Tcap subpart 2-3 MATH part 3 ( theres probably going to be 4 parts)
Quadrilateral qrst and its image, q'r's't" , are shown.
the points of qrst are Q(3,4), T(2,2), R(7,4), S(6,2), And the points of Q'R'S'T T'(4,-4), S(12,-4),
Q (6,-8), R(14,-8
What is the sequence of transformations that results in quadrilateral QSRT
being mapped onto quadrilateral Q'R'S'T ?
The sequence of transformations that results in quadrilateral QSRT being mapped onto quadrilateral Q'R'S'T is as follows:
1. Translation: Shift the quadrilateral QSRT two units to the left and four units down to align point Q with point Q'.
2. Reflection: Reflect the translated quadrilateral over the line y = -6 to flip it horizontally.
3. Translation: Shift the reflected quadrilateral eight units to the right to align point S with point S'.
4. Reflection: Reflect the translated quadrilateral over the line y = -4 to flip it vertically.
Therefore, the sequence of transformations is: Translation, Reflection, Translation, Reflection.
Becky and Luke bought the same kind of pencils and erasers. Becky spent $1.45
for 2 pencils and 3 erasers. luke spent $ 2.65 for 5 pencils and 1 eraser.
What is the cost of 1 eraser
Let's denote the cost of 1 pencil as x and the cost of 1 eraser as y.
From the information given, we can create the following system of equations based on the amounts spent by Becky and Luke:
2x + 3y = 1.45
5x + y = 2.65
Now, we can solve this system of equations to find the values of x and y.
First, we can rewrite the second equation as y = 2.65 - 5x and substitute this into the first equation:
2x + 3(2.65 - 5x) = 1.45
2x + 7.95 - 15x = 1.45
7.95 - 13x = 1.45
-13x = -6.5
x = 0.5
Now that we have found the cost of 1 pencil (x = $0.5), we can substitute this back into the second equation to find the cost of 1 eraser:
5(0.5) + y = 2.65
2.5 + y = 2.65
y = 2.65 - 2.5
y = 0.15
Therefore, the cost of 1 eraser is $0.15.
Which sets of ordered pairs represent a function? Select all that apply.
A(1,1),(1,2),(1,3),(1,4)
B(1,1),(2,2),(3,3),(4,4)
C(1,1),(2,1),(3,1) (4,1)
D(1,4),(2,4),(1,3),(2,3)
E(1,4),(2,2),(3,1),(4,3)
A function is a relation where each input value (x) is associated with exactly one output value (y). This means that for each x, there cannot be multiple y values.
Let's analyze the ordered pairs given in each set:
A(1,1),(1,2),(1,3),(1,4) - This set is not a function because the input value 1 is associated with multiple output values (1, 2, 3, 4).
B(1,1),(2,2),(3,3),(4,4) - This set represents a function because each input value is associated with only one output value.
C(1,1),(2,1),(3,1)(4,1) - This set is a function because each input value is associated with only one output value.
D(1,4),(2,4),(1,3),(2,3) - This set is not a function because the input values 1 and 2 are associated with multiple output values (1→4, 3 and 2→4, 3).
E(1,4),(2,2),(3,1),(4,3) - This set is a function because each input value is associated with only one output value.
Therefore, the sets that represent functions are B, C, and E.
Which equation has infinitely many solutions?
A 5x−5=11x+1
B 4x+5=−4x+5
C 3x+4=3+3x−1
D 3x+2−2x=x+2
An equation will have infinitely many solutions if the variables can be eliminated and the statement simplifies to a true statement. Let's analyze each equation:
A) 5x - 5 = 11x + 1
Solving for x:
5x - 11x = 1 + 5
-6x = 6
x = -1
This equation has a single solution (-1).
B) 4x + 5 = -4x + 5
Solving for x:
4x + 4x = 5 - 5
8x = 0
x = 0
This equation has a single solution (0).
C) 3x + 4 = 3 + 3x - 1
Solving for x:
3x - 3x = 3 - 4 + 1
0 = 0
This equation simplifies to 0 = 0, which is a true statement. This means that this equation has infinitely many solutions.
D) 3x + 2 - 2x = x + 2
Solving for x:
3x - 2x - x = 2 - 2
0 = 0
This equation also simplifies to 0 = 0, indicating infinitely many solutions.
Therefore, equations C and D have infinitely many solutions.
The average distance from Earth to the moon is approximately
238,900 miles. what is this distance, in miles, written in scientific notation?
Enter your answer in the space provided.
The distance from Earth to the moon, which is approximately 238,900 miles, can be written in scientific notation as 2.389 x 10^5 miles.
A cell phone company charges $20 for a customer to open a new account, and $35 for each. month of phone service.
a linear function to represent the total cost, Ya new customer would pay for X months of service.
Enter your answer in the space provided.