Which relation describes a function? What makes it a function?

Answer:

5

Step-by-step explanation:

Answer:

$497.8

Step-by-step explanation:

1. get the pool volume

volume = 8 x 20 x 14 = 2240 ft3

2. convert ft3 to gallons

2240 x 7.481 = 16757.44

3. You need 17000 gallons

4. Fee you have to pay fee + first 1000 gallon + the rest of the gallon

50 + 12.60 + 16 x 27.20 = 497.8

The number of pennies that Anya has is equal to 15.6 pennies.

The number of dimes that Anya has is equal to 2.8 dimes.

In order to solve this word problem, we would assign variables to the number of pennies and dimes, the total number of coins, and then translate the word problem into algebraic equation as follows:

Note: 1 penny is equal to 0.05 dollar and 1 dime is equal to 0.10 dollar.

Therefore, translating the word problem into an algebraic equation, we have the following;

p = 10 + 2d                                ......equation 1.

0.05p + 0.1d = 1.06                   .......equation 2.

Substituting equation 1 into equation 2, we have:

0.05(10 + 2d) + 0.1d = 1.06  

0.5 + 0.1d + 0.1d = 1.06

0.5 + 0.2d = 1.06

0.2d = 1.06 - 0.5

0.2d = 0.56

Dimes, d = 0.56/0.2

Dimes, d = 2.8 dimes.

For the number of pennies, we have:

p = 10 + 2d

p = 10 + 2(2.8)

p = 10 + 5.6

p = 15.6 pennies.

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Answer: An investor bought 500 shares of stock , some at $ 3.50 per share and some at $6.00 per share. If the total cost was $ 2187.50, how many shares of each stock did the investor buy?

(a) How will you set up the problem?

Let # of 3.50 shares be "x" ; value is 3.5x dollars

# of 6.00 shares is "500-x" ; value is 6(500-x)=3000-6x dollars

EQUATION:

value = value = 2187.50

3.5x + 3000-6x = 2187.5

-2.5x = -812.5

x = 325 (# of 3.50 shares)

500-x = 175 (# of 6.00 shares)

Step-by-step explanation:

Answer:

97.59

Step-by-step explanation:

975.90*0.10

97.59

Hope this Helps!!!

Five solutions of the given equation x- (3/2)y = -2 is given by as follow:

( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).

Plotted graph of the given function is attached.

As given in the question,

Given equation is equal to :

x- (3/2)y = -2

Simplify the given equation we get,

2x - 3y = -4

⇒ y = ( 1 / 3) ( 2x + 4 )

Now , five solutions of the given function to be plotted on the graph.

When x = 0

⇒ y = 4/3

When x = 1

⇒ y = (1/3)(2 +4)

⇒ y = 2

When x = 4

⇒ y = (1/3)( 8 + 4)

⇒y = 4

When x = -2

⇒y = (1/3)(-4 +4)

⇒y=0

When x = -5

⇒y = (1/3)(-10 +4)

⇒y= -2

Five solutions are ( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).

Plotted graph of the given function is attached.

Therefore, five solutions of the given equation x- (3/2)y = -2 is given by as follow:

( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).

Plotted graph of the given function is attached

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The value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

First, let us know some laws of exponent:

We are given;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] and [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex].

Now, we will solve one by one;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex]

[tex]= \sqrt[5]{\frac{2^{10}(x^{-10})}{(2^5x^{-15})}}[/tex]

[tex]=[({2^{10}. 2^{-5}) (x^{-10}.x^{15})}]^\frac{1}{5}[/tex]

[tex]=[({2^{10-5}) (x^{-10+15})]^\frac{1}{5}[/tex]

[tex]=[({2^{5}) (x^{5})]^\frac{1}{5}[/tex]

= 2x

So, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x.

Now,

[tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex]

[tex]=\frac{(2^3x^6y^{-3})^\frac{1}{3} }{(2^3x^3y^3)}[/tex]

[tex]=\frac{(2x^26y^{-1})}{(2^3x^3y^3)}[/tex]

[tex]=\frac{1}{(2^{3-1}x^{3-2}y^{3+1})}[/tex]

[tex]=\frac{1}{(2^{2}x^{1}y^{4})}[/tex]

= 1 / 4xy^4

So, the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

Thus, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

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Answer: [tex]2\frac{19}{36}[/tex]

Step-by-step explanation:

You subtract the woman's height from her son:

[tex]60\frac{5}{18} -57\frac{3}{4} =\frac{1085}{18} -\frac{231}{4} =\frac{1085*2}{18*2} -\frac{231*9}{4*9} =\frac{2170-2079}{36} =\frac{91}{36} =2\frac{19}{36}[/tex]

Answer:

16.11 (appx.)

