Write each expression as a single natural logarithm. ln 3-5 ln 3

The energy is 6000 joules.

The stored energy that depends upon the relative position of various parts of a system.

Given:

weight = 60N

height = 10 m

So, the energy is

Energy=mgh,

Energy =60*10*10

Energy =6000 joules

Hence, the energy is 6000 joules.

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the domain is 0...............

Answer:

180= (2x-24 )+ (x+5)

180= 3x-21

+21         +21

201=3x

/3      /3

67=x

The rational number that can be used to represent the number of points needed for Abraham to get an A will be 1.5.

It should be noted that a rational number is the number that can be written as a fraction. It can be while numbers and decimals have well.

Therefore, since Abraham needs one-half of a point to get an A– in Math, the rational number that can be used to represent the number of points needed for Abraham to get an A willbe 1.5.

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Answer:

No, for various value of x the number of tickets sold by me and my friend for the fundraiser can vary but will always remain in the ratio of 11:5.

Step-by-step explanation:

It is given that for a fundraiser, the ratio of tickets you sold to tickets your friend sold was 11:5.

Let us look at the ratio of tickets sold by both the persons.

Now, according to the condition given and the ratio mentioned in the question;

The number of tickets sold by me for the fundraiser be = 11x

and

The number of tickets sold by my friend for the fundraiser be = 5x

It is observed that total number of tickets sold by me and my friend are;

=> 11x + 5x

So, it is inferred that the number of tickets sold by me and my friend are not 11 and 5 respectively and can vary upon the value of x.

For instance, if the value of x = 2 than;

=> 11x + 5x

=> 11 × 2 + 5 × 2

=> 22 + 10

=> 32 tickets

Therefore,

No, for various value of x the number of tickets sold by me and my friend for the fundraiser can vary but will always remain in the ratio of 11:5.

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Answer:

log₇(xy/z)

Step-by-step explanation:

We know that

[tex]\log_ax = b \implies a^b = x[/tex]

we also know that:

[tex]a^b \cdot a^c = a^{b + c}[/tex]

so it follows that

[tex]\log_ax + log_ay = log_a(xy)[/tex]

from:

[tex]\frac{a^b}{a^c} = a^{b - c}[/tex]

follows that

[tex]\log_ax - log_ay = log_a(\frac{x}{y})[/tex]

so

[tex]\log_7x + \log_7y - \log_7z = \log_7(xy) - \log_7z = \log_7(\frac{xy}{z})[/tex]

Applying the midpoint formula, the endpoints for the midsegment are (-0.5, 0.5) and (-5/2, -7/2).

The midsegment of a trapezoid is the line segment that intersects the two legs of the trapezoid at their midpoints.

Hence, to find the endpoint for the midsegment of the other leg of the trapezoid, apply the midpoint formula, M[(x2 + x1)/2, (y2 + y1)/2].

Find the midpoint between A(-2, -5) and B(-3, -2):

A(-2, -5) = (x1, y1)

B(-3, -2) = (x2, y2)

Plug in the values

M[(-3 + (-2))/2, (-2 + (-5))/2]

M(-5/2, -7/2)

Therefore, using the midpoint formula, the endpoints for the midsegment are (-0.5, 0.5) and (-5/2, -7/2).

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Answer:

-2.5,-3.5

Step-by-step explanation:

Answer:

7/5 or 1.4

Step-by-step explanation:

1. Cross multiply. 5(2x-1)= 3(3)

2. Simplify and add 5. 10x -5= 9.     10x = 14

3. Divide by 10. 10x/10 = 14/10

X= 14/10= 7/5 or 1.4

Hope this helps. Please mark Brainliest!

Answer:

am pretty sure its 1/4 bc the first guys answer wasn't provided in the answer choices so i had to ask my teacher for help and the answer is 1/4 for those still stuck on this problem !!

Step-by-step explanation:

  Solving the problem by multiplying and simplifying we have as a result 72x⁴y²

Simplification is a process of reducing terms to expressions, which do not generate changes or values.

  Multiplication is also known as product, and it is a mathematical operation of a successive sum, this operation consists of adding a number a certain number of times:

a x b the number "a" will be added "b" times.

