Does anyone have the answers for the connexus geometry b final? my test has 38 questions
31 answers
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solve for x
x
x+5
8
12
x
x+5
8
12
I'm assuming that the equations are set equal to each other, so we have:
x + x + 5 = 8 + 12
Simplifying the left side of the equation, we get:
2x + 5 = 20
Subtracting 5 from both sides, we get:
2x = 15
Dividing both sides by 2, we get:
x = 7.5
Therefore, the solution for x is 7.5.
x + x + 5 = 8 + 12
Simplifying the left side of the equation, we get:
2x + 5 = 20
Subtracting 5 from both sides, we get:
2x = 15
Dividing both sides by 2, we get:
x = 7.5
Therefore, the solution for x is 7.5.
the lengths of the sides of a triangle are 3, 4, and 5. classify the triangle as acute, right, or obtuse.
We can classify the triangle based on the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
In this case, the lengths of the sides of the triangle are 3, 4, and 5. We can check if it is a right triangle by seeing if:
3² + 4² = 5²
9 + 16 = 25
25 = 25
Since the equation is true, the triangle satisfies the Pythagorean theorem and is therefore a right triangle.
So, the triangle is classified as a right triangle.
In this case, the lengths of the sides of the triangle are 3, 4, and 5. We can check if it is a right triangle by seeing if:
3² + 4² = 5²
9 + 16 = 25
25 = 25
Since the equation is true, the triangle satisfies the Pythagorean theorem and is therefore a right triangle.
So, the triangle is classified as a right triangle.
write the ratio for sin A.
AC = 40
CB = 9
AB = 41
AC = 40
CB = 9
AB = 41
To write the ratio for sin A, we need to use the side opposite angle A and the hypotenuse. In this case, we know that AB is the hypotenuse of the right triangle, and A is the angle opposite to side CB. Therefore, we can write:
sin A = opposite / hypotenuse
sin A = CB / AB
Substituting the values we have:
sin A = 9 / 41
Therefore, the ratio for sin A is 9/41.
sin A = opposite / hypotenuse
sin A = CB / AB
Substituting the values we have:
sin A = 9 / 41
Therefore, the ratio for sin A is 9/41.
A blimp provides aerial television views of a soccer game. the television camera sights the stadium at an 18° angle of depression. the altitude of the blimp is 500m. what is the line-of-sight distance from the television camera to the base of the stadium? round to the nearest hundred meters.
Let's first draw a diagram to visualize the situation. We have a right triangle where the horizontal line represents the distance from the television camera to the stadium, the vertical line represents the height of the blimp, and the hypotenuse represents the line-of-sight distance from the television camera to the base of the stadium.
We know that the altitude of the blimp is 500m and the angle of depression is 18°. Therefore, the angle formed between the horizontal line and the hypotenuse is 90° - 18° = 72°.
Using trigonometry, we can find the distance between the camera and the stadium. We are looking for the adjacent side, so we can use the cosine function:
cos(72°) = adjacent / hypotenuse
We can rearrange this equation to solve for the adjacent side:
adjacent = hypotenuse * cos(72°)
Now, we need to find the value of the hypotenuse. To do this, we can use the height of the blimp as the opposite side, and the angle of depression as the angle opposite the height. Again, using trigonometry, we can use the tangent function to find the hypotenuse:
tan(18°) = opposite / adjacent
opposite (500m) = adjacent / tan(18°)
Now, we can substitute the value of the opposite side and solve for the adjacent side:
adjacent = 500m * tan(18°)
adjacent = 137.6m (rounded to the nearest tenth)
Finally, we can substitute the value of the adjacent side into the equation we found earlier to solve for the hypotenuse:
hypotenuse = 137.6m / cos(72°)
hypotenuse = 455.0m (rounded to the nearest tenth)
Therefore, the line-of-sight distance from the television camera to the base of the stadium is approximately 455 meters.
We know that the altitude of the blimp is 500m and the angle of depression is 18°. Therefore, the angle formed between the horizontal line and the hypotenuse is 90° - 18° = 72°.