Step-by-step explanation:

since l and m are parallel and a line intersects them, so we can say that the line is the transversal. from the figure we see that

7x + 12 = 12x - 28 [they are internal alternate angles and alternate angles are always equal to one another]

now, we can find the value of x from the equation

12x - 7x = 28 + 12

⇒ 5x = 40

⇒ x = 8

so the angle (7x+12)° is ((7*8)+12) = 68°

so (12x-28)° is also equal to 68° [cause of being alternate angles]

now, look at the figure,

angle (9y-77)° & (12x-28)° add upto a straight line as in 180°

and we know (12x-28)° = 68°

so now,

9y-77 = 68

⇒9y = 68+77

⇒9y = 145

⇒y = 16.11 (appx.)

The function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted

The total length of the roll = 66 feet

The perimeter of the rectangular paly area = 66

The perimeter of the rectangle = 2(l + w)

Then the equation will be

2(l + w) = 66

l + w = 66/2

l + w = 33

The function for length when the width is given

l = 33 - w

Therefore the domain of the function is 0 < w < 33

When w = 1

l = 33 - 1

l = 32

The first point is (1, 32)

When w = 32

l = 33 - 32

l = 1

The second point is (32, 1)

Draw the graph of the function

Hence, the function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted

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Answer:

h=24

Step-by-step explanation:

7=3+h/6

-3 -3

4=h/6

x6. x6

24=h

hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

The train A speed is 45 mph.  The train B speed is 70 mph.

Answer: B

Step-by-step explanation:

The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

According to the question,

We have the following information,

The given verbal phrase is one-half times a number m plus twenty-five.

Now, we will solve it step by step.

Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:

m/2

Now, adding 25 to this term, we have the following final expression:

m/2+25

Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

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The cost of repainting the swimming pool is 15,600 pounds

The swimming pool forms a three-dimensional object. Three-dimensional space is a geometric setting in which three values are required to determine the position of an element or its area.

The area of the object is the space the swimming pool occupies

How to find the area of the swimming pool?

Mathematically represented as:  A =lbh metres square

A=40x20x2

A=1200m²

The cost of im² is 13 pounds

Therefore, multiplying the area by cost of 1m per square

Cost=1200x13

Cost=15,600 pounds

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The number of bicycles that are there is 4.

There are a Total of 11 bicycles and tricycles altogether in the shop window.

They have a total of 29 wheels.

Therefore, the number of bicycles that are there can be calculated as follows;

Bicycles has 2 wheels and tricycles has 3 wheels.

Therefore,

let

x = number of bicycle

y = number of tricycle

2x + 3y = 29

x + y = 11

Multiply equation(ii) by 2

2x + 3y = 29

2x + 2y = 22

y = 7

x = 11 - 7

x = 4

Therefore the number of bicycle is 4.

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The transformations to the graphs of each function are presented as follows:

The parent function is defined as follows:

f(x) = log2(x).

Function p(x) is defined as follows:

p(x) = 7log2(x) - 2.

The transformations are listed as follows:

Function r(x) is defined as follows:

r(x) = -2log2(x) + 3.

The transformations are listed as follows:

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Answer:

its c b a

Step-by-step explanation:

other person was wrong

The real roots of the function is {0,-2} and there are no repeated roots.

Given function:

f(x) = [tex]x^{2} +2x[/tex]

[tex]x^{2} +2x=0[/tex]

take x as common

x(x+2) = 0

x = 0 and x + 2 = 0

x+2 = 0

x = -2,0.

Therefore the real roots of the function is {0,-2} and there are no repeated roots.

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22 members were present and 8 members were absent.

There are 30 members in a committee.

On a certain day 11/15 of the total members were present.

Let x be the number of members who were present.

So, we get an equation,

x = 11/15 * 30

We solve above fraction.

x = 11 * 2

x = 22

So, 22 members were present.

And 30 - 22 = 8 members were absent.

Therefore, 22 members were present and 8 members were absent.

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Answer:

  (a)  as x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞

Step-by-step explanation:

You want to know the end behavior of the 4th-degree function shown in the graph.

The graph has an arrow on each end of the curve shown in the figure. The left arrow points upward, indicating a tendency to +∞ as x gets more negative.

The right arrow also points upward, indicating a tendency to +∞ as x gets more positive.

  As x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

Answer:

Down Here ↓↓↓↓↓↓↓

Step-by-step explanation:

Hello!

This is all the information we need to fill up the blank spots:

Two angles whose sum is 180° are supplementary angles.

Vertical angles are formed by the opposite angles when two lines intersect.

Vertical angles are congruent/equal/equal in measure.

A linear pair of angles form adjacent angles, and the sum of their measures is 180°.

