(X^-3y^2/x^3)^-2
Simplify the expression. Your final answer should use positive exponents.

Given

The ordered pair (2,5).

To find which of the functions have the ordered pair as a solution.

Explanation:

It is given that,

The ordered pair (2,5).

Then, put x=2, and y=5 in the function x+3=y.

That implies,

Hence, the ordered pair (2,5) is a solution of the function x+3=y.

Also, substitute x=2, y=5 in the function 7-x=y.

That implies,

Hence, the ordered pair (2,5) is a solution of the function 7-x=y.

We have a segment AC, with the point B lying between A and C.

The ratio AB to BC is 5:6.

The coordinates for A and C are:

A=(2,-6)

C=(-4,2)

We can calculate the coordinates of B for each axis, using the ratio of 5:6.

We can do the same for the y-coordinates:

The coordinates of B are (-8/11, -26/11).

First let's find the missing value of the hypotenuse:

we have that the hypotenuse equals sqrt(41). Now we can find the values of the trigonometric functions:

First, we will find the value of k

We can do this by sybstituting y=24, x=6 in;

y=kx and then solve for k

24= k(6)

divide both-side of the equation by 6

24/6 = k

4 = k

k=4

Then when x = 5, we will substitute x=5 and k=4 in; y=kx and then solve for y

y= (4)(5)

y = 20

What Leslie has is 3 pounds of Peanuts and she has used a fraction of it. That fraction is 1 7/8. To find out how many pounds more she has left, its a matter of subtracting 1 7/8 from 3 whole.

Let the leftover be called x, and you now have;

x = 3 - 1 7/8

Converting the other number to an improper fraction you now have

x = 3 - 15/8

x = 3/1 - 15/8

By using the LCM of both denominators which is 8, the expression now becomes,

x = 24/8 - 15/8

x = 9/8

x = 1 1/8

Les

The range in the average rate of change in temperature of the substance is from a low temperature of -[tex]22^{0}[/tex]F to a high of [tex]16^{0}[/tex]F

The domain of the function f(x) = sin x includes all real numbers, but its range is  −1 ≤ sin x ≤ 1. The sine function has different values depending on whether the angle is measured in degrees or radians. The function has a periodicity of 360 degrees or 2π radians.

Given f(x) = -19sin(7/3x + 1/6) – 3

We have to the range in the average rate of change in temperature of the substance is from a low temperature of ___F to a high of ___F

We know that the range of sin x is [-1, 1]

f(x) = -19 sin(7/3x + 1/6) – 3

We know

-1 ≤ sin(7/3x + 1/6) ≤ 1

Now multiply with -19 on both sides

19 ≥ -19sin(7/3x + 1/6) ≤ -19

-19 ≤ -19sin(7/3x + 1/6) ≤ 19

Now subtract 3 from both sides

-19 - 3 ≤ -19sin(7/3x + 1/6) - 3 ≤ 19 - 3

-22 ≤ -19sin(7/3x + 1/6) ≤ 16

-22 ≤ f(x) ≤ 16

Therefore the range in the average rate of change in temperature of the substance is from a low temperature of -220F to a high of 160F

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Part A

The net force is 4 N up

Part B

The net force is 3 N to the left

We need to find the points at which the expression below intercept the axis of the coordinate plane:

To find the "x" intercept we need to find the value of "x" that results in a value of "y" equal to 0. We have:

To find the "y" intercept we need to find which value of "y" the function outputs when we make x equal to 0.

The x intercept is -1 and the y intercept is -3.

Given data:

The given inequality is 3(x+5) >12.

The given inequality can be written as,

The graph of the above solution is,

Thus, the solution of the given inequality is (-1, ∞).

The correct answer is option A;

The graph shifts right 5 and up 1

15 = 4n -5

Add 5 to both sides of the equation

15 +5 = 4n -5 + 5

20 = 4n

Divide both sides by 4:

20/4 = 4n /4

5 = n

n= 5

Price of one pound of mercury is derived as follows;

This means 1 pound of mercury costs $1.98

1 pound = 453.6 grams

Therefore;

The price of 1 gram of mercury would be;

This means 1 gram of mercury costs $0.004365

Note that you have 13.534 grams per cubic centimeter of mercury. Therefore, the price of 1 cubic centimeter of mercury shall be calculated as follows;

This means 1 cubic centimeter of mercury would cost $0.059

Note also that, 1 cubic inch = 16.387 cubic centimeters. Hence,

This means 1 cubic inch costs $0.9668

It takes 4.800 cubic inches to make 1 manometer.

