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MissTica
1 year ago
8

Solve by completing the square:

Mathematics
1 answer:
dlinn [17]1 year ago
7 0

Answer:

d. x = -5 or 1

Step-by-step explanation:

x² + 4x - 5 = 0

completing the square means that we find an expression in the form

(x + a)(x+a) = (x+a)²

or

(x - a)(x - a) = (x - a)²

the fact that the middle term is +4x tells us we are looking for

(x + a)²

so,

(x + a)² = x² + 2ax + a²

now let's compare this with what we have :

x² = x²

2ax = 4x

2a = 4

a = 2

that means the full square is

(x + 2)² = x² + 4x + 4

but we have -5 in our original equation.

what do we need to do to change this to +4 ?

we have to add 9.

and to keep the equation true, we need to do this on both sides :

x² + 4x -5 + 9 = 0 + 9

x² + 4x + 4 = 9

(x + 2)² = 9

x + 2 = ±3

x + 2 = +3

x = 1

x + 2 = -3

x = -5

and that gives us answer option d. -5 or 1

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2 1/2 yds = 2.5 x 36 = 90 inches...what she started with

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90 - x = 32 
90 - 32 = x
x = 58 inches....so she used 58 inches


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5 0
3 years ago
On Monday Harold picked up four donuts and two large coffees for the office staff. He paid 4.08. On Tuesday Melinda picked up tw
Mandarinka [93]
One way to look at this is to make 2 equations and treat it as a set of equations. We will make the cost of a donut equal to x, and the cost of a coffee equal to y.

Harold's order:
4x + 2y = 4.08

Melinda's order:
2x + 3y = 3.92

To combine these equations, we need to cancel out either x or y:
4x + 2y = 4.08
<span>2x + 3y = 3.92
</span>
4x + 2y = 4.08
<span>4x + 6y = 7.84
</span>
4x + 2y = 4.08
<span>-4x - 6y = -7.84
</span>
We can now combine these equations:
4x + 2y = 4.08
<span>-4x - 6y = -7.84
</span>
-4y = -3.76

y = 0.94

Therefore the cost of a large coffee is $0.94. We can plug this into either original equation to find the cost of a donut.
<span>4x + 2y = 4.08
</span>4x + 2(0.94) = 4.08
4x + 1.88 = 4.08
4x = 2.20
x = 0.55

The cost of a donut is $0.55, and the cost of a large coffee is $0.94.
8 0
3 years ago
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