Adjacent angles share a common vertex and side.

The standard form of the equation of the circle is (x-5)² + (y+3)² = 9² and the general form is x² + y² + 10x + 6y - 47 = 0 .

We know that the general form of the equation of a circle is given by the following equation:

(x-h)² + (y-k)² = r² . Where r is the radius of the circle and (h, k) is the center of the circle.  

So the general equation of the circle is (x-5)² + (y+3)² = 9² .

Let's first define a circle in order to determine its equation. A circle is formed by every point in a plane that is uniformly spaced from another point.

The constant point is located at the center of the circle. The radius of a circle is the separation between its center and any point along its circumference.

(x-5)² + (y+3)² = 9²

or, x² + 10x + 25 + y² + 6y + 9 = 81

or, x² + y² + 10x + 6y - 47 = 0

Hence the general form of the circle is x² + y² + 10x + 6y - 47 = 0.

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Answer:

                             [tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]

Step-by-step explanation:

Coplanar: In the same plane.

The notation for a line is a double-ended arrow placed above two points contained on the line.

The symbol denotating two objects are parallel is a vertical double line.

A plane can be named by a capital letter (often written in script), or by the letters naming three non-collinear points in the plane.

The symbol denotating two objects are parallel is a vertical double line.

                             [tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]

The notation for a line segment is a bar placed above the endpoints of the line segment.

Answer:

8c³

Step-by-step explanation:

What is a coefficient?

A coefficient is a number that does not stand alone. For example, 3w means 3 times w, and "w" is a variable, so 3 is a coefficient.

How do we find the first term?

We can find the first term by putting the numbers from greatest to least. For example, if we had the numbers: 3x+7p+2 we would rearrange the series to this: 7p+3x+2. The number that comes first in the series would be the first term.

A number is divisible by 3 it the sum of its digits is divisible by 3. In this case, we have

which is not divisible by 3. The nearest multiples of 3 are 1623 and 1626. If you divide these numbers by 3, you have

So, the result of our division is between 541 and 542.

If these numbers are too complex to divide, we have to choose easier numbers, but we will lose some accuracy. For example, we can see that 1624 is between 1500 and 1650, which are very easily divisible by 3. We have

So, the result of our division is between 500 and 550. This is still true, but as you can see it is a much looser approximation than the one before.

Answer:

D ,

Step-by-step explanation:

4cd(6-9c)

5(x+5)

By evaluating a linear equation, we can see that 677.25 mL will be infused in 5.25 hours.

We know that the solution is being infused at a rate of 2.15 mL per minute.

So, t minutes after the infusion starts, the volume infused is given by the linear equation:

V(t) = 2.15mL*t

Here we want to see how many mL would infuse in 5.25 hours, to do that, we need to write that time in hours:

We know that one hour = 60 min, then:

5.25 h = 5.25*60 min = 315 min

Then the volume infused is:

V(315) = 2.15mL*315 = 677.25 mL

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The features from the graph of the function are given as follows:

a) The domain is {x | x ≠ -2}.

b) The range is {y | y ≠ 1}.

c) The x-intercept is: x = 0.

d) The y-intercept is: y = 0.

The domain of the function is the set of input values of the function, hence the values of x from the graph.

From the graph, the function is not defined at x = -2, hence the domain is:

{x | x ≠ -2}.

The range of the function is the set of input values of the function, hence the values of y from the graph.

From the graph, the function has an asymptote at y = 1, hence the range is:

{y | y ≠ 1}.

The x-intercept is the value of x at which the function crosses the x-axis, hence:

x = 0.

The y-intercept is the value of y at which the function crosses the y-axis, hence:

y = 0.

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V+12 is the expression that shows how many volunteers there are now

An expression is combination of variables, numbers and operators.

Given,

At the start of the year, the soup kitchen had v volunteers.

During the year, 12 more volunteers joined them

Joined them means added, it means 12 volunteers are added to the v volunteers

v plus twelve.

v+12

Hence v+12 is the expression that shows how many volunteers there are now

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The Sum is 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)

A finite series is one that has a finite number of terms.

If the series [tex]a_1[/tex]+ [tex]a_2[/tex] + [tex]a_3[/tex] +... + a has n terms and is a finite series with n terms.

As a result, [tex]S_n[/tex] is used to represent the series' sum as follows:

[tex]S_n[/tex]=∑ [tex]a_n[/tex]

Given:

1 + x + x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex]

let P= 1/ 1-x

P - Px= 1

P= 1+ Px

 = 1 + (P)x

 = 1 + (1+ Px) x

 = 1+ x + Px²

 = 1+ x + (1+ Px)x²

 = 1+ x + x² + Px³ and so on

So, 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)

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