Graphs of Polynomial Functions Gizmo

5 Answer Review


1. What are the degree and leading coefficient of the function y=4x2-3x+7?


A. degree=4 leading coefficient=2

B. degree=2 leading coefficient=4

C. degree=2 leading coefficient=7

D. degree=3 leading coefficient=4


2. What is the lowest degree of the function graphed here? (image is attached to this)


A. 1

B. 2

C. 3

D. 4


3. what is the maximum of x-intercepts that can be found on a graph with equation y=ax5+cx2+f? (the values a, c, and f are real numbers)


A. 2

B. 3

C. 4

D. 5


4. Which polynomial function has a y-intercept of 3?


A. y=2x4+x2-3

B. y=3x2+4

C. y=-4x7-5x+3

D. y=9x3+3x2


5. What is the end behavior of y=-2x13+25x8-3 as x approaches infinity?


a. y=-3

b. y=13

c. y approaches infinity

d. y approaches negative infinity

Answer:

[tex]x^3-3x^2+2x-\frac{3}{2}[/tex]

Step-by-step explanation:

We can divide polynomials by other polynomials by dividing each term by the denominator. Remember, when we divide a variable by itself, we must change the exponent in our answer according to exponent rules.

[tex]\frac{ (2x^4-6x^3+4x^2-3x)}{2x}=\frac{2x^4}{2x} -\frac{6x^3}{2x} +\frac{4x^2}{2x} -\frac{3x}{2x} =x^3-3x^2+2x-\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

1. The graph of y=2/3x-2 is the top right corner, the -2 in the equation makes the line cross the y axis at -2

2. The slope is always with x and the y intercept is the second part of the equation.

The equation would be y = 5/6x -3

3.  The slope is the change in Y over the change in X

slope = 10-7 / 2 -  -1 = 3/3 = 1

Using the line formula y = mx+b, solve for b using the first point and the slope:

7 = 1 (-1)x +b

b = 7+1

b =8

The equation is -x +y =8

4. the jar starts with 6 , then they add 2 each day, multiply 2 by the number of days (x) and add it to 6:

The equation would be y = 2x + 6

5. point (5,9) slope = 2

Point-slope formula is written as y - y1 = m(x-x1)

y1 = 9, x1 = 5, m = 2

equation becomes y-9 =2(x-5)

Answer:

The answer is the first graph

The equation is y = 5/6x -3

The next equation is -x +y =8

The equation after would be y = 2x + 6

And, the final answer is y-9 =2(x-5)

Hope this helps!

Answer:

The correct answer has already been given (twice). I'd like to present two solutions that expand on (and explain more completely) the reasoning of the ones already given.

One is using the hypergeometric distribution, which is meant exactly for the type of problem you describe (sampling without replacement):

P(X=k)=(Kk)(N−Kn−k)(Nn)

where N is the total number of cards in the deck, K is the total number of ace cards in the deck, k is the number of ace cards you intend to select, and n is the number of cards overall that you intend to select.

P(X=2)=(42)(480)(522)

P(X=2)=61326=1221

In essence, this would give you the number of possible combinations of drawing two of the four ace cards in the deck (6, already enumerated by Ravish) over the number of possible combinations of drawing any two cards out of the 52 in the deck (1326). This is the way Ravish chose to solve the problem.

Another way is using simple probabilities and combinations:

P(X=2)=(4C1∗152)∗(3C1∗151)

P(X=2)=452∗351=1221

The chance of picking an ace for the first time (same as the chance of picking any card for the first time) is 1/52, multiplied by the number of ways you can pick one of the four aces in the deck, 4C1. This probability is multiplied by the probability of picking a card for the second time (1/51) times the number of ways to get one of the three remaining aces (3C1). This is the way Larry chose to solve the this.

Step-by-step explanation:

Hi There!

Answer:

4/52 (With cards picked before put back.)

3/48 (With cards picked before not put back.)

Step-by-step explanation:

A standard deck of cards is made up of 52 cards.