Using trigonometry, we can find the distance between the camera and the stadium. We are looking for the adjacent side, so we can use the cosine function:
cos(72°) = adjacent / hypotenuse
We can rearrange this equation to solve for the adjacent side:
adjacent = hypotenuse * cos(72°)
Now, we need to find the value of the hypotenuse. To do this, we can use the height of the blimp as the opposite side, and the angle of depression as the angle opposite the height. Again, using trigonometry, we can use the tangent function to find the hypotenuse:
tan(18°) = opposite / adjacent
opposite (500m) = adjacent / tan(18°)
Now, we can substitute the value of the opposite side and solve for the adjacent side:
adjacent = 500m * tan(18°)
adjacent = 137.6m (rounded to the nearest tenth)
Finally, we can substitute the value of the adjacent side into the equation we found earlier to solve for the hypotenuse:
hypotenuse = 137.6m / cos(72°)
hypotenuse = 455.0m (rounded to the nearest tenth)
Therefore, the line-of-sight distance from the television camera to the base of the stadium is approximately 455 meters.
how do you find the area of a kite?
To find the area of a kite, you can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
where diagonal 1 and diagonal 2 are the lengths of the two diagonals of the kite.
If the lengths of the diagonals are not given, you can use the formula:
Area = (product of the lengths of the two adjacent sides) x (sin of the angle between those two sides)
where the angle is the angle between the two adjacent sides of the kite.
Here's an example: Suppose we have a kite with two adjacent sides measuring 8 cm and 10 cm, and the angle between these sides is 60 degrees. To find the area of the kite, we can use the formula:
Area = (product of the lengths of the two adjacent sides) x (sin of the angle between those two sides)
Area = (8 cm x 10 cm) x sin(60 degrees)
Area = 40 cm² x 0.866
Area = 34.6 cm²
Therefore, the area of the kite is approximately 34.6 square centimeters.
Area = (diagonal 1 x diagonal 2) / 2
where diagonal 1 and diagonal 2 are the lengths of the two diagonals of the kite.
If the lengths of the diagonals are not given, you can use the formula:
Area = (product of the lengths of the two adjacent sides) x (sin of the angle between those two sides)
where the angle is the angle between the two adjacent sides of the kite.
Here's an example: Suppose we have a kite with two adjacent sides measuring 8 cm and 10 cm, and the angle between these sides is 60 degrees. To find the area of the kite, we can use the formula:
Area = (product of the lengths of the two adjacent sides) x (sin of the angle between those two sides)
Area = (8 cm x 10 cm) x sin(60 degrees)
Area = 40 cm² x 0.866
Area = 34.6 cm²
Therefore, the area of the kite is approximately 34.6 square centimeters.
find the area of a kite with a diagonal 1 of 8 m and a diagonal 2 of 8 m
If both of the diagonals of the kite are 8 m, that means they have the same length, and they are also perpendicular bisectors of each other (meaning that they divide each other into two equal halves).
Since the diagonals are perpendicular, we can use them to find the area of the kite using the formula:
Area = (diagonal 1 x diagonal 2) / 2
Substituting the values we have:
Area = (8 m x 8 m) / 2
Area = 64 m² / 2
Area = 32 m²
Therefore, the area of the kite is 32 square meters.
Since the diagonals are perpendicular, we can use them to find the area of the kite using the formula:
Area = (diagonal 1 x diagonal 2) / 2
Substituting the values we have:
Area = (8 m x 8 m) / 2
Area = 64 m² / 2
Area = 32 m²
Therefore, the area of the kite is 32 square meters.
how to find the area of a trapezoid
To find the area of a trapezoid, you can use the formula:
Area = (base1 + base2) x height / 2
where base1 and base2 are the lengths of the two parallel sides of the trapezoid, and height is the perpendicular distance between these two parallel sides.
Here's an example: Suppose we have a trapezoid with base1 of 10 cm, base2 of 6 cm, and height of 5 cm. To find the area of the trapezoid, we can use the formula:
Area = (base1 + base2) x height / 2
Area = (10 cm + 6 cm) x 5 cm / 2
Area = 16 cm x 5 cm / 2
Area = 80/2
Area = 40 cm²
Therefore, the area of the trapezoid is 40 square centimeters.
Area = (base1 + base2) x height / 2
where base1 and base2 are the lengths of the two parallel sides of the trapezoid, and height is the perpendicular distance between these two parallel sides.
Here's an example: Suppose we have a trapezoid with base1 of 10 cm, base2 of 6 cm, and height of 5 cm. To find the area of the trapezoid, we can use the formula:
Area = (base1 + base2) x height / 2
Area = (10 cm + 6 cm) x 5 cm / 2
Area = 16 cm x 5 cm / 2
Area = 80/2
Area = 40 cm²
Therefore, the area of the trapezoid is 40 square centimeters.
find the area of the regular polygon with the given apothem a and side length s.
decagon, a=15 m, s=9.7 m
decagon, a=15 m, s=9.7 m
To find the area of a regular decagon (a polygon with 10 sides) with apothem a and side length s, you can use the formula:
Area = (5 x s x a²) / 2
where s is the length of the side of the decagon, and a is the apothem (the distance from the center of the decagon to the midpoint of a side).