  The algebraic expression that we must simplify to its minimum expression is:

6√4 x² . 2√9 x² y²  we can see that it is an expression that has two variables

6×2x² × 2×3x²y²  

12x² × 6x²y²      ; multiply power of equal base

72x⁴y²

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Answer:

y = (C-Ax)/B

Step-by-step explanation:

We first move Ax to the right by subtracting from both sides

Ax+By=C

Ax+By - Ax = C - Ax

By = C - Ax

Now we divide by B

y = (C - Ax)/B

note that it only works if B ≠ 0

Answer:

y = [tex]\frac{C-Ax}{B}[/tex]

Step-by-step explanation:

Ax + By = C ( subtract Ax from both sides )

By = C - Ax ( divide both sides by B )

y = [tex]\frac{C-Ax}{B}[/tex] (B ≠ 0 )

Given:

Solution in Exact Form:

Hope this helps!

Answer:

I did number 11 and 13 for you and gave an explanation, I hope this helped, if you need more help just comment and let me know, have a great day! <3

Step-by-step explanation:

If the equation is addition like number 11, all you have to do is subtract 1.7 from the solution; which is 4.98. It will look like this:

4.98 - 1.7 = 3.28

if the equation is subtraction like number 13, then you have to add 6.55 with the solution, which is 2.45, it will look like this:

6.55 + 2.45 = 9

Answer:

[tex]\sin ^2\left(\theta\right)[/tex]

Step-by-step explanation:

Pythagorean identity

[tex]1=\cos ^2\left(x\right)+\sin ^2\left(x\right)\\1-\cos ^2\left(x\right)=\sin ^2\left(x\right)\\=\sin ^2\left(\theta\right)[/tex]

Solution of the equation a x ² + b x + c = 0 for b is b = ( - c - a x ² ) / x

Given,

the polynomial to be solved

a x ² + b x + c = 0

Solving the equation for b implies that we get the value of b from the above given polynomial

We can solve the given polynomial a x ² + b x + c = 0 by rearranging the terms of the polynomial and taking the LHS as b and the RHS as a term consisting of a, c and x

a x ² + b x + c = 0

=> b x = - c - a x ²

=> b = ( - c - a x ² ) / x

This gives us the required answer. It matches with option G among the given multiple choices.

Therefore, we get the solution of the equation a x ² + b x + c = 0 for b as b = ( - c - a x ² ) / x

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Based on the alternate exterior angles theorem, the equation is: 15x - 3 = 14x + 2

The value of x = 5.

The angles, (15x - 3) and (14x + 2) are alternate exterior angles. Based on the alternate exterior angles theorem/postulate, they are congruent to each other.

Thus, the equation to create in solving for the value of x would be:

15x - 3 = 14x + 2

Subtract 14x from both sides of the equation

15x - 3 - 14x = 14x + 2 - 14x [subtraction property of equality]

x - 3 = 2

Add 3 to both sides

x - 3 + 3 = 2 + 3 [addition property of equality]

x = 5

In summary, based on the alternate exterior angles theorem, the equation is: 15x - 3 = 14x + 2

The value of x = 5.

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The required solution of the following are,
(a) All values at which / has a local maximum: -2 and 4
(b) All local maximum values of  3 and 2

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
looking over the curve there are two maxima
first at (-2,3) and the second is at (4, 2)
So the local maximum is at x = -2 , 4
And maximum is y = 3 ,2

Thus, the required solution of the following are,
(a) All values at which / has a local maximum: -2 and 4
(b) All local maximum values of  3 and 2.

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Answer:

-a²,a, a²,2a²,a³,2ab

Step-by-step explanation:

-------

Using scientific notation, the total kilowatt-hours of electricity used during these two years is:

(6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For two numbers in scientific notation to be added or subtracted, they need to have the same exponent.

Thus, the first amount has to have an exponent of 10^11, meaning that the exponent has to be added by 2 = equivalent to addition by 100, and to compensate the base has to be divided by 100, hence:

(6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11

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Answer: 5

Step-by-step explanation:

Answer: Total temperature = -6.66ºF

Step-by-step explanation:

Given data,

First temperature = 1.3ºF

Second temperature = -2.8ºF

Fest = 10.000

So,

We can write,

                      1.3º x + (-2.8º) x = 10.000

                          x (1.3º - 2.8º) = 10.000

                            x (-1.5º) = 10.000

                               x = 10.000/-1.5º

                               x = -6.66ºF

Therefore,

          Total temperature = -6.66ºF

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Answer:

81?

