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vitfil [10]
2 years ago
11

Find the unknown side length. Write your answer in simplest radical form.

Mathematics
1 answer:
Eva8 [605]2 years ago
5 0

Answer: 1. x= 20 units,   2. x= 5\sqrt{3} units    3. x= 4\sqrt{2} units.

Step-by-step explanation:

In a right triangle,

Hypotenuse^2= Perpendicular^2+Base^2  (Pythagoras theorem)

1. Hypotenuse = x , Base = 16, Perpendicular = 12

\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=\sqrt{400}=20

2. Hypotenuse = 14 , Base = 11, Perpendicular = x

\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}

3.  Hypotenuse = 9 , Base = x, Perpendicular =7

\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}=\sqrt{16\times2}\\\\\Rightarrow\ x=4\sqrt{2}

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3 years ago
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PLEASE HELP ME!!!!!!!!!!
nikklg [1K]

Answer:

-7/10

Step-by-step explanation:

To find the slope of a line, you need to find the \frac{rise}{run} between two points. I will be using the points (-3, 5) and (7, -2).

\frac{rise}{run} = \frac{-2-5}{7-(-3)}

     = \frac{-7}{10}

     = -7/10

8 0
2 years ago
76 POINTS IF YOU CAN ANSWER THIS!!!The amount of water an electric dishwasher uses to wash dishes varies directly with the numbe
Vladimir79 [104]

Answer:

80

Step-by-step explanation:

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5 0
3 years ago
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Please help me with these two questions, 10 points for each so in total 20!!
saul85 [17]

Answer:

\large\boxed{Q2.\qquad C.\ -2x+y=-2}\\\boxed{Q4.\qquad C.\ y=3x+12}

Step-by-step explanation:

Q2:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

m - slope

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (4, 6) and (6, 10). Substitute:

m=\dfrac{10-6}{6-4}=\dfrac{4}{2}=2

y-6=2(x-4)           <em>use distributive property</em>

y-6=2x-8      <em>add 6 to both sides</em>

y=2x-2          <em>subteact 2 from both sides</em>

-2x+y=-2

Q4:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

Put the slope m = 3 and the coordinateso f the point (-2, 6) to the point-slope form of an equation of a line:

y-6=3(x-(-2))

y-6=3(x+2)         <em>use distributive property</em>

y-6=3x+6     <em>add 6 to both sides</em>

y=3x+12

4 0
2 years ago
What is the value of x, when -9(x-5)=x+22 1/2​
Kipish [7]

Answer:

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Step-by-step explanation:

 -9(x - 5) = x + 22 1/2

Distribute the nine and then add 9x to both sides

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+ 9x        + 9x

Then try to get x alone

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   \frac{22.5}{10} = \frac{10x}{10}

   2.25 = x

4 0
3 years ago
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