Substituting the values we have:
Area = (5 x 9.7 m x 15 m²) / 2
Area = 5 x 9.7 x 225 / 2
Area = 10837.5 m²
Therefore, the area of the regular decagon is approximately 10837.5 square meters.
Area = (5 x s x a²) / 2
where s is the length of the side of the decagon, and a is the apothem (the distance from the center of the decagon to the midpoint of a side).
Substituting the values we have:
Area = (5 x 9.7 m x 15 m²) / 2
Area = 5 x 9.7 x 225 / 2
Area = 10837.5 m²
Therefore, the area of the regular decagon is approximately 10837.5 square meters.
find the surface area of a cylinder with a radius of 5 inches and a height of 8 inches.
To find the surface area of a cylinder with a radius of 5 inches and a height of 8 inches, we need to find the lateral surface area and the surface area of the top and bottom circular faces separately, and then add them together.
The lateral surface area of a cylinder can be found using the formula:
Lateral surface area = 2πrh
where r is the radius and h is the height.
Substituting the values, we get:
Lateral surface area = 2 x π x 5 in x 8 in
Lateral surface area = 80π in²
The surface area of each circular face of the cylinder can be found using the formula:
Circular surface area = πr²
Substituting the values, we get:
Circular surface area = π x 5 in²
Circular surface area = 25π in²
To find the total surface area, we add the lateral surface area and the surface area of the top and bottom circular faces. Since there are two circular faces, we multiply the surface area of one circular face by 2 before adding:
Total surface area = 2(Circular surface area) + Lateral surface area
Total surface area = 2(25π in²) + 80π in²
Total surface area = 50π in² + 80π in²
Total surface area = 130π in²
Therefore, the surface area of the cylinder is approximately 130π square inches or 408.4 square inches, rounded to one decimal place.
The lateral surface area of a cylinder can be found using the formula:
Lateral surface area = 2πrh
where r is the radius and h is the height.
Substituting the values, we get:
Lateral surface area = 2 x π x 5 in x 8 in
Lateral surface area = 80π in²
The surface area of each circular face of the cylinder can be found using the formula:
Circular surface area = πr²
Substituting the values, we get:
Circular surface area = π x 5 in²
Circular surface area = 25π in²
To find the total surface area, we add the lateral surface area and the surface area of the top and bottom circular faces. Since there are two circular faces, we multiply the surface area of one circular face by 2 before adding:
Total surface area = 2(Circular surface area) + Lateral surface area
Total surface area = 2(25π in²) + 80π in²
Total surface area = 50π in² + 80π in²
Total surface area = 130π in²
Therefore, the surface area of the cylinder is approximately 130π square inches or 408.4 square inches, rounded to one decimal place.
find the surface area of a pyamid with a slant height of 11 inches and a base length of 12 inches.
To find the surface area of a pyramid with a slant height of 11 inches and a base length of 12 inches, we will use the formula:
Surface area = 1/2 (perimeter of base x slant height) + base area
First, let's find the perimeter of the base. Since the base is a square with a length of 12 inches, all four sides are equal and the perimeter is 4 x 12 = 48 inches.
Next, we can use the formula to find the surface area of the pyramid:
Surface area = 1/2 (perimeter of base x slant height) + base area
Surface area = 1/2 (48 inches x 11 inches) + (12 inches x 12 inches)
Surface area = 1/2 (528 inches²) + 144 inches²
Surface area = 264 inches² + 144 inches²
Surface area = 408 inches²
Therefore, the surface area of the pyramid is 408 square inches.
Surface area = 1/2 (perimeter of base x slant height) + base area
First, let's find the perimeter of the base. Since the base is a square with a length of 12 inches, all four sides are equal and the perimeter is 4 x 12 = 48 inches.
Next, we can use the formula to find the surface area of the pyramid:
Surface area = 1/2 (perimeter of base x slant height) + base area
Surface area = 1/2 (48 inches x 11 inches) + (12 inches x 12 inches)
Surface area = 1/2 (528 inches²) + 144 inches²
Surface area = 264 inches² + 144 inches²
Surface area = 408 inches²
Therefore, the surface area of the pyramid is 408 square inches.
find the volume of a cylinder with a radius of 8 inches and a height of 5 inches.
