equation for the line described. Write the equation in the form specified. parallel to \( y+5 x=4 \), through \( (3,5) \); slope-intercept form

Transpose \( V=\frac{1}{3} \pi r^{2} h \) for \( h \)

Write out in full and verify the statements \( \mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4} \), and \( \mathrm{S}_{5} \) for the following. Then us \( 18+54+90+\cdots+(36 n-18)=18 \mathrm{n}^{2} \) \( 18+54+90+126+162=\square \) (Do not simplify.) Are \( \mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4} \), and \( \mathrm{S}_{5} \) true statements? No Yes A. Show that \( \mathrm{S}_{\mathrm{k}+1} \) is true. B. Show that if \( \mathrm{S}_{\mathrm{k}} \) is true, then \( \mathrm{S}_{\mathrm{k}+1} \) is true. C. Show that \( \mathrm{S}_{\mathrm{n}} \) is true. D. Show that if \( \mathrm{S}_{\mathrm{k}+1} \) is true, then \( \mathrm{S}_{\mathrm{k}} \) is true. Write the statement \( \mathrm{S}_{\mathrm{k}} \) and \( \mathrm{S}_{\mathrm{k}+1} \).

6. \( |7 x|=-63 \)

Write out in full and verify the statements \( S_{1}, S_{2}, S_{3}, S_{4} \), and \( S_{5} \) for the follow \( 18+54+90+\cdots+(36 n-18)=18 n^{2} \) \( 18+54+90+126+162=\square \) (Do not simplify.) Are \( S_{1}, S_{2}, S_{3}, S_{4} \), and \( S_{5} \) true statements? No Yes Which of the following is the next step of the proof? A. Show that \( S_{k+1} \) is true. B. Show that if \( S_{k} \) is true, then \( S_{k+1} \) is true. C. Show that \( S_{n} \) is true. O D. Show that if \( S_{k+1} \) is true, then \( S_{k} \) is true. Write the statement \( S_{k} \) and \( S_{k+1} \).

4. Transpose \( I=\frac{E-e}{R+r} \) for \( E \)