MATHEMATICS HIGH SCHOOL

How do I have to interpret the 2 in the next log?Is it the same as saying (logx)^2?

I need to calculate the derivative of this function but it will be difficult without even knowing what the 2 means lol.

Thnx in advance
log^2 x

Answers

Answer 1
Answer:

It means you have to multiply log(x) by itself.

(d)/(dx)(log(x))^2 \n (d)/(d(log(x)))(log(x))^(2) * (d)/(dx)(log(x)) \n 2log(x) * (1)/(ln(10)x) \n (2log(x))/(ln(10)x)

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What number should be added to both sides of the equation to complete the square?x2 + 12x = 11

Answers

given:
x² + 12x = 11

perfect square:

a² + 2ab + b²

a² = x² ⇒ x * x
2ab = 12x ⇒ 2(6)x
b² = 6² ⇒ 36

x² + 12x + 36 = 11 + 36

(x+6)(x+6) = 47

Both sides must be added with 36.

Answer:

36.

Step-by-step explanation:

We have been given an equation x^2+12x=11 and we are asked to find the number that should be added to both sides of the equation to complete the square.

To complete the square we divide the constant with x term by two and add the square of that number to both sides of equation to complete the square.

((b)/(2))^2

We can see that constant of x term is 12, so let us divide 12 by 2.

(12^2)/(2^2)

(144)/(4)

36

Therefore, we should add 36 to both sides of our equation to complete the square.

After adding 36 to both sides of our equation we will get,

x^2+12x+36=11+36

x^2+12x+6^2=47

(x+6)^2=47

Stephanie uses a ride service to get to different places in her city. If Stephanie uses Uber the service charges 1.50 per mile . If Stephanie uses lift the service charges $2.00 per mile. Let m represent the number of miles traveled. Which of the following statements are true . Select all that apply

Answers

Answer:

By a small online search, i found that the actual question seems to be:

"Stephanie uses a ride service to get to different places in her city. If Stephanie uses Uber the service charges $5.00 plus 1.50 per mile . If Stephanie uses lift the service charges $2.00 per mile. Let m represent the number of miles traveled. Which of the following statements are true . Select all that apply"

The statements are not provided, so i will answer it in a general way.

We have two different equations:

1) a fixed amount of $5.00 plus $1.50 for each mile, m.

This is a linear equation:

y1 = $1.50*m + $5.00

2) No fixed amount, only $2.00 for each mile, m.

y2 = $2.00*m

Now, the things we can see are which service will be cheaper as a function of m.

To see this, we can see the difference between y1 and y2.

When the difference is negative, this means that y1 is cheaper.

When the difference is positive this means that y2 is cheaper.

When the difference is zero, both services charge the same.

D = y1 - y2 = $1.50*m + $5.00 - $2.00*m

                 = (-$0.50)*m + $5.00

First let's find when it is zero.

              0 =  (-$0.50)*m + $5.00

            5.00/0.5 = m = 10

So for 10 miles, both services charge the same.

As the coefficient that multipies m is negative, if we have m > 10, then the difference will be negative.

This means that for m > 10, y1 is cheaper.

Then for m < 10, y2 is cheaper.

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Answers

Since Brigitte in shorter or lesser than 5 feet, h ges on the right of the lesser than symbol.
5 < h

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Answers

Answer:

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Step-by-step explanation:

you just need to do 8.58/3

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Answers

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
The triangles ΔLNO and ΔLMO have the same leg Lo, therefore you need the equality of hypotenuses LM=LN.

For a better understanding of the solution given here please find the diagram in the file attached.

We know from the Hypotenuse Leg Theorem (the HL theorem) that "if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent."

Thus, as can be seen from the diagram, Side LO (also called leg LO) is common to both the triangles LMO and LNO. Therefore, the additional information that will be required to prove the congruence is that the respective hypotenuses, MO and NO are equal.

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Answers

Since the line is parallel to AB, the two slopes are the same
        
                      slope of AB = m = (y₂-y₁)/(x₂-x₁)
                                     
                                           m= (5-0)/(-6-(-3))= - 5/3
The equation of the line is y-y₁=m(x-x₁)
                      The origin    P(0,0) 
                                       y=mx
                                       y= -(5)/(3)x   Solution
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