For each relation, decide whether or not it is a function.

Okay, here we have this:

Let's decompose each number and then we see their common factors:

64=2*2*2*2*2*2

72=2*2*2*3*3

The factors common to both are: 2*2*2, and by multiplying we obtain that the greatest common divisor is 8. The correct answer is option A.

The equation for the Volume (V) of the cone given is,

We are to isolate 'h' in the equation above

SOLUTION

Multiply both sides by 3

Simplify

Divide both sides by πr²

Simplify

Hence, the answer is

The total loss after 4 years is $47840.

From the information, we want to calculate the total loss after 4 years of 299000 is reduced by 4% per annum.

It should be noted that this simply means the calculation using the interest formula. In this case, the total loss will be gotten by knowing the interest.

In this case, the interest formula can be illustrated as:

Interest = PRT / 100

where P = Principal = 299000

R = Rate = 4%

T = Time = 4 years

Interest = (299000 × 4 × 4) / 100

Interest = 4784000 / 100

Interest = 47840

In this case, the calculation of the interest is the loss that the person gets.

Therefore, the loss is $47840.

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Number..................Difference1........... Difference 2.....Difference 3

6...........................................................................................

1................................ -5......................................................

0.............................. -1....................................4..............

10.............................. 10..................................11......................7

38.............................. 28................................18..................... 7

91.............................. 53................................25................... 7

176............................85..............................32

Answer:

Next number in sequence 176

Answer:

Triangle UVT and TSR are isosceles triangles (two equal sides).

Angle WUV = Angle WTV (base angles of isosceles triangle)

Angle RTS = Angle TRS (base angles of isosceles triangle)

Line VW is perpendicular to line UT.

Angle WTV = Angle RTS (vertically opposite angles)

Angle WTR = Angle VTS (vertically opposite angles)

If 2+[tex]\sqrt{3}[/tex] is a polynomial root, then the another root of the polynomial will be 2 -[tex]\sqrt{3}[/tex]

The root of the polynomial =  2 +[tex]\sqrt{3}[/tex]

We know by using the quadratic equation we can find the solution of the polynomial

The quadratic equation of the polynomial

= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Then the root of the polynomial is [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Here one root is given that 2 + [tex]\sqrt{3}[/tex]

Then using the quadratic equation of the polynomial, the other root of  the polynomial will be the conjugate of the given root.

The other root of the polynomial = 2 - [tex]\sqrt{3}[/tex]

Hence, If 2 + [tex]\sqrt{3}[/tex] is a polynomial root, then the another root of the polynomial will be 2 - [tex]\sqrt{3}[/tex]

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The augmented matrix is [tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex].

What is a matrix?

A rectangular array or table containing numbers, symbols, or phrases that are arranged in rows and columns is known as a matrix.

The given system of equations is:

9y - 5 +9z = 0

7x = -3y +7 + z

5x + 7y = 5

Rewrite the equations as:

0x + 9y + 9z =  5

7x +3y -1z = 7

5x + 7y + 0z= 5

Therefore, the augmented matrix for the system of equations is:

[tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex]

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Solution

For the solid line we can select two points:

(0,2) and (1,0)

We can calculate the slope and we have:

Then we can find the intercept and we got:

0= -2*1+ b

b =2

Then the equation is:

y= -2x +2

For the dashed line we can select (0,1) and (1,2) then the slope is:

The intercept is:

2= 1*1 +b

b=1

Then the equation is:

y= x +1

First, 1 dozen is 12 units, so

Now, to solve the exercise you can use the rule of three. So, you have

*How many pounds of meat are recommended to feed 1 dozen people?

Therefore, 3 pounds of meat is recommended to feed a dozen people.

*How many pounds are recommended to feed 4 people?

Therefore, 1 pound of meat is recommended to feed 4 people.

*How many pounds are recommended to feed 1 person

Therefore, 1/4 pound of meat is recommended to feed 1 person.