There are 4 kings in a deck.

4/52

Bob has a 4/52 chance of picking a king.

I don't know if the cards he picked prior to this he put back or not. If he didn't then it's 3/48.

Hope This Helps :)

Answer:true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

the answer is x=5 for a fact

Step-by-step explanation:

Answer:

the answer would be x=5

Answer:

He now makes 16.50 per hour

Step-by-step explanation:

15.00 x .10 = 1.50

15.00 + 1.50 = 16.50

f(x) + n - translate the graph n units up

f(x) - n - translate the graph n units down

f(x + n) - translate the graph n units left

f(x - n) - translate the graph n units right

|f(x)| - reflect over x-axis for x < 0.

[tex]f(x)=|x+2|-5[/tex]

Graph g(x) = x

g(x + 2) = x + 2 → translate 2 units left

|g(x + 2)| = |x + 2| → reflect over x-axis for x  < 0

|g(x + 2)| - 5 = |x + 2| - 5 → translate 5 units down

Answer:

See below

Step-by-step explanation:

The units are stokes per hole or strokes / hole

Jordan had the lowest number of strokes / hole followed by Rickie and finally Rory.

Answer:

Jordan had the lowest number of strokes per hole

Step-by-step explanation:

1) Total holes played by Rory = 9

Total strokes of Rory = 42

Number of stroke per hole: Rory

[tex]\frac{42 strokes}{9 hole}=4.667 strokes/hole[/tex]

2)Total holes played by Jordan = 18

Total strokes of Jordan = 79

Number of stroke per hole: Jordan

[tex]\frac{79 strokes}{18 hole}=4.389 strokes/hole[/tex]

3) Total holes played by Rickie  = 27

Total strokes of Rickie = 123

Number of stroke per hole: Rickie  

[tex]\frac{123 strokes}{27 hole}=4.556 strokes/hole[/tex]

4.667 strokes/hole > 4.556 strokes/hole > 4.389 strokes/hole

Rory > Rickie > Jordan

Jordan had the lowest number of strokes per hole

The shaded region, which is approximately 251.74 cm².

For the area of the shaded region, we need to calculate the area of a trapezium and the area of two semicircles.

Given data: AB = 28 cm , DC = 12cm and h = 14 cm

The formula for the Area of Trapezium:
Area of trapezium = 1/2 × (AB + DC) × h
Substituting the given values:
Area of trapezium = 1/2 × (28 + 12) × 14 = 280 cm²

The formula for the Area of a Semicircle:
Area of semicircle = πr²/2
Given that the radius r is 3 cm:
Area of two semicircles = 2 × π × 3²/2 = 28.26 cm²

Area of the Shaded Region:
Area of shaded region = Area of trapezium - Area of two semicircles
Area of shaded region = 280 - 28.26 ≈ 251.74 cm²

Therefore, the area of the shaded region is approximately 251.74 cm².

Answer:

the only point is (0,1) if u would look at the graph i post

Step-by-step explanation:

The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph thus option (D) is correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

As per the given function,

f(x) = (1/3)x

Substitute, x = 0,

y = f(0) = (1/3)0 = 0

So,(0,1) will not lie on the graph.

Similarly, (3, 27) and (−2, 9) also do not lie on the graph.

Substitute (-1,-1/3)

-1/3 = (1/3)(-1) = -1/3

Thus, it will be the point of the function.

Hence "The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph".

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Add 350 mL of the 90% alcohol mixture to obtain a 70% alcohol solution.

Let V be the volume of the 90% alcohol solution needed

Set up the equation

The final mixture volume will be 200 + V mL.

- The total amount of alcohol in the final mixture should be 70% of the total volume.

Calculate the total amount of alcohol

- Amount of alcohol from 200 mL of 35% solution: 0.35 * 200 = 70 mL.

- Amount of alcohol from V mL of 90% solution: 0.90 * V mL.

Total amount of alcohol in the final solution

- Total alcohol = 70 + 0.90V mL.

