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2 years ago

Solve the equation Square root of x minus 5+ 7 = 11 for the variable. Show each step of your solution process. (10 points)

Mathematics

1 answer:

Murrr4er [49]2 years ago

5 0

$\sqrt{x - 5} + 7 = 11$

$(\sqrt{x-5}) ^{2} = (4)^{2}$

|x - 5| = 16

x - 5 = +/- 16

x - 5 = 16 or x - 5 = -16

+5 +5 +5 +5

x = 21 or x = -11

Answer: x = {21, -11}

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1 year ago

Find the perimeter of Triangle ABC with the verticies A(-5,5) B(3,-5) and C(-5,1

finlep [7]

Hello!

Let's calculate a distance between two points using the Pythagorean theorem:

 $d ^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2$

Data:

$x_B = 3 

x_A = -5 

y_B = -5 

y_A = 5 

d_ {AB} =?$

Solving: distance from A to B

$d^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2 

d^ 2_ {AB} = (3 - (-5)) ^ 2 + (-5 - 5) ^ 2 

d^ 2_ {AB} = (8) ^ 2 + (-10) ^ 2 

d^ 2_ {AB} = 64 + 100 

d^ 2_ {AB} = 164 

d_{AB} = \sqrt {164} 

d_{AB} = \sqrt {2 ^ 2 * 41} 

\boxed {d_ {AB} = 2 \sqrt {41}}$

Solving:

distance from A to C

$d ^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2$

Data:

$x_C = -5
 
x_A = -5
 
y_C = 1 

y_A = 5 

d_ {AC} =?$

$d^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2 

d^ 2_ {AC} = (-5 - (-5)) ^ 2 + (1 - 5) ^ 2 

d^ 2_ {AC} = (0) ^ 2 + (-4) ^ 2 

d^ 2_ {AC} = 0 + 16 

d^ 2_ {AC} = 16 

d_ {AC} = \sqrt {16} 

\boxed {d_ {AC} = 4}
$

Solving:

distance from B to C

$d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2$

Data:

$x_C = -5 

x_B = 3 

y_C = 1 

y_B = -5 

d_ {BC} =?$

$d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2
 
d^ 2_ {BC} = (-5 - 3) ^ 2 + (1 - (-5)) ^ 2

d^ 2_ {BC} = (-8) ^ 2 + (6) ^ 2 

d^ 2_ {BC} = 64 + 36

d^ 2_ {BC} = 100 

d_ {BC} = \sqrt {100}

\boxed {d_ {BC} = 10}$

Now let's calculate the perimeter of the triangle ABC, knowing that the perimeter is the sum of the sides, then:

$p = d_ {AB} + d_ {AC} + d_ {BC} 

$

$p = 2\sqrt {41} + 4 + 10$

$
\boxed {\boxed {p = 14 + 2 \sqrt {41}}} \end {array}} \qquad \quad \checkmark$

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Answer:

Step-by-step explanation:

L = Length

W = Width

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2(2L) + 2L = 174

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2 years ago

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Answer:

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Step-by-step explanation:

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