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UkoKoshka [18]
3 years ago
7

A rectangular garden originally measured 5 feet by 10 feet as shown below.a path was created by increasing each side of the orig

inal rectangle by x-feet on both sides.if the area of the path that rings the garden is 54 square feet,find the value of x.
Mathematics
1 answer:
kotegsom [21]3 years ago
3 0
The area is given by
 A = (5 + 2x) * (10 + 2x) - 50
 Rewriting we have:
 A = 50 + 10x + 20x + 4x ^ 2 -50
 Rewriting we have:
 A = 4x ^ 2 + 30x
 Substituting the value of the area we have:
 54 = 4x ^ 2 + 30x
 Rewriting:
 4x ^ 2 + 30x - 54 = 0
 We look for the roots:
 x1 = -9
 x2 = 3/2
 We take the positive root:
 x2 = 3/2
 Answer:
 
the value of x is:
 
x = 3/2
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ohaa [14]

The equation can be used to find the time in hours, \dfrac{t}{4}+\dfrac{t}{7}=1 and the time will be 2.5 hours. So the correct answer is option A.

<h3>What is an equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Layna can paint a 350-square-foot room in 4 hours.It takes Bebe 7 hours to paint the same room.

Let t be the total time taken by both to paint.They are completing 1 job so the equation will be :

\dfrac{t}{4}+\dfrac{t}{7}=1

Further solving it we get;

7 t + 4 t = 28

11t  =  28

t = 2.5 hours.

Therefore the equation can be used to find the time in hours, \dfrac{t}{4}+\dfrac{t}{7}=1 and the time will be 2.5 hours. So the correct answer is option A.

To know more about equations follow

brainly.com/question/2972832

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8 0
2 years ago
A+b : [(4+5i) + (1+5i)] . (1+i) =a+bi
r-ruslan [8.4K]
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3 0
3 years ago
Complete the square to find the minimum value of the expression 4x2 + 8x + 23.
Tcecarenko [31]
So you need to come up with a perfect square that works for the x coefficients.
like.. (2x + 2)^2
(2x+2)(2x+2) = 4x^2 + 8x + 4
Compare this to the equation given. Our perfect square has +4 instead of +23. The difference is: 23 - 4 = 19

I'm going to assume the given equation equals zero..

So, If we add subtract 19 from both sides of the equation we get the perfect square.

4x^2 + 8x + 23 - 19 = 0 - 19
4x^2 + 8x + 4 = - 19
complete the square and move 19 over..
(2x+2)^2 + 19 = 0
factor the 2 out becomes 2^2 = 4
ANSWER: 4(x+1)^2 + 19 = 0

for a short cut, the standard equation
ax^2 + bx + c = 0 becomes a(x - h)^2 + k = 0
Where "a, b, c" are the same and ..
h = -b/(2a)
k = c - b^2/(4a)

Vertex = (h, k)
this will be a minimum point when "a" is positive upward facing parabola and a maximum point when "a" is negative downward facing parabola.


3 0
3 years ago
Please can anyone help what is AC
Nesterboy [21]

The answer is C.

You need you use Pythagoras theorem 2 times to have 2 equations with the same sides i.e. for example a2 + b2 = 81 and a2 - b2 = 9.

You can do it as you have different triangles but with the same sides.

7 0
3 years ago
What is the solution of sqrt (x-4)+5=2
worty [1.4K]

Answer:

x = 13

Step-by-step explanation:

<em>sqrt (x-4) + 5 = 2</em>

<em>The equation is √(x+4) + 5 = 2</em>

√(x-4) = 2 - 5

√(x-4) = -3

x-4 = (-3)²

x-4 = 9

x = 9 + 4

x = 13

Therefore, the second option x = 13 is correct.

!!

7 0
3 years ago
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