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Snezhnost [94]
3 years ago
14

The length of a rectangle is 2 units more than the width. The area of the rectangle is 63 units. What is the length, in units, o

f the rectangle?
Mathematics
1 answer:
Keith_Richards [23]3 years ago
7 0

Answer:

Length = 9units

Width = 7units

Step-by-step explanation:

It is said that the length is 2units more than the width

Assume that the width is x, then the length will be 2 + x

ie

Width = x

Length = 2 + x

Area of the rectangle = 63units

Area of rectangle = l * b

l - length of the rectangle

b - width of the rectangle

A = l * b

63 = (2 + x) * x

63 = ( 2 + x) x

63 = 2x + x^2

Let's rearrange it

x^2 + 2x - 63 = 0

Let's find the factor of 63

A factor that can be multiplied to give -63 and that can be added to give +2

Let's use -7 and +9

x^2 - 7x + 9x - 63 = 0

Separate with brackets

( x^2 - 7x) + ( 9x - 63) = 0

x( x - 7) + 9(x - 7) = 0

( x + 9)(x - 7) = 0

( x + 9) = 0

( x - 7) = 0

x + 9 = 0

x = -9

x - 7 = 0

x = 7

Note: the length of a rectangle can not be negative

So therefore,

x = 7

Length = 2 + x

= 2 + 7

= 9units

Width = x

= 7units

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Lines a and b are perpendicular. Which statements below must be true? Select all that apply. The slopes of lines a and b are rec
Semenov [28]

Answer:

When the slopes of lines a and b are multiplied, the product is −1.

Line a and line b intersect to form four right angles.

Step-by-step explanation:

Given

Perpendicular lines a and b

Required

Select the true statements

Represent the slope of line a with m_1 and the slope of b with m_2.

The condition for perpendicularity is:

m_1 * m_2 = -1

Solving further:

m_1 = -\frac{1}{m_2}

To solve further, we need to analyze each of the given options

(a) This is not true because the slope of perpendicular lines are not reciprocal

(b) This is also not true because perpendicular lines do not necessarily have to intersect at their midpoints

(c) This is true because of the condition stated above: m_1 * m_2 = -1

(d) This is also true because perpendicular lines form right angles when they intersect

(e) This is not true because of the condition stated above: m_1 = -\frac{1}{m_2}

(f) This is not true because of the condition stated above: m_1 = -\frac{1}{m_2}

5 0
3 years ago
Find the odds of an answer if the probability of the event is given to be 3/8
yKpoI14uk [10]

The Probability of winning is 5/8.

7 0
3 years ago
3-(x-3)=25 solve the equation
kherson [118]

Answer:

x= -19

Step-by-step explanation:

3-(x-3)=25

Distributive property to cancel out the paranthesis

3-x+3=25

Add the number

6-x=25

Subtract 6 on both sides

-x=19

Divide by -1 on both sides so the x to eliminate the negative sign

x=-19

7 0
3 years ago
Which operation should be performed first according to the order of operations? 3(4)^2/4+16-9
skad [1K]
PEMDAS
Parenthesis
Exponent
Multiplication
Division
Addition
Subtraction

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5 0
3 years ago
100 points!!!
Bogdan [553]

Answer:

(1, 5)

Step-by-step explanation:

The solution to the system of equations is the point of intersection of the two lines.  From inspection of the graph, the point of intersection is at (1, 5).

<u>Proof</u>

The solution to a system of equations is the point at which the two lines meet.  

⇒ g(x) = f(x)

⇒ 3x + 2 = |x - 4| + 2

⇒ 3x = |x - 4|

⇒ 3x = x - 4   and   3x = -(x - 4)

⇒ 3x = x - 4

⇒ 2x = -4

⇒ x = -2

Inputting x = -2 into the 2 equations:

⇒ g(-2) = 3 · -2 + 2 = -4

⇒ f(-2) = |-2 - 4| + 2 = 8

Therefore, as the y-values are different, x = -2 is NOT a solution

⇒ 3x = -(x - 4)

⇒ 3x = 4 - x

⇒ 4x = 4

⇒ x = 1

Inputting x = 1 into the 2 equations:

⇒ g(1) = 3 · 1 + 2 = 5

⇒ f(1) = |1 - 4| + 2 = 5

Therefore, as the y-values are the same, x = 1  IS a solution

and the solution is (1, 5)

8 0
2 years ago
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