A fifth-degree polynomial equation with rational coefficients has the roots 3, 8i, and 7- radical 5. Which are also roots of the polynomial equation?

Step-by-step explanation:

Given the linear equation, y = ⅔x + 1, where the slope, m = ⅔, and the y-intercept, (0, 1) where b = 1.

In order to graph the given linear equation, start by plotting the coordinates of the y-intercept, (0, 1). As we know, the y-intercept is the point on the graph where it crosses the y-axis. It coordinates are (0, b), for which the value of b represents the value of the y-intercept in slope-intercept form, y = mx + b.

From the y-intercept, (0, 1), we must use the slope, m =  ⅔ (rise 2, run 3) to plot the other points on the graph. Continue the process until you have sufficient amount of plotted points on the graph that you could connect a line with.

Attached is a screenshot of the graphed linear equestion, which demonstrates how I plotted the other points on the graph using the "rise/run" techniques" discussed in the previous section of this post.    

[tex]\huge\boxed{Hello,\:hope\:you\:are\:having\:a\:wonderful\:day.}[/tex]We are asked to graph the line y=2/3x+1.

2/3 is the slope of this line (Rise/Run)

The rise is how many units we move up; the run is how many units we move left or right.

For this line, 2 is the rise, and 3 is the run.

Now, 1 is the y-intercept. (where the graph touches the y-axis)

First, plot this point: (0,1)

Then, move 2 units up and 3 to the left (Up 2, over 3, up 2, over 3)

When you have a line, take a ruler and connect these points, and you will have the graph of y=2/3x+1.

[tex]\huge\bold{Hope\:it\:helps!}[/tex]

[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]

[tex]\huge\sf{Good\:luck}[/tex]

Answer:

C is the answer because it makes the most sense

Answer:

D -1

Step-by-step explanation:

[tex]-6(3a+4)=3a-3[/tex]

[tex]-18a-24=3a-3[/tex]

[tex]-18a-3a=-3+24[/tex]

[tex]-21a=21[/tex]

a = [tex]\frac{21}{-21} =-1[/tex]

Hope this helps

Scatter plots are used to relate variables using scattered dots.

The best prediction for the number of baskets made in 16 minutes is (c) 14 baskets

From the graph, we can see that the number of baskets made in 14 minutes is 12.

Also, from the graph; as the minutes increases, the number of baskets either remain the same or increases.

This means that, for 16 minutes, the number of baskets would either be 12 (same as 14 minutes) or greater.

The closest to 12 baskets in the option is 14.

Hence, the best prediction for the number of baskets made in 16 minutes is (c) 14 baskets

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Answer:

A

Step-by-step explanation:

can't tell you

The bar graph represents the value of Profit (X) for the different probabilities of stocks x and y.

It can be drawn as follows.

Let x and y denote the two stocks .

The probability of success of x is p=50%= 50/100=1/2 = 0.5

The probability of failure of x is q= 50%= 50/100= 1/2= 0.5

Similarly

The probability of success of y is p=50%= 50/100=1/2 = 0.5

The probability of failure of y is q= 50%= 50/100= 1/2= 0.5

Then their joint distribution can be calculated from the following table.

        x              0.5               0.5               h(y)

y

0.5                  0.25            0.25              0.5

0.5                  0.25             0.25             0.5

g(x)                 0.5                 0.5               1.0

It is evident from the data that x and y have the same probability at each point  when both x and y are at

But the random variable X will have different values for

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The bar graph will appear as follows.

Answer:

Step-by-step explanation:

Answer: 24$

Step-by-step explanation:

The probability that a randomly selected girl does not have brown hair is 34.54%.

Given that in a certain school, 45% of the students are boys, and 80% of the boys have brown hair while 50% of those with brown hair are girls, to determine what is the probability that a randomly selected girl does NOT have brown hair, the following calculation must be performed:

Therefore, the probability that a randomly selected girl does not have brown hair is 34.54%.

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a) Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

b) since  the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equation

In order to show if the given point corresponds to the given function, we will have to substitute the value of x into the function to see if we will have its corresponding y-value

For the point (-0.8, -0.6), substitute x = -0.8 into both functions as shown:

f(x)  = 2x + 1

f(-0.8) = 2(-0.8) + 1

f(-0.8) = -1.6  + 1

f(-0.8) = -0.6

Simiarly;

y = -3(-0.8)- 3

y = 2.4 - 3

y = -0.6

Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

For the point (1/3, 2), substitute x = 1/3 into both functions as shown:

x = (y+2)/2

x = (2+2)/2

x = 4/2

x = 2

Simiarly;

x + 2 = 3

x = 3-2

x = 1

Since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equations

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Answer:

187.96cm

Step-by-step explanation:

first convert 6 feet to cm=182.88

then convert 2 inches to cm=5.08

add your answers together=187.96

Answer:

3600 seconds

Step-by-step explanation:

Answer:

Answer=C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Parallel lines hAve no solutions

Two lines intersection point gives one solution only

One single line denotes to infinite solutions

Option C is correct

The solution to the systems of equations is (7, 3)

Given the systems of equations expressed as:

-x + 4y = 5 ....................1

x - 5y = -2 ...................... 2

Add both equations to have:

-x+x + 4y - 5y = 5 - 2

4y-5y = -3

-y = -3

y = 3

Substitute y = 3 into equation 1:

-x + 4(3) = 5

-x + 12 = 5

-x = 5 - 12

-x = -7

x = 7

Hence the solution to the systems of equations is (7, 3)

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Answer: it’s infinite

Step-by-step explanation:

Answer:

I believe the answer is 16    Don't get mad if incorrect just trying my best

Answer:

A. 16

Step-by-step explanation:

If a 20 ft piece of metal is cut in 1 1/4 feet pieces you would divide the total length (20) by each of the pieces length (1 1/4) to find the answer. 20 ÷ 1 1/4 = 16.