Therefore, the cost of 4.800 cubic inches would be;

If it costs 4.800 cubic inches to make 1 manometer, then the cost of 1 manometer would be $4.64

Therefore, to make 21 manometers, we would have;

ANSWER:

The price of mercury required to make 21 manometers would be $97.44

Answer:

Explanation:

If we have a linear equation of the form

then m = slope and b = y-intercept.

Now in our case, we have

which means that slope = 2 and y-intercept = 3

Therefore, we graph a line that has a slope of 2 and a y-intercept of 3.

A slope of 2 means that for every step you take to the right on a graph, you move 2 steps up to get to a point on the line.

The y-intercept of 3 means that the line passes through the point (0, 3).

Using these two facts about the line, we draw the following line.

From the above plot, we can clearly see that the line has a slope of 2 and a y-intercept of 3 - the same line described by y = 2x + 3.

The data that can be determined from the box plots are

a)

This is because the line in the middle of the box plot is the median of the box plot.

b)

The upper quartile of a box plot is the part of the box plot that is to the right of the line. In this case the median line is at the same location and the upper quartile ends at the same location.

and

The data that can not be determined is

c)

The reason this can not be determined is because the median is the average of the grades. This could mean some students scored in the higher levels and more scored below the median, which in turn drags it down.

d)

Would be following the same reason as C. It can be determined that there was a larger range lower grades in period 5 over period 3, but it can't be determined how many.

The carnival ride is in shape of wheel with 25ft radius.

The wheel has 20 cars attached to the center of the wheel. Since the cars are evenly distributed, we can thus find the

the measure of the angle between each car by dividing 360 degrees by 20.

#A:

The measure of each central angle between any two cars is:

#B:

Hence, we can find the length of the arch between any two cars is given by the length of arc formula given below:

Let us calculate this length below:

#C:

We are asked to find the area of each sector between two cars.

The area of a sector of a circle is:

Since we have all the parameters, let us calculate this area:

Therefore, the final answers are:

#A: angle = 18 degrees

#B length = 7.85 feet

#C Area = 98.13 squared feet

Answer:

Explanation: We have to find the vertex form of the parabola equation from the given standard form of it:

The general form of the vertex parabola equation is as follows:

Comparing the equation (2) with the original equation (1) by looking at the graph of (1) gives the following:

Therefore the vertex form of the equation is as follows:

Therefore the answer is Option(A).

His brother spent talking on the phone

Step - by - Step Explanation

What to find?

Time Nimol's brother spent talking on phone.

Let x be the time Nimol spent in talking on phone.

Let y be the time Nimol's brother spent talking on phone.

x = y + 3 1/2

x =2/5 ( y + 3 1/2)

It is given that Circumference of circle is 26П feet

The expression for the Circumference of circle is 2Пr.

So,

Radius of the circle is 13 feet

The expression for the area of circle is ПRadius²

Answer: 530.9

10 years

1) Considering that we can call the age of a stamp by "s" and the age of a coin by "c" we can write out the following system of Linear Equations:

Note that we can solve it using the Elimination Method.

2) So let's add simultaneously both equations:

We can plug into that s=10 and find the age of a coin as well:

Note that we subtracted 20 from both sides.

3) Hence, the age of a stamp is 10 years

Given

Answer

height of tower is 105 ft

Answer: Provided the sunglasses inventory which has the number of sunglasses and days in two columns, we have to find the graph which represents this table.

The table can be modeled by a linear equation:

Finding the slope and y intercept of this equation (1) leads to the following:

The answer, therefore, is the plot of equation (2) which is as follows:

Given

The system of equations,

20x − 5y = 20

8x − 2y = 8

To find: The solution.

Explanation:

It is given that,

20x − 5y = 20 _____(1)

8x − 2y = 8 _____(2)

That implies,

Divide (1) by 5 and (2) by 2.

