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vovangra [49]
3 years ago
12

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

Mathematics
1 answer:
Rzqust [24]3 years ago
5 0

Answer:

a = 6 or 9

Step-by-step explanation:

The "a", "b", and "c" of the quadratic formula are the coefficients of a², a, and the constant term in the given equation:

... a = 2, b = -30, c = 108

Then the quadratic formula tells you the solutions are ...

... (-b ± √(b² -4ac))/(2a)

... = (-(-30) ± √((-30)² -4(2)(108)))/(2(2))

... = (30 ± √(900 -864))/4

... = (30 ± √36)/4

... = (30 ± 6)/4 = {24, 36}/4

... = {6, 9}

_____

The <em>a</em> variable should not be confused with the "a" that is used to name the coefficient of the square of the variable in the quadratic formula. If it is too confusing, rewrite one or the other. For example, you could write ...

... The solution to pa² +qa +r = 0 is ... a = (-q ± √(q²-4pr))/(2p)

where p=2, q=-30, r=108 in the given equation.

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If f(x) = 3x2 – 4 and g(x) = 2x - 6, what is g(f(2))?
saveliy_v [14]

Answer:

10

Step-by-step explanation:

find out f(2)

f(2)= (3×2×2) - 4= 8

then g(8) = 16 - 6= 10

4 0
3 years ago
10. There are nine golf balls numbered from 1 to 9 in a bag. Three balls are randomly selected without replacement to form a 3-d
lbvjy [14]

Answer:

a) 504

b) 56

c) 0.111

Step-by-step explanation:

Data provided in the question:

There are nine golf balls numbered from 1 to 9 in a bag

Three balls are randomly selected without replacement

a) 3-digit numbers that can be formed

= ^nP_r

n = 9

r = 3

= ⁹P₃

= \frac{9!}{9!-3!}

= 9 × 8 × 7

= 504

b)  3-digit numbers start with the digit 1

=  _ _ _

in the above 3 blanks first digit is fixed i.e 1

we and we have 8 choices left for the last 2 digits

Thus,

n = 8

r = 2

Therefore,

= 1 × ⁸P₂

= 1 × \frac{8!}{8!-2!}

= 1 × 8 × 7

= 56

c) Probability that the 3-digit number formed is less than 200

Now,

The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)

and total 3-digit numbers that can be formed is part a)

therefore,

Probability that the 3-digit number formed is less than 200

= 56 ÷ 504

= 0.111

5 0
3 years ago
Work out the value of 10^6 it is uuuuurrrrrrrrgggaaaaaaannnntttttt.
mojhsa [17]

Answer:

1000000

Step-by-step explanation:

10x10x10x10x10x10=1000000

3 0
3 years ago
Read 2 more answers
How do you find fh if ️fgh ~ ️kjh​
Lostsunrise [7]
What is that ? are you joking ?
5 0
2 years ago
If √2 = 1.414 then the value of 5+√2 / 5-√2 is
Gala2k [10]

Answer:

1.787

Step-by-step explanation:

\\  \sf \frac{5 +  \sqrt{2} }{5 -  \sqrt{2} }  \times  \frac{5 +  \sqrt{2} }{5  +   \sqrt{2} }

\\   \sf =  \frac{(5 +  \sqrt{2}) }{5 -  \sqrt{2} }  \times  \frac{(5 +  \sqrt{2}) }{5 +  \sqrt{2} }

\\  \sf =  \frac{25 + 5 \sqrt{2 } + 5 \sqrt{2} + 2  }{( {5})^{2}  - ( \sqrt{ {2}})^{2} }

\\  \sf =  \frac{27 + 10 \sqrt{2} }{25 - 2}

\\  \sf =  \frac{27 - 10 \sqrt{2} }{23}

Now putting the value of√2

\\  \sf =  \frac{27 + 10 \times 1.414}{23}

\\  \sf =  \frac{27 + 14.14}{23}

\\  \sf =  \frac{41.14}{23}

\\ \sf = 1.787

3 0
2 years ago
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