​

15/x = 3

Total number of slices = 15

Number of students = x

Each student's share = 3

(Total number of slices)/(Number of students) = Each student's share

Therefore, the mathematical statement representing the illustration is:

15/x = 3

The probability that an odd number or a perfect square greater than one shows is 2/3.

Probability -  The area of mathematics known as probability deals with numerical representations of the like that an event will occur or that a statement is true.

total no. of outcomes - 1,2,3,4,5,6

odd number = 1,3,5

or a perfect square = 4

probability - dividing the favorable number of outcomes by the total number of possible outcomes.

probability =  favorable outcomes  / total no. of outcomes

= 4/6

= 2/3

The probability that an odd number or a perfect square greater than one shows is 2/3.

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Part 1

The y-intercept is when x=0, and [tex]f(0)=(0-7)(0+6)(0-5)=210[/tex]. So, the y-intercept is at (0, 210).

Part 2

The x-intercept(s) are when y=0, so:

[tex]f(x)=0\\\\(x-7)(x+6)(x-5)=0\\\\x-7=0, x+6=0, x-5=0\\\\x=-6, 5, 7[/tex]

So, the x-intercepts are: (-6, 0), (5, 0), (7, 0)

Using our roots from Part 2, we know that:

Part 3: [tex](-6, 5) \cup (7, \infty)[/tex]

Part 4: [tex](-\infty, -6) \cup (5, 7)[/tex]

Answer:

they both go up by 2

Answer:

y = 0.75x + 2

Step-by-step explanation:

Take two distinct points on the graph

Compute the slope m and y-intercept b

Equation of line in slope-intercept form is
y = mx + b

Take points (0, 2) and (4, 5)

Slope m = (5 - 2) /(4-0) = 3/4

y-intercept from the graph is 2

So y = 3/4 x + 2 =0.75x + 2

Given:

The functions

Required:

Determine changes made in g(x) to get f(x).

Explanation:

The steps are:

So. fourth option is describing the f(x).

The graph

Answer:

Completed the answer.

1) 1/6

3) -7/6

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Explanation

Step 1

the distance between 2 points P1 and P2 is given by:

Step 2

let

P1=M(4,0)

P2=N(-2,-3)

replace

I hope this helps you

Based on the probability values, it will take the student 2 hours to stay outside the home

The given parameters are:

Probabilities

P(1) = 0.4

P(2) = 0.3

P(3) = 0.3

Time

Time 1 = 2 hours

Time 2 = 3 hours

Time 3 = 1 hour

When the above are represented on a table, we have the following table of values

Time (x)                    |   2        3          1

Probability (P(x))       | 0.4      0.3     0.3

The expected value of the student is then calculated as

E(x) = ∑ x * P(x)

Substitute the known values in the above equation

E(x) = 2 * 0.4 + 3 * 0.3 + 1 * 0.3

Evaluate the products

E(x) = 0.8 + 0.9 + 0.3

Evaluate the sum

E(x) = 2

Hence, the expected value is 2

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Parts C, D and E

Answer:

Explanation:

C) The maximum height is the highest point on the graph. On the x axis of the graph, each small square is 0.25 units. Thus, the x coordinate of the maximum height is is 1.25. The ball reached maximum height after 1.25 seconds

D) There were two different times when the ball was at 10m.

When y = 10 m, x = 0.5

when y = 10, x = 2

At 0.5 and 2 seconds, the ball was at 10m

E) A the time the when the ball hit the ground, the height is 0. Thus, the time when the ball hits the ground is 3 seconds

The dime has a cost in 2014 that is less than 0.95 times the cost in 2007.

To solve this problem by finding out the ratio. We can solve this problem by following a few steps.

According to the question, the cost in 2014 is less than 0.95 times the cost in 2007.

So the ratio is 1: 0.95. Which can be written as, 1/ 0.95 = 100/95 = 20/19 = 20: 19.

Now, we have to find among all those coins which follow the trend of 20: 19.

Here only the price of a dime has declined 0.95 times.

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Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

Hello there. To solve this question, we'll have to remember some properties about the pythagorean theorem and right triangles.

