Which of the following shows the length of the third side, in inches, of the triangle below? (1 point)
A right triangle is shown. One side of the triangle is labeled as 61 inches. The height of the triangle is labeled as 11 inches.
Square root of 3842 inches
60 inches
Square root of 50 inches
72 inches
To find the length of the third side of the triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the two sides as a and b, and the hypotenuse as c.
Given that one side is 61 inches (a = 61) and the height is 11 inches (b = 11), we can use the Pythagorean theorem to solve for c:
c^2 = a^2 + b^2
c^2 = 61^2 + 11^2
c^2 = 3721 + 121
c^2 = 3842
Taking the square root of both sides, we get:
c = √3842 inches
So, the length of the third side of the triangle is the square root of 3842 inches. Therefore, the correct answer is "Square root of 3842 inches."
The picture below shows a pole and its shadow:
A pole is shown with a right triangle side. The right triangle has hypotenuse 221 cm and base 21 cm.
What is the height of the pole? (1 point)
121 centimeters
220 centimeters
225 centimeters
231 centimeters
To find the height of the pole, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length of the hypotenuse (c) is given as 221 cm and the length of one of the other sides (the base, b) is given as 21 cm.
Let the height of the pole be h.
Using the Pythagorean theorem, we can solve for h:
c^2 = a^2 + b^2
221^2 = h^2 + 21^2
221^2 = h^2 + 441
h^2 = 221^2 - 441
h^2 = 48841 - 441
h^2 = 48400
h = √48400
Calculating the square root of 48400, we get:
h ≈ 220.03 cm
Rounded to the nearest whole number, the height of the pole is approximately 220 cm. Therefore, the correct answer is "220 centimeters".
Look at triangle ABC.
Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 2, 2, and C at ordered pair 4, 2.
What is the length of side AB of the triangle? (1 point)
3
5
Square root of 6
Square root of 13
To find the length of side AB of the triangle, we can use the distance formula. The distance formula calculates the distance between two points (x1, y1) and (x2, y2) as follows:
√((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point A are (4, 5) and the coordinates of point B are (2, 2). Plugging these values into the distance formula, we get:
√((2 - 4)^2 + (2 - 5)^2)
√((-2)^2 + (-3)^2)
√(4 + 9)
√13
Therefore, the length of side AB of the triangle is the square root of 13. Hence, the correct answer is "Square root of 13".
What is the volume of a sphere with a radius of 9 inches? (1 point)
108π
242π
642π
972π
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
Given that the radius of the sphere is 9 inches, we can substitute this value into the formula:
V = (4/3)π(9)^3
V = (4/3)×π×729
V = 972π
Therefore, the volume of the sphere with a radius of 9 inches is 972π. Hence, the correct answer is "972π".
Look at the cups shown below (please note images are not drawn to scale):
A cone is shown with width 2 inches and height 4 inches, and a cylinder is shown with width 2 inches and height 6 inches.
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth. (1 point)
8.8 cubic inches
10.1 cubic inches
14.7 cubic inches
22.3 cubic inches
26.
To find the difference in volume between cup B (cylinder) and cup A (cone), we need to calculate the volume of each shape.
Starting with cup A (cone), the formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height.
The width of the cone is given as 2 inches, which means the radius is 1 inch. The height is given as 4 inches.
V(A) = (1/3)π(1^2)(4)
V(A) = (1/3)π(1)(4)
V(A) = (4/3)π
Moving on to cup B (cylinder), the formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height.
The width of the cylinder is given as 2 inches, which means the radius is 1 inch. The height is given as 6 inches.
V(B) = π(1^2)(6)
V(B) = π(1)(6)
V(B) = 6π
To find the difference in volume, we subtract V(A) from V(B):
V(B) - V(A) = 6π - (4/3)π
V(B) - V(A) = (18/3)π - (4/3)π
V(B) - V(A) = (14/3)π
To round to the nearest tenth, we can approximate π as 3.14:
V(B) - V(A) ≈ (14/3) × 3.14
V(B) - V(A) ≈ 14.14
Therefore, cup B will hold approximately 14.1 cubic inches more juice than cup A when both are completely full. Hence, the closest answer is "14.7 cubic inches".
Look at the following function:
x y
−3 −8
−2 −6
−1 −4
0 0
Matt said that the function is linear.
Justine said that the function is nonlinear.
Which of the following explains who is correct? (1 point)
Matt, because for every 1-unit increase in x, there is an increase in y by 2
Matt, because for every 2-unit increase in x, there is an increase in y by 1
Justine, because the point (−3, −8) does not lie on the straight line that contains the other points
Justine, because the point (0, 0) does not lie on the straight line that contains the other points