The amount of money a worker makes varies directly with the hourly rate of pay. Worker A earns $168 for an 8-hour period. Worker B earns the same hourly rate as Worker A but works for only 6 hours. What does Worker B earn?
Responses
If Worker A earns $168 for an 8-hour period, their hourly rate of pay is $168/8 = $21/hour.
Worker B earns the same hourly rate as Worker A, which is $21/hour.
If Worker B works for only 6 hours, they will earn $21/hour * 6 hours = $126.
The baseball diamond is really a square. The distance between each of the bases is 90 feet.
How far does the catcher have to throw the ball to get from home plate to second base? Round your answer to the nearest foot.
To determine the distance from home plate to second base, we need to consider that the bases form the vertices of a square. The distance from home plate to second base is the same as the length of one side of the square.
Given that the distance between each base is 90 feet, the distance from home plate to second base is also 90 feet.
identify the rotation rule on a coordinate plane that verifies that triangle A(2,-1), B(4,1), C(3,3) and triangle A'(1,2), B'(-1,4), C'(-3,3) are congruent when rotated 90°.
Responses
To verify that the triangles A(2,-1), B(4,1), C(3,3) and A'(1,2), B'(-1,4), C'(-3,3) are congruent when rotated 90 degrees, we can use the rotation rule.
The rotation rule for a point (x, y) by 90 degrees counterclockwise is:
(x', y') = (-y, x), where (x', y') represents the coordinates of the rotated point.
Applying this rule to each point of triangle A(2,-1), B(4,1), C(3,3) gives us the following rotated points:
A' = (-(-1), 2) = (1, 2),
B' = (-1, 4),
C' = (-3, 3).
Comparing these rotated points with the coordinates of triangle A'(1,2), B'(-1,4), C'(-3,3), we can see that they are indeed congruent when rotated 90 degrees.
Point E(−5, 3) and point D(−4, −3) are located on the grid. Which measurement is closest to the distance between point E and point D in units?
To find the distance between two points (x1, y1) and (x2, y2) on a coordinate grid, you can use the distance formula.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point E are (-5, 3) and the coordinates of point D are (-4, -3). Plugging these values into the distance formula, we get:
d = √((-4 - (-5))^2 + (-3 - 3)^2)
= √(1^2 + (-6)^2)
= √(1 + 36)
= √37
Rounding the value to the nearest whole number, we find that the distance between point E and point D is closest to 6 units.
Point E(−5, 3) and point D(−4, −3) are located on the grid. Which measurement is closest to the distance between point E and point D in units?
Responses
A 6.1 units6.1 units
B 5.3 units5.3 units
C 6.5 units6.5 units
D 6.7 units
To find the distance between two points (x1, y1) and (x2, y2) on a coordinate grid, we can use the distance formula.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point E are (-5, 3) and the coordinates of point D are (-4, -3).
Plugging these values into the distance formula:
d = √((-4 - (-5))^2 + (-3 - 3)^2)
= √((1)^2 + (-6)^2)
= √(1 + 36)
= √37
The closest measurement to the distance between point E and point D is approximately 6.1 units. Thus, the correct answer is A.
Find the value of c.
Responses
A 5
B 6
C 10
D 25
Find the value of c.
Responses
A 55
B 66
C 1010
D 2525
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