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alina1380 [7]
3 years ago
5

The width of a rectangle is the length minus 3 units. The area of the rectangle is 54 units. What is the width, in units, of a r

ectangle
Mathematics
1 answer:
saul85 [17]3 years ago
4 0

Width of the rectangle is 9 units

Step-by-step explanation:

  • Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units

Area of the rectangle = length × width

54 = x (x - 3)

54 = x² - 3x

x² - 3x - 54 = 0

x² + 6x - 9x - 54 = 0 (Using Product Sum rule to factorize)

x(x + 6) - 9(x + 6) = 0

(x + 6)(x - 9) = 0

x = -6, 9 (negative value is neglected)

x = 9 units

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9.

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Count the number of digits after the first digit,

This is 9.

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6 0
3 years ago
Can you guys help me with this question? PLEASEEEEE
Andreyy89

Answer:

Walker County (0,4) (1, 6) (5, 14) (4,12)

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6 0
3 years ago
A (0, 2) and B (6,6) are points on the straight line ABCD.
elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points (x_1,y_1) and (x_2,y_2), the distance is denoted by: \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}. Let's find the distance between A and B:

d = \sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = \sqrt{(6-a)^2+(6-b)^2}

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0
3 years ago
Read 2 more answers
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