Which statements are true? Select the five correct answers.
StartRoot 1.8 EndRoot < 1.8
StartRoot 1.8 EndRoot greater-than 1
StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
The five correct statements are:
1.8 < 1.8
1.8 > 1
1.8 < 1.9
1.3 < 1.8 < 1.4
1.9 + 1.8 > 2
What is the distance between the points (7, 8) and (–8, 0) on a coordinate grid?
To find the distance between two points on a coordinate grid, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first point are (7, 8) and the coordinates of the second point are (-8, 0).
Using the distance formula, we have:
d = √((-8 - 7)^2 + (0 - 8)^2)
= √((-15)^2 + (-8)^2)
= √(225 + 64)
= √289
= 17
Therefore, the distance between the points (7, 8) and (-8, 0) on the coordinate grid is 17 units.
Each point on the edge of a circle is equidistant from the center of the circle. The center of a circle is located at (6, 3). Which point on the y-axis could be on the edge of the circle if the distance from the center of the circle to the edge is 10 units?
(0, –1)
(0, 1)
(0, 5)
(0, –5)
To determine which point on the y-axis could be on the edge of the circle, we need to find the distance between each point on the y-axis and the center of the circle. If the distance is equal to 10 units, then that point could be on the edge of the circle.
The distance between two points in a coordinate plane can be found using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the center of the circle is located at (6, 3), and we are looking for a point on the y-axis, meaning the x-coordinate is 0.
Let's calculate the distance between (0, -1) and (6, 3):
d = √((0 - 6)^2 + (-1 - 3)^2)
= √((-6)^2 + (-4)^2)
= √(36 + 16)
= √52
The distance between (0, -1) and (6, 3) is not equal to 10 units.
Now let's calculate the distance between (0, 1) and (6, 3):
d = √((0 - 6)^2 + (1 - 3)^2)
= √((-6)^2 + (-2)^2)
= √(36 + 4)
= √40
The distance between (0, 1) and (6, 3) is not equal to 10 units.
Next, let's calculate the distance between (0, 5) and (6, 3):
d = √((0 - 6)^2 + (5 - 3)^2)
= √((-6)^2 + 2^2)
= √(36 + 4)
= √40
The distance between (0, 5) and (6, 3) is not equal to 10 units.
Lastly, let's calculate the distance between (0, -5) and (6, 3):
d = √((0 - 6)^2 + (-5 - 3)^2)
= √((-6)^2 + (-8)^2)
= √(36 + 64)
= √100
= 10
The distance between (0, -5) and (6, 3) is equal to 10 units.
Therefore, the point (0, -5) on the y-axis could be on the edge of the circle if the distance from the center of the circle to the edge is 10 units.
Fahim is 6 feet tall. At noon, he stands with the sun behind him casting a shadow. The distance from the top of Fahim’s head to the furthest tip of the shadow is 13 feet.
A right triangle with side length 6 feet, s, and hypotenuse 13 feet.
[Not drawn to scale]
What is the length of Fahim’s shadow? Round to the nearest tenth of a foot.
7.0 feet
8.5 feet
11.5 feet
14.3 feet
The length of Fahim's shadow can be found by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, one side (a) represents Fahim's height, which is 6 feet. The other side (b) represents the length of his shadow, which is unknown. The hypotenuse (c) represents the distance from the top of Fahim's head to the furthest tip of the shadow, which is 13 feet.
To find the length of Fahim's shadow, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
6^2 + b^2 = 13^2
36 + b^2 = 169
b^2 = 169 - 36
b^2 = 133
b ≈ √133
b ≈ 11.5
Therefore, the length of Fahim's shadow is approximately 11.5 feet.