To find the volume of a cylinder with a radius of 8 inches and a height of 5 inches, we can use the formula:
Volume = πr²h
where r is the radius of the cylinder and h is its height.
Substituting the values, we get:
Volume = π x (8 in)² x 5 in
Volume = π x 64 in² x 5 in
Volume = 320π in³
Therefore, the volume of the cylinder is approximately 320π cubic inches or 1005.31 cubic inches, rounded to two decimal places.
Volume = πr²h
where r is the radius of the cylinder and h is its height.
Substituting the values, we get:
Volume = π x (8 in)² x 5 in
Volume = π x 64 in² x 5 in
Volume = 320π in³
Therefore, the volume of the cylinder is approximately 320π cubic inches or 1005.31 cubic inches, rounded to two decimal places.
find the volume of a right cone with a radius of 2 cm and a height of 4 cm
To find the volume of a right cone with a radius of 2 cm and a height of 4 cm, we can use the formula:
Volume = (1/3)πr²h
where r is the radius of the cone, and h is its height.
Substituting the values, we get:
Volume = (1/3) x π x (2 cm)² x 4 cm
Volume = (1/3) x π x 4 cm² x 4 cm
Volume = (1/3) x π x 16 cm³
Volume = 16π/3 cm³
Therefore, the volume of the cone is approximately 16π/3 cubic centimeters or 16.76 cubic centimeters, rounded to two decimal places.
Volume = (1/3)πr²h
where r is the radius of the cone, and h is its height.
Substituting the values, we get:
Volume = (1/3) x π x (2 cm)² x 4 cm
Volume = (1/3) x π x 4 cm² x 4 cm
Volume = (1/3) x π x 16 cm³
Volume = 16π/3 cm³
Therefore, the volume of the cone is approximately 16π/3 cubic centimeters or 16.76 cubic centimeters, rounded to two decimal places.
use the given circumference to find the surface area of the spherical object.
a pincushion with C=18 cm
a pincushion with C=18 cm
To find the surface area of a spherical object with a circumference of 18 cm, we need to first use the formula for the circumference of a sphere to find its radius:
C = 2πr
Solving this equation for r, we get:
r = C / 2π
Substituting the value of the circumference C, we get:
r = 18 cm / 2π ≈ 2.87 cm
Now that we know the radius of the spherical object, we can use the formula for its surface area:
Surface area = 4πr²
Substituting the value of the radius r that we just found, we get:
Surface area = 4π(2.87 cm)²
Surface area = 104.97 cm²
Therefore, the surface area of the pincushion is approximately 104.97 square centimeters.
C = 2πr
Solving this equation for r, we get:
r = C / 2π
Substituting the value of the circumference C, we get:
r = 18 cm / 2π ≈ 2.87 cm
Now that we know the radius of the spherical object, we can use the formula for its surface area:
Surface area = 4πr²
Substituting the value of the radius r that we just found, we get:
Surface area = 4π(2.87 cm)²
Surface area = 104.97 cm²
Therefore, the surface area of the pincushion is approximately 104.97 square centimeters.
find the volume of a sphere with a surface area of 2916 pi in^2
To find the volume of a sphere with a surface area of 2916π square inches, we can use the formula for the surface area of a sphere:
Surface area = 4πr²
where r is the radius of the sphere.
We can rearrange this formula to solve for the radius:
r = sqrt(Surface area / 4π)
Substituting the value of the surface area, we get:
r = sqrt(2916π / 4π)
r = sqrt(729)
r = 27
Now that we know the radius of the sphere, we can use the formula for its volume:
Volume = (4/3)πr³
Substituting the value of the radius r that we just found, we get:
Volume = (4/3)π(27³)
Volume ≈ 81,487π cubic inches
Therefore, the volume of the sphere is approximately 81,487π cubic inches or approximately 256,609 cubic inches, rounded to the nearest whole number.
Surface area = 4πr²
where r is the radius of the sphere.
We can rearrange this formula to solve for the radius:
r = sqrt(Surface area / 4π)
Substituting the value of the surface area, we get:
r = sqrt(2916π / 4π)
r = sqrt(729)
r = 27
Now that we know the radius of the sphere, we can use the formula for its volume:
Volume = (4/3)πr³
Substituting the value of the radius r that we just found, we get:
Volume = (4/3)π(27³)
Volume ≈ 81,487π cubic inches
Therefore, the volume of the sphere is approximately 81,487π cubic inches or approximately 256,609 cubic inches, rounded to the nearest whole number.
42 answers