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kompoz [17]
1 year ago
11

Write an equation for each sentence.

Mathematics
1 answer:
almond37 [142]1 year ago
3 0

52 21 76 7673838877oehs

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Find the missing variables pythagorean theorem
worty [1.4K]

Answer:

y = 12     x = 12√2     z  = 12√3

Step-by-step explanation:

The 45° triangle will also have a height of y so....

    y² + y² = x²          2y²  = x²     y² = x²/2       y = √(x²/2)

The 30°  triangle

    y² + z² = 24²                          y² = 24² - z²          y = √(24² - z²)

                               

sin 30 = y/24          1/2 = y/24      y = 12    

          y² = x²/2

         12² = x²/2²

    2(144)  = x²         x = √(288)       x = 12√2  

      y² + z² = 24²

           z² = 24² - y²

           z² = 24² - 12²

           z² = 576 - 144

            z² = 432      

                =  √(16·9·3)

            z  =  4·3√3

            z  = 12√3

     y² + z² = 24²

    12² + (12√3)² = 24²

    144 + 144·3    =   576

     2y²  = x²

     2(12)²  = x²

      288  =  (12√2)  = 144·2  = 288

5 0
3 years ago
A person standing at the edge of a cliff throws a rock upward from a height of 180ft above ground level with an initial velocity
taurus [48]

Answer: 8.73 ft/s

Step-by-step explanation:

We have the following equation that models the motion of the rock:

h(t)=-16t^{2}+64t+180

Where h(t) is the height of the rock at a time t.

Now, if  h(t)=48 ft we can find t and then the velocity of the rock at that height:

48=-16t^{2}+64t+180

Rearranging the equation:

-16t^{2}+64t+132=0

Multiplying the equation by -1:

16t^{2}-64t-132=0

Solving with the quadratic formula t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}  , where a=16, b=-64, c=-132 .

t=\frac{-(-64)\pm\sqrt{(-64)^{2}-4(16)(-132)}}{2(16)}

Choosing the positive result of the equation:

t=5.5 s  

Since velocity V is defined as the traveled distance h(t) in a given time t, we have:

V=\frac{h(t)}{t}

V=\frac{48 ft}{5.5 s}

V=8.727 ft/s \approx 8.73 ft/s This is the velocity of the rock at the height of 48 feet

7 0
3 years ago
What is the domain of the function represented by this graph? the graph of a quadratic function y = x^2 – 4 with a minimum value
Kobotan [32]

Answer:

A

Step-by-step explanation:

In this function, the domain, or the x value, has no limits. You can substitue any value of x into (x^2-4) and any result is valid.

I hope this helped!

4 0
3 years ago
Read 2 more answers
Just number 9 not the other one please help
Paladinen [302]

Answer:

I do believe the answer is C

Step-by-step explanation:

.004 / .0004 =

4 0
3 years ago
Read 2 more answers
What is the simplified form of expression<br> -4xy/3x
DiKsa [7]

Answer:

(-4/3)y

Step-by-step explanation:

The x cancels out, leaving:

-4y/3 or (-4/3)y

7 0
3 years ago
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