Set up the equation for the final concentration

- Final concentration: 70%

0.70 *(200 + V) = 70 + 0.90V

Solve the equation

0.70 * (200 + V) = 70 + 0.90V

140 + 0.70V = 70 + 0.90V

140 - 70 = 0.90V - 0.70V

70 = 0.20V

V = 70 / 0.20 = 350 mL.

Answer: 1) 9 days

2) a)37.5%

b)50%

c) 33.33%

Step-by-step explanation:

1) - Let's call:

x: number of days the company supposed to finish the order.

- You know that the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. Therefore, you can express this as following:

[tex]40x=(40+20)(x-3)\\40x=60(x-3)[/tex]

- Solve for [tex]x[/tex]:

[tex]40x=60x-180\\-20x=-180\\x=9[/tex]

(The answer is 9 days)

2) a) The percent that belongs to three people if eight eight people share equally in an inheritance, can be calculated as following:

[tex]\frac{3}{8}*100=37.5[/tex]%

b) The percent that belongs to three people if six people share equally in an inheritance (because two of the people are disinherited) can be calculated as following:

[tex]\frac{3}{6}*100=50[/tex]%

c) - The increase goes from 1/8 to 1/6, therefore, you must subtract them:

[tex]\frac{1}{6}-\frac{1}{8}=\frac{1}{24}=0.04167[/tex]

- Divide the result by 1/8 and multiply by 100 to obtain the percent:

[tex]\frac{0.04167}{\frac{1}{8}}*100=33.33[/tex]%

Answer:

55

Step-by-step explanation:

The equation of inverse variation is

y = k/x,

where k is a constant.

We can use the given x- and y-coordinates to find k.

y = k/x

15 = k/11

k = 165

The inverse variation equation for this problem is

y = 165/x

For y = 3,

3 = 165/x

3x = 165

x = 55

Answer:

C

Step-by-step explanation:

given x varies inversely as y then the equation relating them is

x = [tex]\frac{k}{y}[/tex] ← k is the constant of variation

To find k use the given condition x = 11 when y = 15

k = xy = 11 × 15 = 165 , hence

x = [tex]\frac{165}{y}[/tex] ← inverse variation equation

when y = 3, then

x = [tex]\frac{165}{3}[/tex] - 55 → C

The solution is Option B.

The number of old houses in the city are 35 houses

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the proportion be represented as A

Now , the value of A is

The number of new houses = 3

The number of old houses = 7

So , the ratio of old houses to new houses = number of old houses : number of new houses

Substituting the values in the equation , we get

Ratio of old houses to new houses = 7 : 3

Now , the number of new houses = 15

So , the number of old houses A is given by the proportion equation ,

7 : 3 : : A : 15

On simplifying the equation , we get

7/3 = A / 15

Multiply by 15 on both sides of the equation , we get

A = ( 7 x 15 ) / 3

A = 7 x 5

A = 35 houses

Therefore , the value of A is 35 houses

Hence , the number of old houses is 35

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Final answer:

The correct number of old houses is found by determining how many times the 3:7 ratio of new to old houses fits into the 15 new houses and then applying that to the 7 old houses in the ratio, which results in 35 old houses.

Explanation:

The question asks to find the number of old houses in a city given the ratio of new to old houses and the number of new houses. There is a ratio of 3 new houses for every 7 old houses. If there are 15 new houses, we need to find how many times the ratio fits into the number of new houses and then apply that same multiplier to the number of old houses.

To find this, we divide the number of new houses by the number of new houses in the ratio:

Number of times the ratio fits = 15 new houses ÷ 3 new houses per ratio = 5 times

Now, we multiply the number of old houses in the ratio by 5:

Number of old houses = 7 old houses per ratio × 5 times = 35 old houses

Therefore, the correct answer is B. 35.

Answer:

[tex]f(t)=43,200-7200t[/tex]

Step-by-step explanation:                      

We have been given that a delivery company purchased a new delivery truck for $43,200. The depreciated value of the truck can be estimated by the number of t years in service. The truck depreciates at a rate of $7,200 per year.

