4 over 3i,4 over 3 i
– Image with alt text: 4 over 3 i, Image with alt text: 4 over 3 i
– 3 over 4 , 3 over 4
– Image with alt text: 3 over 4 , Image with alt text: 3 over 4
–9 over 16i, 9 over 16i
To solve the quadratic equation 16x^2 + 9 = 0, we can start by subtracting 9 from both sides:
16x^2 = -9
Next, divide both sides by 16 to isolate x^2:
x^2 = -9/16
To solve for x, we can take the square root of both sides:
x = ±√(-9
e graphing to find the solutions to the system of equations.
system
(1 point)
Responses
graph aThe line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma negative 3 right-parenthesis. The quadratic function has a maximum at left-parenthesis negative 3 comma 1 right-parenthesis.
(—4, 0)
(—1, —3)
Image with alt text: graph a The line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma negative 3 right-parenthesis. The quadratic function has a maximum at left-parenthesis negative 3 comma 1 right-parenthesis. (—4, 0) (—1, —3)
graph bThe line and the quadratic function both pass through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis negative 2 comma 1 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma 0 right-parenthesis and also passes through the point left-parenthesis negative 4 comma 1 right-parenthesis.
(—3, 0)
(—2, 1)
Image with alt text: graph b The line and the quadratic function both pass through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis negative 2 comma 1 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma 0 right-parenthesis and also passes through the point left-parenthesis negative 4 comma 1 right-parenthesis. (—3, 0) (—2, 1)
graph cThe line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma 3 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma negative 1 right-parenthesis.
(—4, 0)
(—1, 3)
Image with alt text: graph c The line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma 3 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma negative 1 right-parenthesis. (—4, 0) (—1, 3)
graph dThe line and the quadratic function both pass through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis negative 2 comma negative 1 right-parenthesis. The quadratic function has a maximum at left-parenthesis negative 3 comma 0 right-parenthesis and also passes through the point left-parenthesis negative 4 comma negative 1 right-parenthesis.
(—3, 0)
(—2, —1)
What is the solution of the system of inequalities?
system
(1 point)
Responses
graph aA quadratic function is graphed with a solid line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The interior of the graph of the quadratic function is shaded.
A second quadratic function is graphed with a dashed line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The interior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. The region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis.
Image with alt text: graph a A quadratic function is graphed with a solid line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The interior of the graph of the quadratic function is shaded. A second quadratic function is graphed with a dashed line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The interior of the graph of the quadratic function is shaded. The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. The region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis.
graph bA quadratic function is graphed with a dashed line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The interior of the graph of the quadratic function is shaded.
A second quadratic function is graphed with a solid line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The interior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. The region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis.
Image with alt text: graph b A quadratic function is graphed with a dashed line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The interior of the graph of the quadratic function is shaded. A second quadratic function is graphed with a solid line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The interior of the graph of the quadratic function is shaded. The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. The region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis.
graph cA quadratic function is graphed with a dashed line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The exterior of the graph of the quadratic function is shaded.
A second quadratic function is graphed with a solid line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The exterior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. This region is outside the graphs of both quadratic functions.
Image with alt text: graph c A quadratic function is graphed with a dashed line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The exterior of the graph of the quadratic function is shaded. A second quadratic function is graphed with a solid line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The exterior of the graph of the quadratic function is shaded. The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. This region is outside the graphs of both quadratic functions.
graph d
Simplify the number using the imaginary unit i.
Root negative 25 EndRoot
(1 point)
Responses
Negative 5i
Image with alt text: Negative 5i
5i
5 i
negative 5
Image with alt text: negative 5
5