Step-by-step explanation:

-

frac

5

4

t

= -4 ×

5

×

xt =

frac

(5

4

t)=-4

x 5 x x t

→ -

9×9

=

81

Answer:

8q + 32 that is the answer to the problem using the distributive property

Answer:

-3

Step-by-step explanation:

yes the expressions are equivalent to each other.

as,

A=-5+y, B=-5+y, C=y-5

Solving the inequality for the absolute value of x gives x < 1

Inequalities are simply defined as mathematical expressions showing comparison between two equations that are unequal.

They are known for explaining the relationship between values that are not equal to each other.

It is also important to note that absolute values of numbers holds that no number carries the negative sign

It is denoted with the symbol ' | | '

Given the expression;

| | 3x - 1 | + 5 | < 1

expand the bracket

3x - 1 + 5 < 1

Take absolute value

3x - 1 + 5 < 1

collect like terms

3x - 1 < 1 - 5

3x < -4

3x < - 4 + 1

3x < - 3

Make 'x' the subject

x < -3/ 3

x < - 1

x < 1

Thus, solving the inequality for the absolute value of x gives x < 1

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Answer:

10g+15

Step-by-step explanation:

5x2g=10g

5x3=15

1. The slope-intercept equation of the line is: y = x - 3.

2. The equation of the line in standard form is: -1/5x + y = 5

3. The equation in point-slope form is: y + 7 = 14(x + 2)

4. The value of x ≈ 5.94

Slope (m) = y2 - y1/x2 - x1.

There are three ways too write the equation of a line, they include:

1. find the slope (m) of the line that passes through (8, 5) and (7, 4):

Slope (m) = (5 - 4)/(8 - 7)

Slope (m) = 1/1

Slope (m) = 1

Substitute m = 1 and (a, b) = (8, 5) into y - b = m(x - a):

y - 5 = 1(x - 8)

y - 5 = x - 8

y = x - 8 + 5

y = x - 3

The slope-intercept equation is: y = x - 3.

2. The slope of perpendicular lines are negative reciprocals, therefore, the slope of the line perpendicular to the line that has a slope of -5 would be, m = 1/5.

Substitute m = 1/5 and (a, b) = (-15, 2) into y - b = m(x - a):

y - 2 = 1/5(x - (-15))

y - 2 = 1/5(x + 15)

y - 2 = 1/5x + 3

y = 1/5x + 3 + 2

y = 1/5x + 5

-1/5x + y = 5 [standard form]

3. Parallel lines have the same slope. The slope of y = 14x - 3 is 14. The line that is parallel to y = 14x -3 would also be, m = 14.

Substitute m = 14 and (a, b) = (-2, -7) into y - b = m(x - a):

y - (-7) = 14(x - (-2))

y + 7 = 14(x + 2) [point-slope equation]

4. y = kx

1.4 = k3.2

1.4/3.2 = k

The equation would be: y = 1.4/3.2x

Substitute y = 2.6 to find x:

2.6 = 1.4/3.2x

(2.6)(3.2) = 1.4x

8.32 = 1.4x

8.32/1.4 = x

5.94 ≈ x

x ≈ 5.94

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I just answered something very similar to this haha, but the sum of all exterior angles, regardless of the polygon's sides is always equal to 360 degrees, so our sum is 360°

Answer: 42

Step-by-step explanation:

70% = 70/100 as a fraction. 60 is 60/1 as a fraction.

Using this information, set up your question.

--> 70/100 x 60  

Multiply the fractions together and you get 4200/100. This then simplifies/is equivalent to 42. Therefore, 70% of 60 is 42.

The relationship is proportional because, the points lie on a straight line that goes through the origin.

A relationship that is proportional has a straight line graph that must pass through the origin, whereby the constant of proportionality, k = y/x, where x and y are the variables of the proportional relationship.

An example of a graph that represents a proportional graph is shown in the attachment below. The graph is a straight line graph that passes through (0, 0), which is the origin. The constant of proportionality, k = 21/7 = 3.

Thus, for the relationship between time spent swimming and the number of weeks to be proportional, it means that:

the points lie on a straight line that goes through the origin.

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