This means that after t years truck will depreciate 7200t. To find the truck's depreciated value after t years we will subtract 7200t from the cost of new delivery truck (43,200).  

[tex]f(t)=43,200-7200t[/tex]          

Therefore, the function [tex]f(t)=43,200-7200t[/tex] could be used to estimate the truck's depreciated value after t years.

The depreciated value of the truck after t years can be estimated by the linear function ƒ(t) = 43200 - 7200t, reflecting a straight-line depreciation method at a rate of $7,200 per year.

To estimate the depreciated value of the delivery truck after t years, we can use a linear equation which reflects a straight-line depreciation method. Since the truck cost $43,200 and depreciates at a rate of $7,200 per year, the equation representing the depreciated value of the truck after t years would be ƒ(t) = 43200 - 7200t. This equation starts with the initial value of the truck and subtracts the depreciation cost multiplied by the number of years the truck has been in service.

Depreciation is a way businesses can allocate the cost of a physical asset over its useful life. In this case, each year the truck is in service, it loses $7,200 in value. After one year, the value of the truck would be $43,200 - $7,200, which equals $36,000, and you would continue to subtract $7,200 for each additional year to determine the truck's value at any given time.

Answer:

2.5 rad ( to the nearest tenth )

Step-by-step explanation:

the time difference between the given times is 24 minutes

In 1 hour the hand moves 2π radians, hence in 1 minute moves

[tex]\frac{2\pi }{60}[/tex], thus in 24 minutes moves

[tex]\frac{2\pi }{60}[/tex] × 24 ≈ 2.5 radians

18. Answer: D

Step-by-step explanation:

First, find the measure of the missing angle.

65° + 57° + x = 180°

      122° + x = 180°

                x = 58°

Next, match up the angles with the opposite sides:

65° ⇄ Swim

58° ⇄ Bike

57° ⇄ Run

Lastly, put them in order from least to greatest:

   57° < 58° < 65°

⇒ Run < Bike < Swim

The only multiple choice option that is correct is Bike > Run.

*****************************************************************************

19. Answer: 22.3°

Step-by-step explanation:

[tex]sin\theta = \dfrac{opposite}{hypotenuse}[/tex]

[tex]sinD= \dfrac{EF}{DE}[/tex]

[tex]sinD= \dfrac{19}{50}[/tex]

[tex]D= sin^{-1}\bigg(\dfrac{19}{50}\bigg)[/tex]

D = 22.3°

Answer:

The opposite of Carlos's elevation would be +12ft.

Step-by-step explanation:

This question is using positive and negative integers to represent elevation and descending.  The surface of the pool would represent an elevation of 0, where we are level.  However, when Carlos descends (swims to the bottom) of the pool, he is at an elevation of -12 because he is below the surface.  The opposite of -12 would be +12.  So the opposite of where Carlos is -12ft below the surface of the water would be +12 foot above the surface of the water.  

Answer:

I'd say about 720 hotdogs.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The expansion of (x +y)⁴ is ...

... x⁴ +4x³y +6x²y² +4xy³ +y⁴

The expansion coefficients are 1, 4, 6, 4, 1; the sum of exponents is always 4, and there are 5 terms.

Answer:

$ 25.31 finance charges  he can save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle

Step-by-step explanation:

In the beginning of Month ,  ADB will be on the total amount of balance and the purchase that means ADB = 0.21 (2360 + 1500)/12

= $ 67.55

ADB at the end of the month  

Part of 2360 for 27 days = (2360 x 27)/28 = $ 2275.71

Part of 3860 for 1 day = (3860 x 1)/28 = $ 137.85

So the total becomes $ 2275.71 + $ 137.85 = $ 2413.56

So , ADB will be $ 2413.56 x (0.21)/12

= $ 42.23  

Difference in the finance charges at the beginning and at the end of the month is  

$ 67.55 - $ 42.23

= $ 25.31

6 hours

The two hoses together take 1/3 the time (4/12 = 1/3), so the two hoses together are equivalent to 3 of the first hose.

