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viva [34]
3 years ago
12

The length of a rectangle is 3 centimeters less than twice the width. If the perimeter of the rectangle is 24 centimeters, find

its dimensions.
Mathematics
1 answer:
yarga [219]3 years ago
3 0

Answer:

Width = 5 cm

Length = 7 cm

Step-by-step explanation:

Width = w

Length = 2w - 3

Perimeter = 24 cm

2* (length + width ) = 24

2*(2w-3 +w) = 24

2*(3w -3) = 24

3w - 3 = 24/2

3w - 3 = 12

3w = 12+ 3

3w = 15

w = 15/3

w = 5cm

Length = 2w - 3 = 2*5 - 3 = 10-3 = 7 cm

length = 7 cm

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What is the quotient
mario62 [17]

Answer:

The quotient is 3x - 11 + 60/(x + 5) ⇒ 2nd answer

Step-by-step explanation:

* We will use the long division to solve the problem

- The dividend is 3x² + 4x + 5

- The divisor is x + 5

- The quotient is the answer of the division

- If the divisor not a factor of a dividend, the quotient has

  a remainder

* Lets solve the problem

- At first divide the first term in the dividend by the first term in

 the divisor

∵ 3x² ÷ x = 3x

- Multiply the divisor by 3x

∴ 3x (x + 5) = 3x² + 15x

-Subtract this expression from the dividend

∴ 3x² + 4x + 5 - (3x² + 15x) = 3x² + 4x + 5 - 3x² - 15x = -11x + 5

- Divide the first term -11x in the new dividend by the first

 term x in the divisor

∴ -11x ÷ x = -11

- Multiply the divisor by -11

∴ -11(x + 5) = -11x - 55

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5 0
3 years ago
find the equation of a circle which passes through the point (2,-2) and (3,4) and whose centre lies on the line x+y=2
Nadusha1986 [10]

Answer:

Equation of the circle

(x - 0.7)² + (y - 1.3)² = 12.58

Step-by-step explanation:

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle.

a) We are told in the question that the equation of the circle passes through point(2, -2)

Hence,

Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(2 - a)² +(-2 - b)² = r²

Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

4 - 2a - 2a +a² +4 +2b +2b +b² = r²

4 - 4a + a² + 4 + 4b + b² = r²

a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

9 - 3a - 3a +a² +16 -4b -4b +b² = r²

9 -6a + a² + 16 -8b + b² = r²

a² + b² -6a -8b + 9 + 16 = r²

a² + b² -6a -8b + 25 = r²..........Equation 2

The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0

2a + 12b -17 = 0

2a + 12b = 17...........Equation 3

Step 2

We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

Therefore, we have

a + b = 2

a = 2 - b

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Substituting 2 - b for a in

2(2 - b) + 12b = 17

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b = 13/10

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Substituting 1.3 for b in

a + b = 2

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a = 2 - 1.3

a = 0.7

hence, a = 0.7, b = 1.3

Step 3

We have to find the value of r using points (2, -2)

(x - a)² + (y - b)² = r²

Where x = 2 and y = -2

(-2 - 0.7)² + (-2 - 1.3)² = r²

(-2.7)² + (-3.3)² = r²

1.69 + 10.89 = r²

r² = 12.58

r = √12.58 = 3.55

Step 4

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle

a = 0.7

b = 1.3

r² = 12.58

Equation of the circle =

(x - 0.7)² + (y - 1.3)² = 12.58

7 0
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Answer:

A

Step-by-step explanation:

This notation says that x+x+x+x+37=69

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