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Marysya12 [62]
3 years ago
8

A^2-a+12=0 I need the roots

Mathematics
1 answer:
kumpel [21]3 years ago
8 0

Answer:

a = 1/2 (1 ±sqrt(47))

Step-by-step explanation:

a^2-a+12=0

We will complete the square

Subtract 12 from each side

a^2-a+12-12=0-12

a^2-a=-12

The coefficient of a = -1

-Divide by 2 and then square it

(-1/2) ^2 = 1/4

Add it to each side

a^2 -a +1/4=-12 +1/4

(a-1/2)^2 = -11 3/4

(a-1/2)^2= -47/4

Take the square root of each side

sqrt((a-1/2)^2) =sqrt(-47/4)

a-1/2 = ±i sqrt(1/4) sqrt(47)

a-1/2= ±i/2 sqrt(47)

Add 1/2 to each side

a-1/2+1/2 = 1/2± i/2 sqrt(47)

a =  1/2± i/2 sqrt(47)

a = 1/2 (1 ±sqrt(47))

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The birth rate in an area is increasing 6% per annum. If there 20,000 children born in this area 2009 how many will be in 2018?
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Answer:

Step-by-step explanation:

Compound increase

20,000 x 1.06 to power of 9 = 33789 <u><em>OR</em></u>  33790

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               increase by 6%    9 years

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3 years ago
The measures of two angles of a triangle are 23 and 67. Is the triangle acute, right, or obtuse. Use geometric terms in explanat
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3 years ago
You buy 1.75 pounds of apples and 2.05 pounds of oranges. Apples and oranges sell for the same price per pound. The total​ cost,
dlinn [17]

Answer:

1.75c+2.05c=4.18\\\\Per\ pound\ cost=c=\$1.1

Step-by-step explanation:

Cost\ of\ per\ pound\ apple=Cost\ of\ per\ pound\ oranger=c\\\\

Cost of Apples:

Amount\ of\ apples=1.75\ pounds\\\\Cost\ of\ apples=Amount\times per\ pound\ cost\\\\Cost\ of\ apples=1.75\times c\\\\Cost\ of\ apples=1.75c

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Amount\ of\ oranges=2.05\ pounds\\\\Cost\ of\ oranges=Amount\times per\ pound\ cost\\\\Cost\ of\ oranges=2.05\times c\\\\Cost\ of\ oranges=2.05c

Total cost:

Total\ cost\ of\ fruits=cost\ of\ apple+cost\ of\ oranges\\\\Total\ cost\ of\ fruits=1.75c+2.05c\\\\After\ coupon\ cost=\$ 3.43\\\\ Original\ cost=After\ coupon\ cost+coupon\ amount\\\\ Original\ cost=3.43+0.75=4.18

1.75c+2.05c=4.18\\\\3.8c=4.18\\\\c=\frac{4.18}{3.8}\\\\c=1.1\\\\Per\ pound\ cost\ of\ fruits=\$1.1

4 0
3 years ago
8
STatiana [176]

Answer:

(e^3 / e^2n)

Step-by-step explanation:

isn't this the same question

5 0
3 years ago
What the correct answer do not want the wrong answer please
Crank

Answer:

388.5yd²

Step-by-step explanation:

We have Triangle TUV

In the question, we are given already

Angle U = 32°

Angle T = 38°

Angle V = ???

Side t = 31yd

Side u = ?

Side v = ?

Area of the triangle= ?

Step 1

We find the third angle = Angle V

Sum of angles in a triangle = 180°

Third angle = Angle V = 180° - (32 + 38)°

= 180° - 70°

Angle V = 110°

Step 2

Find the sides u and v

We find these sides using the sine rule

Sine rule or Rule of Sines =

a/ sin A = b/ Sin B

Hence for triangle TUV

t/ sin T = u/ sin U = v/ sin V

We have the following values

Angle T = 38°

Angle U = 32°

Angle V = 110°

We are given side t = 31y

Finding side u

u/ sin U= t/ sin T

u/sin 32 = 31/sin 38

Cross Multiply

sin 32 × 31 = u × sin 38

u = sin 32 × 31/sin 38

u = 26.68268yd

u = 26.68yd

Finding side x

v / sin V= t/ sin T

v/ sin 110 = 31/sin 38

Cross Multiply

sin 110 × 31 = v × sin 38

v = sin 110 × 31/sin 38

v = 47.31573yd

v = 47.32yd

To find the area of triangle TUV

We use heron formula

= √s(s - t) (s - u) (s - v)

Where S = t + u + v/ 2

s = (31 + 26.68 + 47.32)/2

s = 52.5

Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)

Area of the triangle = √150967.6032

Area of the triangle = 388.5454973359yd²

Approximately to the nearest tenth =388.5yd²

5 0
3 years ago
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