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Marat540 [252]
3 years ago
7

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that

can be evaluated without a calculator.
log4(2x2 - 20x + 12y)
Mathematics
1 answer:
sweet [91]3 years ago
3 0

Answer:

f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})

Step-by-step explanation:

Let be f(x,y) = \log_{4}(2\cdot x^{2}-20\cdot x +12\cdot y), this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:

r_{1,2} = \frac{20\pm \sqrt{(-20)^{2}-4\cdot (2)\cdot (12\cdot y)}}{2\cdot (2)}

r_{1,2} = 5\pm \sqrt{25-6\cdot y}

The polynomial in factorized form is:

(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})

The function can be rewritten and simplified as follows:

f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})]

f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})

You might be interested in
Which of the following functions computes a value such that 2.5% of the area under the standard normal distribution lies in the
fiasKO [112]

Answer:

a) NORM.S.INV(0.975)

Step-by-step explanation:

1) Some definitions

The standard normal distribution is a particular case of the normal distribution. The parameters for this distribution are: the mean is zero and the standard deviation of one. The random variable for this distribution is called Z score or Z value.

NORM.S.INV Excel function "is used to find out or to calculate the inverse normal cumulative distribution for a given probability value"

The function returns the inverse of the standard normal cumulative distribution(a z value). Since uses the normal standard distribution by default the mean is zero and the standard deviation is one.

2) Solution for the problem

Based on this definition and analyzing the question :"Which of the following functions computes a value such that 2.5% of the area under the standard normal distribution lies in the upper tail defined by this value?".

We are looking for a Z value that accumulates 0.975 or 0.975% of the area on the left and by properties since the total area below the curve of any probability distribution is 1, then the area to the right of this value would be 0.025 or 2.5%.

So for this case the correct function to use is: NORM.S.INV(0.975)

And the result after use this function is 1.96. And we can check the answer if we look the picture attached.

6 0
3 years ago
I need help tried to solve it, but can't....
fiasKO [112]

Answer:

B

Step-by-step explanation:

I would say B because if only 30 people said water and there is 65 that said something then it would almost be half of what you started with

8 0
2 years ago
Read 2 more answers
Help me answer this question
borishaifa [10]
To find the answer you would need to add 11 to 75 and then that is 86 so then divide that by 1 and the answer is 86
7 0
2 years ago
10. Mr. Guerrero left his house and drove north at an average speed of 40 mph.Two hours later, his daughter Miranda left the hou
Charra [1.4K]
Speed=distance / time  ⇒ distance=time x speed
distance=d
time=t
speed= s

d=s*t

Distance  traveled by Mr Guerrero, when his daugther left the house
Data:
s=40 miles/ hour
t=2 hours
d=40 miles/ hour * 2 hours=  80 miles

Total distance traveled by Mr Guerrero:
d=80 miles + 40 miles/hourt    ⇒d=80+40t      (1)

d=total distance.
s=speed.
t=time spent by Miranda for she overtook her father.

Distance traveled by Miranda.
data:

s=48 miles/ hour
d=total distance.
t=time spent by Miranda for she overtook her father.

d=48 miles/hour * t      ⇒d=48t       (2)

With the equations (1) and (2), we make an system of equations:

d=80+40t
d=48t

We can solve this system of equation by equalization method.

80+40t=48t
80=48t-40t
80=8t
t=80/8=10

d=48t
d=48*10=480

Answer: the thistance will be 480 miles.
3 0
3 years ago
270 peaches are placed into three groups: small peaches,
Ghella [55]

Answer:

$0.45

Step-by-step explanation:

ratio is 2:4:3

total is 9

270 ÷ 9 = 30

smoll

60 × 0.25 = $15

med

120 × 0.30 = $36

Big

91.50 - 15 - 36 = 40.5

40.5 ÷ 90 = $0.45

4 0
2 years ago
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