That is, the second hose is equivalent to 2 of the first hose. Two of the first hose could fill the vat in half the time one of them can, so 6 hours.

The second hose alone can fill the vat in 6 hours.

_____

The first hose's rate of doing work is ...

... (1 vat)/(12 hours) = (1/12) vat/hour

If h is the second hose's rate of doing work, then working together their rate is ...

... (1/12 vat/hour) + h = (1/4 vat/hour)

... h = (1/4 - 1/12) vat/hour = (3/12 -1/12) vat/hour = 2/12 vat/hour

... h = 1/6 vat/hour

so will take 6 hours to fill 1 vat.

The second hose can fill the vat alone in 6 hours, calculated by subtracting the work rate of the first hose from their combined work rate.

The question is about the time it would take for the second hose to fill the large vat alone, given that the first hose takes 12 hours alone, but together they take 4 hours. We are not given any info about the hose size or flow rate, so those don't need to be involved here.

We can analyze this problem in terms of work done. We know that one hose can fill the vat in 12 hours, so its work rate is 1/12 of the vat per hour. When we add the second hose, the vat is filled in 4 hours. The combined work rate of both hoses is 1/4 of the vat per hour.

To find the work rate for the second hose, we subtract the work rate of the first hose from the combined work rate: 1/4 - 1/12 = 1/6. This means the second hose can fill the vat in 6 hours alone.

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Considering the expression of a line, the equation of the line that passes through the pair of points (-66) and (3,-2) is 8/9x +y= 2/3.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.

The standard form of the line is Ax +By= C

Equation in this case

In this case, being (x₁, y₁)= (-6, 6) and (x₂, y₂)= (3, -2), the slope can be calculated as:

m= (-2 - 6)÷ (3 - (-6))

m= (-2 - 6)÷ (3 + 6)

m= (-8)÷ 9

m= -8/9

Considering point 2 and the slope, you obtain:

-2= (-8/9)×3 + b

-2= -8/3 + b

-2 +8/3= b

2/3= b

The equation of the line is y= -8/9x +2/3.

Finally, the standard form of the line is 8/9x +y= 2/3

Answer:

The gratuity  added is $28.2 .

Step-by-step explanation:

As given

A restaurant automatically charges a 20% gratuity if a party has 6 or more people.

The bill of the party is $141.

20% is written in the decimal form.

[tex]= \frac{20}{100}[/tex]

= 0.20

Gratuity is added to a party = 0.20 × 141

                                             = $28.2

Therefore the gratuity added is $28.2 .

Answer: The gratuity added is $28.2.

Answer: 23.13 lbs

Step-by-step explanation:

Weight in May + Weight gained = Weight in July

       4.5            +         18.63        =

                     23.13                      =

NOTE: Make sure to line up the decimal point when adding decimals:

    4.50

+  18.63

   23.13

Answer:

x is greater than or equal to 358

Step-by-step explanation:

1. Subtract 100 from 18,000

2. Divide by 50 to get your number of seven letter words

The simplest form of  [tex]2\frac{5}{8}[/tex] ÷ [tex]2 \frac{1}{2}[/tex]  is  [tex]1\frac{1}{20}[/tex] .

               [tex]2\frac{5}{8}[/tex]  ÷ [tex]2\frac{1}{2}[/tex]

       write the mixed fraction to improper fraction

             = [tex]\frac{21}{8}[/tex] ÷ [tex]\frac{5}{2}[/tex]

  Now change the division sign to the multiplication sign by writing the second number as [tex]\frac{2}{5}[/tex] .

             = [tex]\frac{21}{8}[/tex] × [tex]\frac{2}{5}[/tex]

             = [tex]\frac{21}{20}[/tex]

  Write the above improper fraction into a mixed fraction.

            = [tex]1\frac{1}{20}[/tex]  

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