pre calc
combine radicals/fractional exponents

The Prime Factorization of 16807 are:7, 7, 7, 7, 7. This implies 7 raise to power 5.

The term "Prime Factorization" refers to determining which prime numbers multiply together to produce the original number.

The process of writing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We can divide this into two categories. "Well, that's 2 time 2 times 5," we can say. Also, 5 is a prime number.

In this case 16807 will be:

16807 ÷ 7 = 2401

2401 ÷ 7 = 343

343 ÷ 7 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

Again, all the prime numbers you used to divide above are the Prime Factors of 16807. Thus, the Prime Factors of 16807 are:7, 7, 7, 7, 7.

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The distance between the cars increasing three hours later rate (in km/h) is 70km/h.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have given information:

Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h.

Now, we will calculate the distance between the cars increasing three hours later,

S² + W² = D²

where S is the southbound car,

W is the westbound car,

D is the distance,

2 * S  dS/dt  + 2 W dW/dt = 2 D dD/dt

S  dS/dt  +  W dW/dt =  D dD/dt

In 3 hours,

S=3*56 = 168 and W = 3*42 = 126

and D = [tex]\sqrt{(168)^{2}+ (126)^{2}}[/tex] = 210

168 * 56 + 126 * 42 = 210 * dD/dt

(168 * 56 + 126 * 42) / 210 = dD/dt

dD/dt = (9408+5292)/210

dD/dt = 14700/210 = 70

Therefore, the distance between the cars increasing three hours later rate (in km/h) is 70km/h.

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a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the values of x are in set P = { 57 , 63 , 66 }

The values of y are in the set Q = { 19 , 21 , 22 }

a)

From the data set of P and Q , we can see that when the value of y increase the value of x also increases

Therefore , the value of variable y varies directly with x

And , y ∝ x

b)

The value of variable y varies directly with x

And , y ∝ x

So , y = kx

Substituting the value for x and y from the data set , we get

The equation will be

y = kx

19 = 57k

Divide by 57 on both sides of the equation , we get

k = 19 / 57

k = 1/3

Therefore , the constant of variation k is 1/3

c)

The function rule is given by the equation

y = kx

Substituting the value for k in the equation , we get

y = ( 1/3 ) x

y = x/3

Hence ,

a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

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Answer:

its six hundred men

Step-by-step explanation:

its Six hundred men, six hundred men under my command

With only one goal in mind

Make it back alive to our homeland

Six hundred men, six hundred miles of open sea

But the problem's not the distance

It's what lies in between

And Ithaca's waiting Ithaca's waiting

My kingdom is waiting The kingdom is waiting

Penelope's waiting for me

So full speed ahead, full speed ahead

It doesn't seem like there is enough information to solve the scenario.

The biggest part we are missing to properly solve this would be:

The value of the function, f(g(x)), is f(g(x)) = 2√x + 11

From the question, we are to determine the value of the given function f(g(x))

From the given information,

The given functions are

f(x) = 2x - 3

and

g(x) = √x + 7

To determine f(g(x)), we will substitute the value of g(x) for x in f(x)

That is,

f(x) = 2x - 3

f(g(x)) = 2(√x + 7) - 3

Apply the distributive property

f(g(x)) = 2√x + 14 - 3

Simplify

f(g(x)) = 2√x + 11

Hence, the value of f(g(x)) is 2√x + 11

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Answer:

≈5.6

Step-by-step explanation:

Use ratios: 4/3 = 7.5/x

3 times 7.5 then divide by 4 to get 5.6

Let me know if this helped you out!

1.The perimeter of a rectangle is found by adding up the length of all four sides. Since the two long sides are 12 cm, and the two shorter sides are 7 cm the perimeter can be found by:

The perimeter is 38 cm.

2.To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

hope this helps

Answer:

Step-by-step explanation:

5x≥15

/5. /5

x≥3

On the number line we put a filled dot since it is both equal to and greater then at 3 and make it point to the right since it is greater it has to go up

Hopes this helps please mark brainliest

Answer:

Choose the bottom right ray and put it at 3.

Step-by-step explanation:

The initial velocity is  0 m/sec

The car speed up to 72km/h which is equivalent to  36m/sec

The acceleration of the car is 2.88 m/sec².

Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken

Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:

Initial Velocity = 0 m/sec

Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec

Time taken = 12.5 second

Now, the car’s acceleration in m/s can be written as,

Acceleration = (Final Velocity - Initial Velocity)/ Time taken

(36 m/sec - 0 m/sec)/12.5 seconds

= 2.88 m/sec²

Hence, the car’s acceleration in m/s is 2.88 m/sec².

