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Helga [31]
3 years ago
10

A square has side lengths of 2x inches. An equilateral triangle has side lengths of (2x+1/3) inches. If the square and the trian

gle have the same perimeter, what is the value of x?
Mathematics
2 answers:
Arte-miy333 [17]3 years ago
7 0
Size square × 4 = size triangle × 3
(2X × 4 ) = [(2X +1/3) × 3]

8X = [(6X+1)/3×3]
8X = 6X+1
8X -6X = 1
2X = 1
X= 1/2
raketka [301]3 years ago
4 0

Answer : The value of 'x' is \frac{1}{2}

Step-by-step explanation :

As we know that,

The perimeter of square = 4a

The perimeter of equilateral triangle = 3s

('a' is the side square and 's' is the side of equilateral triangle)

Given:

Side of square = a = 2x

Side of equilateral triangle = s = (2x+1/3)

As per question, the square and the triangle have the same perimeter. That means,

Perimeter of square = Perimeter of equilateral triangle

4a = 3s

Now put the value of 'a' and 's', we get the value of 'x'.

4\times (2x)=3\times (2x+\frac{1}{3})

8x=6x+1

8x-6x=1

2x=1

x=\frac{1}{2}

Therefore, the value of 'x' is \frac{1}{2}

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Given f ( x ) = 3 x 2 + k x − 13 f(x)=3x 2 +kx−13, and the remainder when f ( x ) f(x) is divided by x + 4 x+4 is 15 15, then wh
Varvara68 [4.7K]

Answer:

k=5

Step-by-step explanation:

We are provided with function, f ( x ) = 3 x^{2} + kx − 13

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Here,

since f(x) is divided by x+4 so we can put :

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Putting this in f(x) -----> f(-4)

f(x) = f(-4) = 3 (-4^{2}) + k(-4) − 13

f(-4) = 3(16) - 4k - 13

f (-4) = 48 - 4k - 13                ------------------------------------------Equation 1

Since, when f(x) is divided by x+4 , the remainder is 15 so we can say,

f(-4) = 15

putting in equation 1

f (-4) = 15 = 48 - 4k - 13

48 -4k - 13 = 15

35 - 4k = 15                      

35 - 15 = 4k                         (Moving - 4k on right hand side and 15 on the left)

or 20 = 4k

or 4k = 20

k = \frac{20}{4}

<h2>k = 5</h2>

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