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3 years ago

The length of a rectangle is twice the width. The perimeter is 25. The system to help find the length and width is:

Mathematics

2 answers:

svet-max [94.6K]3 years ago

8 0

9514 1404 393

Answer:

(L, W) ≈ (8.33, 4.17)

Step-by-step explanation:

Substituting for L, we have ...

2(2W) +2W = 25

6W = 25

W = 25/6 ≈ 4.17

L = 25/3 ≈ 8.33

The rounded "exact" solution is ...

(L, W) = (8.33, 4.17)

user100 [1]3 years ago

5 0

Let the width be x
Since the question mentions the length is twice the width,
let the length be 2x
The total perimeter given is 25cm and as we know, perimeter for a rectangle :
=> P = 2(Length + width)
So,

25cm = 2(2x + x)
25 = 4x + 2x
25 = 6x
25/6 = x
4.166666667 = x

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Solve the quadratic equation by completing the square. 6x2 + 4x - 5 = 0

Nikitich [7]

Answer:

$x_{1}=-\frac{2+\sqrt{34}}{6}$

$x_{2}=-\frac{2-\sqrt{34}}{6}$

Step-by-step explanation:

Quadratic Equation given:

$6x^2 + 4x - 5 = 0$

Start dividing both sides by 6.

$\frac{6}{6} x^2 +\frac{4}{6} x - \frac{5}{6} = \frac{0}{6}$

$x^2 +\frac{2}{3} x - \frac{5}{6} = 0$

$x^2 +\frac{2}{3} x = \frac{5}{6}$

Once, $\left( \frac{2}{3} \cdot \frac{1}{2} \right)^2=\frac{1}{9}$

$x^2 +\frac{2}{3} x+\frac{1}{9} = \frac{5}{6}+\frac{1}{9}$

$\left(x+\frac{1}{3} \right)^2 = \frac{17}{18}}$

$x+\frac{1}{3} =\pm\sqrt{\frac{17}{18}} }$

Solving $\sqrt{\frac{17}{18}}$

$\sqrt{\frac{17(18)}{18(18)}}= \sqrt{\frac{306}{324}}=\frac{3\sqrt{34} }{18} =\frac{\sqrt{34} }{6}$

Then,

$x+\frac{1}{3} =\pm\frac{\sqrt{34} }{6}$

$x =-\frac{1}{3} \pm\frac{\sqrt{34} }{6}$

$x_{1}=-\frac{2+\sqrt{34}}{6}$

$x_{2}=-\frac{2-\sqrt{34}}{6}$

6 0

3 years ago

On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 1), point B is at (3, 2), and points C is at (negativ

oksian1 [2.3K]

The corresponding height of the triangle is 1.6 units

The formula for calculating the area of a triangle is expressed as:

$A=\frac{1}{2} bh$

b is the base of the triangle

h is the height of the triangle

Given the coordinates of the base BC of the triangle given as B(3, 2), and C(-1,-1). Using the distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\BC= \sqrt{(-1-2)^2+(-1-3)^2}\\BC=\sqrt{3^2+4^2}\\BC=\sqrt{25}\\BC=5units$

The area of the triangle passing through the coordinate points A(-1, 1), B(3,2), and C(-1, -1) is expressed as:

$A=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]\\$

Substituting the coordinate points:

$A=\frac{1}{2}[(-1)(2-(-1))+3(-1-1)+-1(1-2)]\\A=\frac{1}{2}[(-1)(3)+3(-2)+-1(-1)]\\A=\frac{1}{2}[-3-6+1]\\A=\frac{1}{2} (-8)\\|A| =4 units^2$

Recall that:

$A = 0.5bh\\h=\frac{A}{0.5b}\\h=\frac{4}{0.5(5)}\\h=\frac{4}{2.5}\\h= 1.6 units$

Hence the corresponding height of the triangle is 1.6 units

Learn more on area of triangles here: brainly.com/question/17335144

8 0

2 years ago

Let A = { all odd numbers) and B = {1,3,5,7). Is B a subset of A?

Alchen [17]

Answer:

Step-by-step explanation:

Yes

{1,3,5,7} contains the first 4 odd numbers.

{1,2,3,5,7} would not be a subset.

4 0

3 years ago

Read 2 more answers

Graph linear system and estimate the solution y=5x + 2 y=3x

NeTakaya

Y = 5x + 2
y = 3x

5x + 2 = 3x
- 5x - 5x
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   -2 - 2
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y = 3(-1)
y = -3
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3 years ago

The dual bar chart shows the hair colour of boys and girls in a year group. How many students are in the year group?

notka56 [123]

Answer:

102

Step-by-step explanation:

24+12+5+17+6+19+4+15=102

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3 years ago