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Taking into account the definition of a system of linear equations, the solution of the linear equation is (12,5).

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the system of equations to be solved is

y = 3/4x-4

y= -1/2x+11​

There are several methods to solve a system of equations, it is decided to solve it using the graphical method. This method consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs since the coordinates of said point satisfy both equations.

In this case, graphing both equations, it is obtained that the point of intersection, and therefore the solution, is (12,5).

The graph of the system of equations is attached.

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Answer:

67.38

Step-by-step explanation:

134.76/2 = 67.38

May I please have brainliest for this? Thank you!

Parallel lines have the same slope.

y=2 is a horizontal line and has a slope of 0, so the line parallel to it must also be horizontal and have a slope of 0.

Horizontal lines always have the form " y = k " for some number k and every point on that line has a y-value of k.

In this case, if you want the line to go through the point (-3,4), then the equation will be  " y = 4 ", since that's the y-value of the point on the line.

Answer:

y = 4

Step-by-step explanation:

A line with the equation y = a is a horizontal line that intercepts the y-axis at (0, a).

A line parallel to a horizontal line is another horizontal line.

If a horizontal line passes through point (p, q), then its equation is y = q, where q is the y-value of the point.

Therefore, the equation of a line that passes through (-3, 4) and is parallel to y = 2 is:

Answer:

227

Step-by-step explanation:

I think

The use of volunteer sampling means that the result of the survey is potentially misleading.

Volunteer sampling is a sampling technique in which each participant in the sample opts to join the research, as is the case for this problem, as each participant opted to join in the project to compare their cold lengths.

The drawback of this type of sampling is that it should contain lots of participants that share similar characteristics, such as desiring to weight/diet, and this may influence their recovery to cold. The participants also may lie, which can cause misleading results to the study.

Options to remove misleading conclusions is to use a different type of sampling, such as stratified sampling, as groups of people that are either short or long sleepers are compared to reach a conclusion.

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Answer:

------------------------------

We see two graphs on the opposite sides of the x-axis.

There is no intersection, so no common points. It means there is no solution.

Answer:

Interval for constant cost = [0, 10,000] same as 0 <= x <= 10,000

Interval for increasing cost = (10,000, ∞) same as 10,000 < x < ∞

Be careful! note the use of different types of parentheses for each answer part as explained below

Step-by-step explanation:

We are only being asked for the two intervals, not the function definition itself which would have made it a little bit more work. A function has inputs and outputs. Here the input is gallons of water and output is $ cost.

Normally when asked for intervals we use a variable. Let's call it x which represents the gallons of water used

Since there is a base rate of $11.70 whether or not any water is consumed as long as it is less than or equal to 10,000 gallons we can state that over the interval 0 to 10000 (inclusive), the cost is constant

We can represent this interval in two ways
0 ≤ x ≤ 10,000

Another way of representing this interval is what we call interval notation. In interval notation the same thing  can be expressed as:

[0, 10000]    

Here 0 is referred to as the lower limit or bound(minimum) and the 10,000 is referred to as the upper limit or upper bound

Note the use of square brackets. This means that both upper and lower limits are included in the function. Such an interval is also called a closed interval.

After 10,000 gallons, the cost keeps increasing. There is no upper limit on the usage of water. So the lower limit is 10,000  (but does not include that number) and upper limit is infinity

We represent this interval as
10000 < x < ∞

Note that both upper and lower limits are excluded since ∞ is not realistic.

In interval notation this is represented as
(10000, ∞)

Here we are using regular brackets(parentheses) because this interval does not include lower and upper limits

This kind of interval is known as an open interval

Looks like the purpose of this question is to make sure what you understand in terms of interval notation and possibly open and closed intervals. The only relevant number there is the 10,000 gallons which represents the upper bound on the first interval. All the other numbers can be junked

Hope that is of help even if it was wordy

Answer:

x = 10

Step-by-step explanation:

we see that the two triangle are equivalent and therefore the two angles degrees are the same

set them equal to each other

5x - 11 = 8x - 41

then solve

add 41 to both sides

5x + 30 = 8x

subtract 5x to both sides

30 = 3x

swap them

3x = 30

divide all by 3

x = 10

thats your answer

Answer:

Step-by-step explanation:

y - y₁ = m (x - x₁) would be your formula, since it's parallel you already have your slope, -x (which also equals 1 so technically -1). You have a point (8,9) and a slope -1, all you need to do is plug it in the formula.

Hope this helped!!

