Convert the verbal expression with its equivalent algebraic expression. Use r for any unknowns and simplify your answer. If applicable,

Convert the verbal expression with its equivalent algebraic expression. Use r for any unknowns and simplify your answer. If applicable, put the constant at the beginning of the expression. three-quarters the sum of seven and a number The mathematical equivalent of this phrase is:​

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  1. [tex]9x^2+5[/tex]

    Step-by-step explanation:

    Let x represent the unknown number.

    We are asked to convert the verbal expression with its equivalent algebraic expression..

    Five more than a nine times square of a number.

    Square of the number would be [tex]x^2[/tex].

    Nine times square of the number would be 9 multiplied by  [tex]x^2[/tex] as:

    [tex]9x^2[/tex].

    Five more than a nine times square of a number would be [tex]9x^2[/tex] plus 5 as:

    [tex]9x^2+5[/tex]

    Therefore, our required expression would be [tex]9x^2+5[/tex].

  2. T = 42.08  °C

    Explanation:

    Using the expression,

    [tex]\ln \dfrac{k_{1}}{k_{2}} =-\dfrac{E_{a}}{R} \left (\dfrac{1}{T_1}-\dfrac{1}{T_2} \right )[/tex]

    Wherem  

    [tex]k_1\ is\ the\ rate\ constant\ at\ T_1[/tex]

    [tex]k_2\ is\ the\ rate\ constant\ at\ T_2[/tex]

    [tex]E_a[/tex] is the activation energy

    R is Gas constant having value = 8.314 J / K mol

    Thus, given that, [tex]E_a[/tex] = 45.6 kJ/mol = 45600 J/mol (As 1 kJ = 1000 J)

    [tex]k_2=2\times k_1[/tex]

    [tex]k_1=0.0160s^{-1}[/tex]

    [tex]T_1=30\ ^0C[/tex]

    The conversion of T( °C) to T(K) is shown below:

    T(K) = T( °C) + 273.15  

    So,  

    T = (30 + 273.15) K = 303.15 K  

    [tex]T_1=303.15\ K[/tex]

    So,

    [tex]\ln \dfrac{k_{1}}{2\times k_{1}} =-\dfrac{45600}{8.314} \left (\dfrac{1}{303.15}-\dfrac{1}{T_2} \right )[/tex]

    [tex]\ln \dfrac{1}{2} =-\dfrac{45600}{8.314} \left (\dfrac{1}{303.15}-\dfrac{1}{T_2} \right )[/tex]

    [tex]8.314\ln \left(2\right)=-45600\left(\frac{1}{303.15}-\frac{1}{T_2}\right)[/tex]

    [tex]8.314\ln \left(2\right)=-150.42058+\frac{45600}{T_2}[/tex]

    [tex]144.65775 =\frac{45600}{T_2}[/tex]

    [tex]T_2=\frac{45600}{144.65775}[/tex]

    [tex]T_2=315.23\ K[/tex]

    Conversion to °C as:

    T(K) = T( °C) + 273.15  

    So,  

    315.23 = T( °C) + 273.15

    T = 42.08  °C

  3. Question:

    Select expression that is mathematically equivalent to

    [tex]\frac{x}{y-z} + (a-b)*c[/tex]

    a) [tex]x/y - z + (a - b) * c[/tex]

    b) [tex]x/(y - z) + (a - b) * c[/tex]

    c) [tex]x/y - z + a - b * c[/tex]

    d) [tex]x/(y - z) + a - b * c[/tex]

    [tex]x/(y - z) + (a - b) * c[/tex]

    Step-by-step explanation:

    Given

    [tex]\frac{x}{y-z} + (a-b)*c[/tex]

    Required

    Determine its equivalent

    Start by writing y - z in bracket;

    [tex]\frac{x}{y-z} + (a-b)*c[/tex]

    becomes

    [tex]\frac{x}{(y-z)} + (a-b)*c[/tex]

    When - is used as divide, it is equivalent to /

    The given expression can then be rewritten as

    [tex]x/(y - z) + (a - b) * c[/tex]

    Hence;

    [tex]\frac{x}{y-z} + (a-b)*c[/tex] is equivalent to [tex]x/(y - z) + (a - b) * c[/tex]

  4. 10/60

    step-by-step explanation:

    if you divide 10 by 60 the answer is 0.166666 while if you divide or solve the other problems it equals 0.6

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