Answer:

Adult = $15 pp

Child =  46 pp

Step-by-step explanation:

  Let A and C be the price of Adult and Child's tickets, respectively.

 We can set up equations for each of the two days, Tuesday and Wednesday.  Each equation adds the totals paid for the two ticket levels and set it equal to the total income for that day:

Tues:  8A+9C=174

Wed:   5A+7C=117

We have two equations and two unknowns.  Let's manipulate one of the equations in a way that allows us to eliminate one of the two variables, A or C.  [One can also solve either equation to isolate one of the variables, and then use that in the second equation.]

I chose to multiply the first by 5 and the second by -8, in order to make the coefficients for A the same value in both equations, but opposite in sign:

Tues:   40A+45C   =  870   [Multiply by 5]

Wed:  -40A -56C = -936     [Multiply by -8]

                      -11C = -66      [Add the two equations]

C = 6                                    [Ta Da.  Now use this price for a child's ticket in either of the original equations to find the cost of an adult ticket.]

8A+9C=174

8A+9*(6)=174

8A+54=174

8A   = 120

A  =  15

====

Use these two prices in the original equations to see if they indeed add up to the correct totals for each day.

                                                       Total Sales

Price     Tues     Wed          Tues  Wed    

A   15           8          5              120    75

C    6           9            7               54    42

               174        117              174   117 [The prices are correct]

Adult is $15 and child is $6

Therefore, the above answer is correct.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Adding both of the polynomial equations we get [tex]x^2+y^2+4x+4[/tex].

A polynomial equation exists an equation where a polynomial exists set equivalent to zero. i.e., it exists an equation constructed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It includes different exponents. The highest one demonstrates the degree of the equation.

Given: [tex]x^2 + 2x + 1[/tex] and [tex]y^2 + 2x + 3.[/tex]

Adding both of these two equations, then we get

[tex]x^2+2x+1+y^2+2x+3[/tex]

Group like terms

[tex]=x^2+y^2+2x+2x+3+1[/tex]

Add similar elements [tex]x^2+y^2+4x+4[/tex]

Adding both of the polynomial equations we get [tex]x^2+y^2+4x+4[/tex].

Therefore, the correct answer is [tex]x^2+y^2+4x+4[/tex].

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Answer:

<

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

gradient/slope/m formula:-

(-6,2) (4,10).

m=(10-4)/(-4-6)

m=6/2

m=3

Answer:

At least 5 times

Step-by-step explanation:

Number of balls to be selected for having assurance of at least three balls of the same colour is equals to 5 balls.

" Without replacement means if an item is drawn from the set of items it is not kept back which represents sample space is decrease by as per the number of selection is done in first draw."

According to the question,

Number of red balls in a box = 8

Number of black balls in a box =8

As per the condition of without replacement we get,

In this case worst selection case could be

Alternate balls are of different colour

Black →Red → Black → Red → fifth ball is either Red or Black

Hence, 5balls must be selected for assuring at least three balls of the same colour .

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Answer:

7

Step-by-step explanation:

3x - y = 1

2x + 2y = 14

x = 2

y =  5

x + y = 2 + 5 = 7

Answer:

  multiply by (3-√7)/(3 -√7) and simplify

Step-by-step explanation:

When there are radicals or complex numbers in the denominator, you can rewrite the expression so it has a real, rational denominator. You do this by multiplying numerator and denominator by the conjugate of the denominator. That value is the denominator with its sign changed.

This takes advantage of the factoring of the difference of squares.

  (a -b)(a +b) = a² -b²

__

  [tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\times\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-(\sqrt{7})^2}=\dfrac{2}{9-7}\times(3-\sqrt{7})\\\\=\boxed{3-\sqrt{7}}[/tex]

Answer:

Step-by-step explanation:

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Answer:

r = 3/4

Step-by-step explanation:

If 0 < x < π/2, then both sin(x) and cos(x) are positive.

From the Pythagorean identity, we then have

cos²(x) + sin²(x) = 1

⇒   cos(x) = + √(1 - sin²(x))   and   sin(x) = + √(1 - cos²(x))

Then

√(1 - cos²(x))/sin(x) = sin(x)/sin(x) = 1

and

√(1 - sin²(x))/cos(x) = cos(x)/cos(x) = 1

so that the overall expression reduces to

1 - 1 = 0

move it 0.25 units right

Answer:

  7/9

Step-by-step explanation:

Evaluate the expression at x=8-. You can see from the graph that p(8-) = 3.

  [tex]\displaystyle \lim_{x\to8^-}{\frac{3p(x)-2x}{15-3x}}=\frac{3(3)-2(8)}{15-3(8)}=\frac{-7}{-9}=\boxed{\frac{7}{9}}[/tex]

Answer:

w= 25

Step-by-step explanation:

Cost of water= (w -1)¢

Cost of milk= (2w -11)¢

Let the certain number be x.

x(w -1)¢= 480¢ -----(1)

x(2w -11)¢= 780¢ -----(2)

From (1):

wx -x= 480 -----(3)

From (2):

2wx -11x= 780 -----(4)

(3) ×2:

2wx -2x= 960 -----(5)

(5) -(4):

(2wx -2x) -(2wx -11x)= 960 -780

Expand:

2wx -2x -2wx +11x= 180

9x= 180

Divide both sides by 9:

x= 180 ÷9

x= 20

Substitute x= 20 into (3):

w(20) -20= 480

20w -20= 480

20w= 480 +20

20w= 500

w= 500 ÷20

w= 25