Tutor profile: Vy D.
Right triangle CDE has its right angle at vertex D. The length of DE is 8 feet and the length of CE is 17 feet. What is the length, in feet, of CD? (a) 11 (b) 12 (c) 14 (d) 15
The answer is (d) 15. To solve this question we can use the Pythagorean Theorem, which states that the length of each leg of a right triangle squared added together equals the length of the hypotenuse squared, or a^2 + b^2 = c^2. Because the right angle is at D, we know that CD is a leg of the triangle and CE is the hypotenuse. 82 + b^2 = 172 64 + b^2 = 289 b^2= 289 – 64 b^2= 225 b = 15
Atoms of the elements hydrogen (H) and helium (He) make up over 98% of the atoms in the Solar System. Only six other elements are present in abundances between 0.05% and 1%, and together with H and He these can be considered the "major elements." The other 89 stable elements are even less abundant, and can be considered the "minor elements." In addition, elements with even atomic number are usually more abundant than neighboring elements with odd atomic numbers. (In most cases, an element of even atomic number will be more abundant than the two elements whose atomic numbers are 1 less and 1 greater). Table 1 shows one estimate of the abundance of each element in the Solar System. Table 1. Relative abundances of the elements in the Solar System Element Atomic # Abundance (%) H 1 91.03 He 2 7.24 C 6 0.41 N 7 0.11 O 8 0.79 Ne 10 0.10 Mg 12 0.05 Si 14 0.05 ALL OTHER ELEMENTS >14 < 0.05 According to Table 1, as the atomic number increases from 8 to 9 to 10, the abundances: (a) Decrease, then increase (b) Increase, then decrease (c) Decrease only (d) Increase only
The best answer is (a) Decrease, then increase. The last line of the table says that the abundance of element 9 is less than 0.05%. Therefore, the abundance of element 8 (0.79%) decreases to the abundance of element 9 (<0.05%), and then increases to the abundance of element 10 (0.10%).
Solve the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
Step 1: Expand -15x - 10 - x + 3 = -16x - 20 + 13 Step 2: Combine like terms -16x - 7 = -16x - 7 Step 3: 0 = 0 Because both sides equal 0, the above equation is true for all real values of x
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