Analyze and Solve Linear Equations
Peter is solving the linear equation 7x-5+5x=15x-7-3x+2. His final two steps are:
12x-5=12x-5
-5=-5
This is the solution.
What is infinitely many solutions since -5=-5 is a true statement?
Triangle ABC, A(5, 5), B(1, 3), and C(1, 7), is translated down 7 units to form triangle A'B'C'. True or false: Triangle ABC and A'B'C' are similar and congruent.
What is true?
The number to the tenths place that closest approximates the sqrt(51).
sqrt( ) is the square root symbol
What is 7.1?
A system on two linear equations has infinitely many solutions. One equation is x-2y=6. This is the equation that would make this system have infinitely many solutions.
a. x+2y=6
b. x-2y=4
c. 2y-x=-6
d. -2y+x=4
What is c. 2y-x=-6?
This is the distance between (-5, 3) and (1, -3) on the coordinate plane rounded to the tenths place.
The mistake that was made.
Step 1. 6(x+2)=42-4x
Step 2. 6x+2=42-4x
Step 3. 10x+2=42
Step 4. 10x=40
Step 5. x=4
Where is step 2 when it should be 6x+12 instead of 6x+2?
A parallelogram with coordinates A (-2, 3), B (3, 3), C (4, 6), and D (-1, 6) is first rotated 90 degrees clockwise and then translated 4 units left and 2 units down to form quadrilateral A'B'C'D'. This is the distance, in units, between point C' and point D' in the resulting figure.
What is 5 units?
The fraction that is equivalent to 0.44444...
What is 4/9?
This is the correct statement that describes the solution to this system of equations.
4x+8y=8
2x-3y=4
a. There is no solution
b. There are infinitely many solutions
c. There is exactly one solution at (2,0)
d. There is exactly one solution at (0,2)
What is c. There is exactly one solution at (2,0)?
This is the lenght of the hypotenuse of a right triangle when the legs are lengths 8 in. and 12 in. rounded to the nearest tenths place.
What is 14.4 in.?
Jada and Zeke compare their monthly text message plans. Jada's plan costs $5 plus an additional $0.05 per text. Zeke's plan costs $0.10 per text. The equations below show the cost, c, for each plan depending on how many texts, t, are sent.
Jada's Plan: c=0.05t+5
Zeke's Plan: c=0.10t
In one month, Jada and Zeke paid the same amount. This is the amount.
What is 100 texts?
Kylie draws a triangle on a coordinate grid. She then performs the following transformation in the order below:
a translation of 3 units to the left
a dilation by a factor of 3
a reflection across the x-axis
a rotation of 180 degrees
She claims the resulting triangle is congruent to the original triangle.
This is the transformation she should not have done in order for her claim to be correct.
What is the dilation by a factor of 3?
The approximation of 2*sqrt(29) to the tenths place.
(2 times the square root of 29)
What is any number between 10.6-10.9?
Donica wants to join a gym.
Gym A: $20 joining fee and $40 monthly charge.
Gym B: No joining fee and $45 monthly charge.
This is the number of months it will take for the total cost for both gyms to be equal.
What is 4 months?
This is the length of the missing leg in a right triangle that has a hypotenuse that's 13 ft. long and a leg that is 5 ft. long.
What is 12 ft.?
The value for x that makes the equation 7x-2(x+1)+18=8x-11 true.
What is 9?
Triangle PQR is rotated 180 degrees clockwise around the origin to create triangle P'Q'R'. Select all the equivalent transformations that can be applied to triangle PQR to create triangle P'Q'R'.
a dilation through the origin by a scale factor of 2 followed by a reflection across the line y=x
a reflection across the y-axis followed by a reflection across the x-axis
a rotation of 180 degrees counterclockwise around the origin
a translation of 2 units to the left
a reflection across the x-axis
What is: a reflection across the y-axis followed by a reflection across the x-axis, and a rotation of 180 degrees counterclockwise around the origin?
The closest approximation for the cube root of 94 to the tenths place.
What is any number between 4.4-4.6?
The principal of Lakeshore Middle School wants to buy mechanical pencils with the school name on them for the school store.
The pencils can be bought from Company P for $0.57 each, with free shipping.
The pencils can be bought from Company T for $0.54 each, plus $4.95 for shipping.
This is the true statement about purchasing pencils from the two companies.
a. Only the cost model for Company P results in a linear graph.
b. The graphs of the cost functions for each company will not intersect.
c. Buying pencils from Company T is always more expensive than buying pencils from Company P, regardless of the number of pencils bought.
d. The company with the least expensive option can only be determined once the number of pencils the principal wants to buy is known.
What is d. The company with the least expensive option can only be determined once the number of pencils the principal wants to buy is known.
Brett claims that the Pythagorean theorem can be used to solve for the missing side length of any triangle. Is Brett's claim correct? Why or why not?
a. Yes, Brett's claim is correct because the Pythagorean theorem can be used with any triangle.
b. Yes, Brett's claim is correct because the Pythagorean theorem can be used with any triangle that is approximately right.
c. No, Brett's claim is incorrect because the Pythagorean theorem can only be used with a right triangle.
d. No, Brett's claim is incorrect because the Pythagorean theorem can only be used when the side lengths of a triangle are equal.
What is c. No, Brett's claim is incorrect because the Pythagorean theorem can only be used with a right triangle?
In an experiment, the temperature of a liquid at 16.9 degrees Celsius is decreasing at a rate of 2.3 degrees Celsius per minute and the temperature of a solid at 30.7 degrees Celsius is decreasing at a rate of 6.9 degrees Celsius per minute.
This is the number of minutes it will take the liquid and solid to reach the same temperature.
What is 3 minutes?
Triangle LMN is similar, but not congruent, to Triangle ABC. Triangle ABC underwent two transformations to get Triangle LMN. Select two of the following pairs of transformations that could have occurred.
Dilation of 1/2 and a translation of 8 units down
90-degree counterclockwise rotation and a dilation of 3
Translation of 5 units down left and a reflection over the x-axis
Reflection over y=-x and a 180-degree counterclockwise rotation
These are two examples, 1 of a rational number AND 1 an example of an irrational number.
What is whatever the teacher says is right when you ask them to check?
This is the x coordinate of the solution to this system of equations.
-2x+y=5
-5x+y=-4
What is 3?
A cylindrical can of juice has a height of 5 inches and a radius of 1.25 inches. This is the total volume in cubic inches of the can.
What is 24.5 inches cubed?