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marin [14]
3 years ago
12

the legs of a right triangle are 4 units and 7 units. What is the length of the hypotenuse? Select one: a. square root 33 units

b. square root 65 units c. 33 units d. 65 units
Mathematics
2 answers:
Mrac [35]3 years ago
4 0

\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{4^2+7^2}\implies c=\sqrt{65}

Ilya [14]3 years ago
4 0

The answer is

b. square root 65 units

because those were the only choices but after you square root the answer will be 4225

but as of now and the choices we have its

b. square root 65 units

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So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function. 

The first batch of problems gave you the equation f(x) = \frac{x}{2} + 3. Now, plug in the numbers given for s and solve.

1. f(5) = <span>\frac{x}{2} + 3   Plug in 5 for x
</span>         = \frac{5}{2} + 3   Make three into a fraction over 2
         = \frac{5}{2} + <span>\frac{6}{2}   Add
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For the next set, you have g(x) = x</span>² + 1.

3. Let's split this up. Solve the first equation, then the second, and then put         the answers together to solve it.

g(4) = x² + 1   Plug in 4 for x
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       = 16 + 1   Add
       = 17

g(3) = x² + 1   Plug in 3 for x
       = 3² + 1   Square
       = 9 + 1   Add
       = 10

Now, put the two together.

g(4) + g(3) =    Substitute in the answers you just got.
      17 + 10 =    Add
                  = 27         

4. g(-1) = x² + 1      Substitute in -1 for x
            = (-1)² + 1   Square
            = 1 + 1        Add
            = 2

5. g(-6) = x² + 1       Plug in -6 for x
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For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.

6. h(-6) = x² + 7       Plug in -6 for x
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             = 36 + 7      Add
             = 43

k(4) = 4x - 5     Plug in 4 for x
       = 4(4) - 5   Multiply
       = 16 - 5      Subtract
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Put the two answers into the final equation.

h(-6) + k(4) =    Substitute in the answers you got
       43 + 11 =    Add
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7. k(10) = 4x - 5       Plug in 10 for x
            = 4(10) - 5   Multiply
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h(2) = x² + 7   Plug in 2 for x
       = 2² + 7   Square
       = 4 + 7     Add
       = 11

Now, put those into the equation.

k(10) - h(2) =    Plug in the answers you got
       35 - 11 =    Subtract
                  = 24

8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.

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    x² + 7 + 4x - 5 =   Combine like terms (7 and -5)
         x² + 2 + 4x =    Reorder so the variables come first
                            = x² + 4x + 2

  
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Answer:

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