Write ln8t‾‾√ in expanded form. Note: When entering natural log in your answer, enter lowercase LN as “ln”. There is no “natural log” button on the Alta keyboard.

4. The greatest change in elevation is on Checkpoint 4.

5. The change in elevation on the final checkpoint is of: -62.1 feet.

The change in elevation for each checkpoint is given by the subtraction of the final elevation by the initial elevation. Both these elevations are given on the table.

Hence, for each checkpoint, the changes are given as follows:

Hence the greatest change is of 210.4 feet on checkpoint 4.

The final elevation is of 148.3 feet, hence the change in elevation on the final stage is obtained as follows:

148.3 - 210.4 = -62.1 feet.

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The equations for Mechanic G is y = 30x and for mechanic K is y = 20x + 30

Rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

for mechanic G since he charges 30 dollars per hour, for x hours his charge will be 30x

so that y = 30x

For K since he charges at rate of 20 dollars per hour, his charge after x hours will be 20x. if he takes 30 dollars reservation fee

then his total cost is y = 20x + 30

In conclusion, the equations for mechanic G and K are y = 30x and y = 20x + 30 respectively.

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The factorized form of the given mathematical phrase 12x to the power of 3 - 4xsquared will be 4x²(3x - 1).

An algebraic factor is the multiplication of two algebraic terms.

The root of the quadratic equation formed by the algebraic factor is always real.

That term could be in form of summation multiplication or in subtraction.

As per the given phrase,

12x to the power of 3 - 4xsquared

12x³ - 4x²

Take x² as common,

x²(12x - 4)

Take 4 as common

4x²(3x - 1)

Hence "The factorized form of the given mathematical phrase 12x to the power of 3 - 4xsquared will be 4x²(3x - 1)".

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Mr. Baker moves 2 meters per second while standing on the moving sidewalk, and he walked 20 meters to get to the moving sidewalk. which is the correct answer would be an option (C).

Distance is defined as the product of speed and time.

The function shows Mr. Baker's distance (d), in meters, from the check-in counter while he has been standing on the moving sidewalk for s seconds. d = 2s + 20.

Here He travels at a speed of two meters per second while standing on the moving sidewalk, and he walked 20 meters to get there.

Thus, Mr. Baker moves 2 meters per second while standing on the moving sidewalk, and he walked 20 meters to get to the moving sidewalk.

Hence, the correct answer would be option (C).

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Answer: (8x + 2) = 6

Step-by-step explanation:

Answer:

8(x) + 2 = 6

Step-by-step explanation:

The positive solution for the given equation is 7 .

In the question ,

it is given that ,

when a number 14 is subtracted from the square of number ,

then the result is 5 times the number .

let that number be "x" .

So , the equation representing the amount statement is

x² - 14 = 5x

x² - 5x - 14 = 0

By using splitting the middle term method to find the solution.

we get ,

x² - 7x [tex]+[/tex] 2x - 14 [tex]=[/tex] 0

taking x common ,

x(x - 7) + 2(x - 7) = 0

(x + 2)(x - 7) = 0

we get , x + 2 = 0        and x - 7 = 0

the solution as x = -2     and x = 7 ,

Therefore , The positive solution for the given equation is 7 .

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Answer:7

Step-by-step explanation:

The fraction of another vial could be filled with the leftover medicine is 125 / 128.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the company receives medicine in 1-gallon (128-ounce) jars and then sells the medicine in vials that hold 3 ounces

The fraction left will be:

= 1 - Amount filled

= 1 - 3/128

= 125 / 128

The fraction left is 125 / 128.

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Answer:

The y-intercept is 12

Step-by-step explanation:

the equation is: x - 1/2y = -6

We need to find the y-intercept which is the y value when x=0.

Knowing that, we can just substitute 0 for x to get:

0 - 1/2y = -6

From there, it's just algebra so:

0 - 1/2y = -6

-1/2y = -6

-0.5y = -6

y = 12

Answer: D.

Step-by-step explanation:

Equilateral, scalene, and isosceles are all valid types of triangles.

Answer: 1st and 2nd

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

The value of x is 10, in the diagram, Vertically opposed angles

What is Vertically opposed angles?

Two lines intersecting at a point create vertical angles. Every time they are on an equal footing. Alternatively stated, four angles are created anytime two lines cross or intersect. Two opposed angles are equal and are referred to as vertical angles, as we can see. Due to their position opposite one another, they are also known as "Vertically opposed angles."

Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. The equality of the vertically opposed angles has been established.

Here in the diagram 5x = 2y

y = 5X/2

We have 2y+2y+8x = 180 in a straight line.

So 4y+8x = 180

4(5x/2) +8x = 180

10x+8x = 180

x = 180/18

x = 10

Hence, the value of x is 10, in the diagram.

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Answer:

D: 1+2x6

Step-by-step explanation:

5+2^3

5+8

13

1+2x6

1+12

13

D is the only option equal to 13

Hopes this helps please mark brainliest

(C) This is not a function.

The equation x = 3 represents a vertical line and not a mapping from values of x to values of y.

Hence, its a equation not a function.