Given a triangle with side lengths 10 m, 24 m and 26 m, we have to determine whether this is a right triangle or not.

First, let's assume these are the sides lengths of a right triangle, as follows:

Notice in this case we choose the largest side to be the hypotenuse. We know that the largest side of a triangle has to be less than the sum of the legs and any combination would do, but since we'll apply the Pythagorean theorem, we already know that the hypotenuse has to be the largest side of the triangle.

For a right triangle with legs a, b and hypotenuse c, the Pythagorean theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, that is

Hence we plug a = 10, b = 24 and c = 26.

We have to see if this equality will hold for the values;

On the right hand side, square the number

On the left hand side, square and add the numbers

Notice we got the same answer, then we say that these values satisfy the Pythagorean theorem.

Therefore, this is a right triangle.

Answer:

no

Step-by-step explanation:

because 3*2 isnot equal to13

We can show that one third + one fourth is not equal to 3/7 by following two ways.

We are given to prove that the one third and one forth combination of any object/value does not equals to the 3/7 of that same value/object.

let's Consider we have value as 1.

∴ one third of value will be [tex] \frac{1}{3} [/tex]

∴ one forth of value will be [tex] \frac{1}{4} [/tex]

∴ three of seven of value will be [tex] \frac{3}{7} [/tex]

Now we can do the mathematic calculation on one third and one forth of the value.

As given we have to calculate the addition of  one third and one forth of the value

∴ [tex] \frac{1}{3} + \frac{1}{4} [/tex]

= [tex] \frac{4}{12} + \frac{3}{12} [/tex] --(make base same )

= [tex] \frac{4\ + 3}{12}[/tex]

= [tex] \frac{7}{12}[/tex]

∴ By the calculation we clearly got that the addition of  one third and one forth of the value is equal to the seven of twelve of the value.

We can also prove it by analysis as follows ;

Consider a number say 120.

∴ 1/3 of 120 will be 40

∴ 1/4 of 120 will be 30

∴ 3/7 of 120 will be 51.42

Now Addition of 1/3 and 1/4 of 120 will be 40 + 30 = 70

Comparing it with 3/7 i.e 51.42 ≠ 70

Hence proved 1/3 + 1/4 ≠ 3/7 .

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At first ,we should know that :

The relation between x and y will be a function when each value of x appeared one time

We will check the options:

A. for the figure of option A, each value of x connected one time to a value of y

B . there are 2 arrows from 0 and 1

C. the values of x = -1 , connected four times to the value of y

So, the answer is option A

Answer:

x = 14.12

Explanation:

To find the missing side, we will use the cosine law:

Where a, b, and c are the length of the sides of the triangle and C is the measure of the angle formed by the sides a and b.

So, we can use the equation to find the angle formed by the side of length 35 and the side of length 44 (25 + 19 = 44). So, replacing a by 35, b by 44, and c by 16, we get:

Then, solving for θ, we get:

Now, we can calculate the length of the missing side, using the angle θ = 19.41°, the side with length 35 and the side with length 25 as:

Therefore, the value of x is:

So, the length of the missing side is 14.12

The vertices of the ΔDEF are given by (-4, 2)D',  (-1,  1)E' ,  (1,  5)F' through mapping.

what is mapping?

Any set, including all whole integers, all the points on a line, or all the objects inside a circle, can be mapped. A mapping of the set of all whole numbers onto the set of even numbers is defined by the expression "multiply by two," for instance. A rotation is an internal map of a plane or of all of space.

The vertices of ΔDEF are given by D(2,-4) - D E(1,-1) - E F(5, 1).

According to the rule defining a reflection across the line, y=x should be stated when reflecting a point across the line. Then, the x and y coordinates are switched as follows:

y(x, y) → (y, x)

Let's now use the aforementioned rule to finish mapping the vertices of DEF. Change the x and y coordinate locations as follows:

The vertices of the ΔDEF are given by (-4, 2)D',  (-1,  1)E' ,  (1,  5)F' through mapping.

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Determine the amount paid by the Tony overall.