Then, (1) and (2) becomes,

4x - y = 4.

Hence, there is infinitely many solution.

The distance between the two camper stations are 60.44 km and 62.95 km. as calculated using the law of sines.

Let us consider the the first ranger station is A and the second ranger station is C and the camper is at the position B.

It is given that AC = 10 km

∠BAC = 100°

∠BCA = 71°

∴∠ABC = 180 - (100 + 71) = 9

Now we will use this to find the distance between each ranger station and the camper by using the law of sines.

From the law of sines we know that :

[tex]{\displaystyle {\frac {a}{\sin {\alpha }}}\,=\,{\frac {b}{\sin {\beta }}}\,=\,{\frac {c}{\sin {\gamma }}}\,}[/tex]

Now we will use this ratio to calculate the other sides of the triangle.

10 / sin 9 = BC / sin 100

or, BC = 10 × sin 100 / sin 9

or, BC = 62.95 km

Again:

10 / sin 9 = AB / sin 71

or. AB = 60.44 km

Therefore the distance between the two camper stations are 60.44 km and 62.95 km.

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ANSWER :

5.9 years

EXPLANATION :

Exponential function can be expressed as :

where A = initial amount

r = (+) growth or (-) decay rate

t = time

y = amount after t years

From the problem, the initial value of the car is A = $32,500

It depreciates at a rate of 11.1% annually, so r = -11.1% or -0.111

The value of the car will be 50% of its original value, so y = 0.50(32,500) = $16,250

Using the formula above :

The legth of running around this track will be the length of both semi-circles plus the two bigger sidesof the rectangle.

The length of a semi -circle is half the length of a circle, and can be expressed as:

Where r is the radius of the semi-circle. The diameter of the semi-circles is the same as the smaller sides of the rectangle and its radius is half the diameter, so:

So, the total length, as said above, is the sum of the length of both semi-circles plus two times the bigger side:

Al the measures used were in meters and length is given in meters to the first power, so the unit of the result is also meters, or just "m".

Thus the answer is 374.96 m.

The first step to solve the problem is to create a function that relates the number of quizzes he attends by the number of weeks that elapses. Since he alread took one quizz, then the function must start from that and must grow at a rate of 5 quizzes per week. We have:

We want to know how many weeks until he takes 31 quizzes, then we need to make the expression equal to 31 and solve for the value of w. We have:

Then we subtract both sides by 1.

Then we divide both sides by 5.

It'll take 6 weekes before he have taken a total of 31 quizzes.

Equation in slope intercept form is written as

y = mx + b

If slope m = 1/3 and y-intecept b = 3

Equation form using the information above is

Point slope form using the point (3, 4)

simply use the formula

y - y₁ = m( x- x₁ )

Solution

We have the following values:

68,84,75,82,68,90,62,88,76,93,73,79,88,73,58,93,71,59,

58,51,61,65,75,87,74,62,95,78,63,72,66,96,79,65,74,77,95,

85,78,86,71,78,78,62,80,67,69,83,76,62,71,75,82,89,67,58,

73,74,73,65,81,76,72,75,92,97,57,63,68,83,81,82,53,85,94,

52,78,88,77,71

Part a

Range = Max- Min= 97-51= 46

Part b

The mean is given by:

Part c

The median is given by:

Position 40 ordered= 75 and Position 41 ordered= 75

Then the median is:

Part d

The most is the most frequent value and for this case is:

Repeated 5 times

Mode = 78

Part e

The data within the interval 50-54 is:

51 52 53

The variance is given by:

And the deviation si:

Let's call the numbers a, b and c.

The first statement tells us that the sum of the three numbers is 106, so:

The second statement tells us that the second number is two times the third so:

The final statement tells us that the first number is 6 more than the third, so:

This gives us a system of three equations with three variables. Let's take the value of a given by the third equation, use it in the first one and isolate another variable:

Let's take this value of b and use it in the second equation:

Now we know the exact value of c, so let's go back to the third equation:

and now we also know the exact value of a, so let's go back to the second equation:

So, the first number (a) is 31, the second (b) is 50 and the third (c) is 25.

31+50+25=106.