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Answer:

100

Step-by-step explanation:

Example       33/ 100 = 33%          28/ 100= 28 %      etc

Answer:

90

Step-by-step explanation:

14/20 = 0.7

28/40 = 0.7

63/90 = 0.7

Hope this helps.

Answer:

Step-by-step explanation:

The answer is D. 90 because the other numbers

14/20=.7

28/40=.7

63/90=.7

therefore, it would be 90.

The next step is 4004 x 4004. So option(b) is correct

The process of making something less complicated and thus easier to do or understand, or the result of such a process is a simplification.

Reduce the expression to 3/4x + y/2 (4x + 7). The given expression can be written as 3/4x + y/2 (4x) + y/2 using the distributive property.

Given that

44 x 44 = 1936

404 x 404 = 163216

We have to find the next step

In the first step only fours are there

In the next step 0 is included in between the fours

If we follow the same sequence there will be two zeros coming between fours

= 4004 x 4004

= 16032016

Therefore the next step is 4004 x 4004

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Answer:

(a.):  m∠ ACB = 40°; (b.):  m ∠CBA = 25°; (c.):  m ∠CAB = 115°

Step-by-step explanation:

Because Lines AB and DE are parallel, we can use the angle relationships to find the angles.

(For context of the problem, we can label the 40° angle as ∠C and the 155° as ∠B)

(a.) Angles C and ACB are vertical angles, which means they're congruent.  Thus m ∠ACB = 40°.

(b.) AB is a straight line and angles B and CBA are supplementary angles.  This means their total sum is 180°.  We need to subtract angle B from 180 to find m ∠CBA:

[tex]180-155=CBA\\25=CBA[/tex]

(c.) We know that the sum of all the angles is 180°.  Thus, we can subtract the sum of angles CBA and CBA from 180 to find the m ∠CAB:

[tex]180-(40+25)=CAB\\180-65=CAB\\115=CAB[/tex]

Answer: 71

Step-by-step explanation:

First, plug 11 in for x:  y=6(11)+5

Then, multiply 6 by 11:  6(11)=66

Finally, add 5:  66+5=71

Answer:

Equation: y = -4x + 1

Slope: -4

Y-intercept: y = 1

Step-by-step explanation:

To find the equation of the line you need the gradient and the y-intercept

To find the gradient we need to divide the change in y by the change in x:

As the graph has a negative correlation the gradient would have a minus which is why it would be -4!

To find the y-intercept we need to find the number on the y-axis that the line crosses which in this case would be y = 1!!

Hope this helps, have a great day!!

Answer:

equation:y=4x+1

y-intercept:1

slope:4/1 or 4

Step-by-step explanation

the equation has to be in slope intercept form which is [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept. the y-intercept is when x is 0 in this case when x is 0 y is 1 (0,1) so the y-intercept is 1. the slope is rise/run so pick two points that cross the grid perfectly and count the units rise and run. this line rises 4 and runs 1 so the slope is 4/1 so 4 hence the equation [tex]y=4x+1[/tex]

The domain of relation  {-9, -8, -7, -6} and range of relation is  {3} and the relation represents a function.

A function is defined as a relation between a set of input having only one output.

Now,

The relation is;

{(-9,3),(-8,3),(-7,3),(-6,3)

Hence, The domain of relation = {-9, -8, -7, -6}

And, Range of relation = {3}

Clearly, Each input (domain) has only one output (range)

Hence, The given relation is function.

The domain of relation  {-9, -8, -7, -6} and range of relation is  {3} and the relation represents a function.

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Answer:

600 is the answer to the question

The amount of loan after 2 years will be $6491.4.

What is Simple interest?

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

Interest rate = 4.5%, compounded continuously.

Time = 2 years

Initial value = $3100

Now,

We know that;

The formula for amount after continuous compound interest is,

⇒ [tex]A = P e^r^t[/tex]

Where,  P is principal, r is rate per year, t is time in year.

Substitute all the values, we get;

⇒ [tex]A = P e^r^t[/tex]

⇒ [tex]A = 3100 e^{0.045 * 2}[/tex]

⇒ [tex]A = 3100 e^{0.09[/tex]

⇒ [tex]A = 3100 * 1.094[/tex]

⇒ [tex]A = 6491.4[/tex]

Thus, The amount of loan after 2 years will be $6491.4.

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The maximum height of the object is 88 feet and the time is 2.25 second(s) after launch

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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Answer: $173.96

Step-by-step explanation: If I'm not mistaken first you have to take 106 and multiply it by 2 to count for the round trips so that makes 212 miles for one trip, then you have to multiple by 8 to figure out how many miles in total which equals  1696, then you divide by the 35 to figure out how many gallons she use, which is 48.457(rounded) then you multiple that by the rate of gas which is 3.59 which means she spent 173.96(rounded to the nearest tenth)

Answer:

See below

Step-by-step explanation:

Present Value = 400

Period = 1 month      8 years is    n =   96 periods

Interest per period in decimal form     i =  .076 / 12 = .0063333

Fv = PV ( 1 + i)^n  

Fv = 400 ( 1 + .076/12)^96 = 733.29 dollars