Many students find algebra a difficult subject because letters are used to \( \qquad \) numbers. 1 allege 2 denote 3 accrue 4 disseminate
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- The sentence is discussing why students find algebra difficult. - The key part of the sentence is "letters are used to ______ numbers." Step 2: Analyze the meaning of each option. Show more…
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Inverse functions can be used to send and receive coded information. $A$ simple example might use the function defined by $f(x)=2 x+5 .$ (Note that it is one-to-one.) Suppose that each letter of the alphabet is assigned a numerical value according to its position, as follows. $$ \begin{aligned} &\begin{array}{llllllllll} {A} & {1} & {G} & {7} & {L} & {12} & {Q} & {17} & {V} & {22} \\ {B} & {2} & {H} & {8} & {M} & {13} & {R} & {18} & {W} & {23} \end{array}\\ &\begin{array}{llllllllll} {\mathrm{B}} & {2} & {\mathrm{H}} & {8} & {\mathrm{M}} & {13} & {\mathrm{R}} & {18} & {\mathrm{W}} & {23} \\ {\mathrm{C}} & {3} & {1} & {9} & {\mathrm{N}} & {14} & {\mathrm{S}} & {19} & {\mathrm{X}} & {24} \\ {\mathrm{D}} & {4} & {\mathrm{J}} & {10} & {\mathrm{O}} & {15} & {\mathrm{T}} & {20} & {\mathrm{Y}} & {25} \\ {\mathrm{E}} & {5} & {\mathrm{K}} & {11} & {\mathrm{P}} & {16} & {\mathrm{U}} & {21} & {\mathrm{Z}} & {26} \\ {\mathrm{F}} & {6} & {} & {} & {} & {} \end{array} \end{aligned} $$ Using the function, the word ALGEBRA would be encoded as $7 \quad 29 \quad 19 \quad 15 \quad 9 \quad 41 \quad 7$ because $f(\mathrm{A})=f(1)=2(1)+5=7, \quad f(\mathrm{L})=f(12)=2(12)+5=29, \quad$ and so on. The message would then be decoded by using the imerse of $f,$ defined by $f^{-1}(x)=\frac{x-5}{2}$ $\left(\text {or } f^{-1}(x)=\frac{1}{2} x-\frac{5}{2}\right) .$ For example $f^{-1}(7)=\frac{7-5}{2}=1=A, \quad f^{-1}(29)=\frac{29-5}{2}=12=L,$ and so on. Work Exercises 39– 42 in order. You receive the following coded message today. (Read across from left to right.) $\begin{array}{llllll}{47} & {95} & {23} & {67} & {-1} & {59} & {27} & {31} & {51} & {23} & {7-143} & {779} & {43} & {-175}\end{array}$ $\begin{array}{lllllllllllllll}{31} & {71} & {75} & {27} & {15} & {23} & {67} & {15} & {-1} & {75} & {15} & {71} & {75} & {75} & {27} & {31} & {51}\end{array}$ $\begin{array}{lllllllllllll}{23} & {71} & {31} & {51} & {7} & {15} & {71} & {43} & {31} & {7} & {15} & {11} & {367} & {15} & {-1}\end{array} 11$ Use the letter/number assignment described earlier to decode the message.
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Represent algebraically two numbers so that one is 7 less than three times the other. (a) $x, 3(x-7)$ (b) $x, 3 x$ (c) $x, 3 x+7$ (d) $x, 3 x-7$
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