The height of antennas added to the main roof of the Marriott Rivercenter in San Antonio is 105 feet.

For the stated question-

Height of the main roof of Texas = 441 feet.

Height along with additional height of antennas = 546 feet.

Then,

Height of antennas = Total height - height of main roof.

Height of antennas = 546 feet - 441 feet

Height of antennas = 105 feet.

Thus, the height of the antennas added to the main roof of the Marriott Rivercenter in San Antonio is 105 feet.

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Answer: False

Step-by-step explanation:

This is because when u simplify 32x = 3(5x−8), it is 32x = 15x - 24

When u simplify 3(2x) = 3(5x − 8), you will get 6x = 15x - 24

Answer:

x = 3

Step-by-step explanation:

Notice the markings in the lower two angles of the triangle. We are dealing with Angle Bisectors.

Angle Bisectors of a triangle intersect at the Incenter, which is Equidistant from the sides of the triangle (given by the perpendicular symbols).

Therefore, 2x = x+3  =>  x = 3

The number that the product and 3 is twice the sum of that number and 5 is 10.

The product of a number and 3 is twice the sum of that number and 5.

Therefore,

let

x = the number

Hence,

3 × x = 2(x + 5)

3x = 2(x + 5)

3x = 2x + 10

subtract 2x from both sides of the equation

3x = 2x + 10

3x  - 2x = 2x - 2x + 10

x = 10

Therefore, the number is 10.

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The situation that can be modeled by the linear function y = mx + b is given as follows:

D. The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked.

Situations that can be modeled by linear functions are situations in which there is a constant change per unit interval.

The example in this problem is given by option D, as for each hour worked, the rate of change is given as follows:

8 dollars.

That is, for each hour worked, the total income of the worker increases by $8, hence the slope is of:

m = 8.

Then the intercept b represents the flat pay of the worker, which is how much the worker earns no matter the amount sold.

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The area of the softball field is 4732 yd²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given is a field with side measurements,

To find the area will we divide the field into a trapezium and a triangle,

Area of trapezium = (sum of parallel sides)x height/2

Area of triangle = 1/2xbasexheight

Area of trapezium = (104+52)x26/2 = 2028 yd²

Area of triangle = 2704 yd²

Area of the field = 2704 + 2028 = 4732 yd²

Hence, The area of the softball field is 4732 yd²

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25 persons went on the expedition as the total cost was $4400.

A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value and a, b, and c are known quantities. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler.

x denotes number of people

y denotes cost per person

Total cost =$4400

y = 4400 / x

15 members made the decision not to travel before the trip. The price per person went up by $66.

y +66 =4400 / (x -15)

(y +66) (x -15) = 4400

(4400/x +66)(x -15) = 4400

4400 -66000/x +66x -990 =4400

- 66000/x +66x=990

(- 66000 + 66x²) =990x

66x² - 990x - 66000 =0

x²-15x-1000=0

x =40 and x =-25 are the results of applying the quadratic formula to this quadratic equation. There is only sense in the positive x.

x- 15 =40-15=25 persons participated in the mission.

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Answer:

Step-by-step explanation:

Adding a constant k to the output of a linear function translates the graph vertically by k units. If k < 0 k<0 k<0, then the translation is downwards and if k > 0 k>0 k>0. Adding a constant k to the input of the function translates the graph horizontally by k k k units.

The number of chocolate bars that are in the vending machine are; 27 bars

We are told that the total number of chocolate bars and bags of pretzels in the vending machine is 41.

Let the number of bags of pretzels be x.

Now, we are told that number of chocolate bars is one less than twice the number of bags of pretzels. Thus;

Number of chocolate bars = 2x - 1

Thus, we can develop the algebraic expression as;

x + 2x - 1 = 41

3x - 1 = 41

3x = 42

x = 42/3

x = 14

Number of chocolate bars = 2(14) - 1 = 27 bars

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The object was 334 feet in the air 9 seconds after it was launched.

The height of an object launched from the top of a hill can be modeled by the function h(t) = -16t² + 170t + 100, where t represents the number of seconds after the launch.

This function gives the height of the object in feet at any time t after the launch.

To find the height of the object 9 seconds after it was launched,

Substitute 9 for t in the function h(t) to calculate the height of the object at that time. This gives us the equation :

⇒ h(9)  = -16(9)² + 170(9) + 100

⇒ h(9)  = -16(81) + 1530 + 100

⇒ h(9)  = -1296 + 1530 + 100

⇒ h(9)  = 334 feet.

Therefore, 9 seconds after being launched, the object had reached a height of 334 feet.

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