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Dima020 [189]
3 years ago
8

Solve x2 + 12x + 6 = 0 using the completing-the-square method.

Mathematics
1 answer:
ohaa [14]3 years ago
8 0
X^2+12x+6=0  subtract 6 from both sides...

x^2+12x=-6  halve linear coefficient, square it, and add it to both sides...

x^2+12x+36=30  now the left side is a perfect square...

(x+6)^2=30  take square root of both sides...

x+6=30^(1/2)  subtract 6 from both sides...

x=-6-30^(1/2) and -6+30^(1/2)
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In rectangle QRST, QS = x2 + 6x, and RT = 8x + 3. Find the length of QS.
valentina_108 [34]

The length of QS is 27 units.

<u>Step-by-step explanation:</u>

In the given rectangle QRST QS and RT are the diagonals. In a triangle, the opposite sides are equal and parallel. This implies that the diagonals of a rectangle are equal.

QS=RT \ QS=x^2+6x

RT=8x+3

x^2+6x=8x+3

x^2+6x-8x-3=0

x^2-2x-3=0

We have obtained a quadratic equation here and solving this gives the possible values of QS.This can be solved using quadratic formula

x=(-b\pm \sqrt{(b^2-4ac))}/2a

The quadratic equation is of the form ax^2+bxl+c=0  

here a=1 b=-2 c=-3  

x=(-b\pm \sqrt{(b^2-4ac))}/2a

x=x=(2 \pm \sqrt{ (-2^2-4 \times 1 \times -3))}/(2 \times 1)

x=(2 \pm \sqrt{(4+12))} /2 or  

x=(2 \pm \sqrt{16)}/2 =(2\pm 4)/2 \ \ \ \ x=(2+4)/2=3 \ \ \ \ or  \ \ \ x=(2-4)/2=-1

putting x=3 QS=x^2+6x

=3^2+6 \times 3=9+18=27

putting x=-1

QS=(-1)^2+6 \times -1=1-6=-5

Since a length can have only positive values QS=27 units.

5 0
3 years ago
Find the missing numbers. What's the rule?
damaskus [11]
The answers are 200 and 45720 the rule is for every 1 cm it is 10 mm so basicaly if you have 10cm it would be 100 mm you just need to times your cm number by 10
5 0
3 years ago
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Mary spent $4 more than 1/8 of her original amount of money on a bag. She then
Tanzania [10]

Answer:

464 $

Step-by-step explanation:

8 0
3 years ago
A)x 1/9
STALIN [3.7K]

Answer:

Answer should be x^9

Step-by-step explanation:

This equation looks really complicted, but it's actually much easier when you break it down! First, your going to multiply the fraction 3/2 by 6 - since one is a fraction, youre going to find the GCF, or Greatest Common Factor, and reduce it. The GCF in this equation is 2, so we eliminate the two from the fraction (making it just 3) and divide 6 by 2 (getting 3). Thus, we are left with (x^3)^3 -> 3 x 3 = 9. So we are left with x^9. I hope this helps!

5 0
3 years ago
What is the exact volume of the cylinder enter your answers in the term of pie in the Box 5cm 15cm​
olga_2 [115]

Answer:

Valume of cylinder : πr² × h = π × 5² × 15 = 375π ≈ 1177.5 cm³

8 0
3 years ago
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