Josette found 16 coins in her purse. She had 2 more nickels than pennies and 7 fewer quarters than pennies. Josette modeled the
scenario in a table and then wrote the equation p + (p + 2) + (7 – p) = 16.
Is Josette’s equation correct? If not, what was her mistake.
A): Her equation is correct.
B): The variable should have been the number of nickels.
C): Instead of finding the sum, she needed to write an equation to find the difference.
D): The number of quarters was translated incorrectly and should be p – 7.
Is Josette’s equation correct? If not, what was her mistake.
A): Her equation is correct.
B): The variable should have been the number of nickels.
C): Instead of finding the sum, she needed to write an equation to find the difference.
D): The number of quarters was translated incorrectly and should be p – 7.
2 answers:
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Given the triangle
PQR
with points
P(8,0)
Q(6,2)
R(-2,-4)
And the triangle
P'Q'R'
with points
P'(4,0)
Q'(3,1)
R'(-1,-2)
Part A. Scale factor
Using the vertex
P( 8, 0)
P'(4,0)
the dilatation factor is given by
The triangle has a dilatation factor of 1/2
Part B:
P''Q''R'' after using P'Q'R' reflected about the y axis
to make a reflection over the y axis
coordinates (x,y) turn into coordinates (-x,y)
as follows
Then triangle P''Q''R'' has coordinates
P''(-4,0)
Q''(-3,1)
R''(1,-2)
Part C:
PQR is congruent to P''Q''R''?
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Then the triangles are not congruent
A. Our diagram have six location: my house (2,1), a movie theater (5,3), the school (6,6), the police station (3,-2), the airport (-3,3), and the mall (-2,-3)
B. Distance between my house and the movie theater:
To calculate the distance we are going to use the points (2,1) and (5,3) to create a right triangle with tow legs of measures 3 and 2; the hypotenuse of the right triangle will be the distance between my house and the movie theater.
Using the Pythagorean theorem:
We can conclude that the distance between my house and the movie theater is
Our second distance is the distance between the police station and the airport:
This time we are using the points (3,-2) and (-3,3) to create a right triangle with legs of measures 6 and 5; the hypotenuse of our triangle will be the the distance between our points:
We can conclude that the distance between the police station and the airport is
C. Distance form the park to the Fire Station:
We can conclude that the distance from the park to the Fire Station is
Distance from the stadium to the mall:
We can conclude that the distance from the stadium to the mall is
D. What is the distance between your house and the mall?
Answer:
We can conclude that the distance between my house and the mall is
What is the distance between the movie theater and the school?
answer:
We can conclude that the distance between the movie theater and the school is
B. Distance between my house and the movie theater:
To calculate the distance we are going to use the points (2,1) and (5,3) to create a right triangle with tow legs of measures 3 and 2; the hypotenuse of the right triangle will be the distance between my house and the movie theater.
Using the Pythagorean theorem:
We can conclude that the distance between my house and the movie theater is
Our second distance is the distance between the police station and the airport:
This time we are using the points (3,-2) and (-3,3) to create a right triangle with legs of measures 6 and 5; the hypotenuse of our triangle will be the the distance between our points:
We can conclude that the distance between the police station and the airport is
C. Distance form the park to the Fire Station:
We can conclude that the distance from the park to the Fire Station is
Distance from the stadium to the mall:
We can conclude that the distance from the stadium to the mall is
D. What is the distance between your house and the mall?
Answer:
We can conclude that the distance between my house and the mall is
What is the distance between the movie theater and the school?
answer:
We can conclude that the distance between the movie theater and the school is