An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule (x, y) → (x+7.y-7). Later, the client decides that they would prefer the water fountain's location moved from this new position 5 units left and 4 units up. Find the composition as a single transformation.

The volume of the sun is approximately 1 × 10^18 cu km, while the volume of jupiter is approximately 1 × 10^15 cu km. which of the following is true? a. the volume of jupiter is approximately one thousand times the volume of the sun. b. the volume of jupiter is approximately one hundred times the volume of the sun. c. the volume of the sun is approximately one thousand times the volume of jupiter. d. the volume of the sun is approximately one hundred times the volume of jupiter.

1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2. subtraction property of equality 2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90 substitution 3. m∠1 + m∠2 = m∠3 + m∠2 definition of complementary 4. m∠1 = m∠3 given

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?