State how many imaginary and real zeros the function has. f(x) = x3 + 5x2 - 28x - 32

Answer:

The correct option is 2. The value of n is 3.

Step-by-step explanation:

Circumcenter is the point, where the perpendicular bisectors of a triangle intersect each other.

Circumcenter is also known as the center of the triangle. The distance from circumcenter to each vertex are same.

In triangle DEF, if A is the circumcenter.

[tex]AE=AD[/tex]

[tex]10=2n+4[/tex]

Subtract 4 from both sides.

[tex]10-4=2n[/tex]

[tex]6=2n[/tex]

Divide both sides by 2.

[tex]3=n[/tex]

Therefore the value of n is 3 and option 2 is correct.

Answer:

Option 2 is true

Step-by-step explanation:

We have to find the value of n for which point A becomes circumcenter.

Circumcenter: It is that point where perpendicular bisectors of triangle intersects.

The circumcenter  is also knows as center of triangle.

Circumcenter is at equal distance from each vertex of triangle.

If point A is circumcenter then

AE=AD

We have AE=10 units

AD=2n+4

Substitute the value

10=2n+4

[tex]2n=10-4[/tex]

By subtraction property of equality

[tex]2n=6[/tex]

[tex]n=\frac{6}{2}=3[/tex]

Hence, the value of n is 3 would make point A the circumcenter.

Answer: 1/4

Step-by-step explanation:

Answer: system 2 (5,0)        and                        system 3   (-1 2)

             2x-6y=10                                                      3x-y=-5

                x+8y=5                                                      x+4y=7

Step-by-step explanation:

Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)

system 1

2x - 2y =12          

-2x-3y = -22

solve simultaneous equation

2x - 2y =12          

-2x-3y = -22

add the equations gives

2x +(-2x) =0

-2y+(-3y) =-5y

12+ (-22) = -10

-5y =-10

y =2

2x -2(2) =12

2x-4 =12

2x = 12+4

x= 16/2 =8 x=8 and y =2 = (8,2)

system 2

2x-6y=10  *(-1) = -2x + 6y =-10

x+8y=5 *(2)    = 2x + 16y =10 add the equations

22y =0 y =0

x : 2x - 6(0) =10

x = 10/2 = 5

(5, 0)

 system 3

  3x-y=-5  *(-1) = -3x + y =5

  x+4y=7 * (3) = 3x + 12y = 21

add the equations = 13y = 26  y = 2

3x -2 =-5 = 3x = -3 =x =-1

(-1 2) answer

system 4

x+y=2   *(-2) = -2x -2y = -4

2x+y=13 *(1) = 2x +y = 13

add the two equations = -y =9

y = -9

substitute 2x-9= 13= 2x =22 x =11

(11 -9)

Option B is the correct answer.

We need to check which is the line shown in the figure.

In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher-dimension spaces. The word line may also refer to a line segment in everyday life, which have two points to denote its ends.

Now, from the given figure we can see XZ is a line.

Therefore, option B is the correct answer.

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The distance apart from Washington and Boston is 450 miles.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Trip from Boston to Washington:

Speed (2) = 60 miles per hour

Trip from Washington to Boston:

Speed (1) = 50 miles per hour

Speed = Distance / Time

Time = Distance / Speed

Distance is the same for both trips.

Time taken for the trip from Washington to Boston = t(1)

Time taken for the trip from Boston to Washington = t(2)

His trip to Boston takes an hour and a half longer than his trip to Washington.

This can be written as,

t(1) - t(2) = 1.5 hours

Distance ( 1/50 - 1/60) = 1.5

Distance (  (6 - 5)/300 ) = 1.5

Distance (1 / 300) = 1.5

Distance = 1.5 x 300

Distance = 450 miles

Thus,

The distance apart from Washington and Boston is 450 miles.

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Answer:

Option B. Graph B

Step-by-step explanation:

The given system of the inequalities are 6x + y > -3 and 2x + y ≤ 4

If we take the first inequality which represents the area below the line 6x + y = -3 or y = -6x - 3 (Slope of the line -6 and y-intercept is -3)

Second graph is represented by 2x + y ≤ 4 which represents the area below  the line y = 4 - 2x ( slope = -2 and y intercept = 4)

Option B shows the shaded area which the common area representing the solution set of these systems.

to factor something with an exponent you need to take the square root of it 

 sqrt (0.64) = 0.8, sqrt(t^24) = t^12)

 Answer is B

Answer:

The equation of the parabola which opens left or right is [tex]x=ay^2+by+c[/tex].

Step-by-step explanation:

We know that,

If in the equation of the parabola,

1. If x is squared, then the parabola opens upwards or downwards.

2. If y is squared, then the parabola opens towards left or right.

Since, we want the equation of the parabola which opens left or right.

So, we get that,

The variable 'y' is being squared in the equation of the given parabola (from 1).

Answer:

x = ay^2 + by + c

Step-by-step explanation:

it was correct for me

Shade 0.08 3 times

In total that's 24 hundreths to shade

all im doing is trying to get points Lol

Answer:

Option B. 25 ft

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=157\ ft[/tex]

assume

[tex]\pi =3.14[/tex]

substitute in the formula

[tex]157=2(3.14)r[/tex]

Solve for r

Divide by 2(3.14) both sides

[tex]r=157\(2(3.14))[/tex]

[tex]r=25\ ft[/tex]

Answer: 12

Step-by-step explanation:

To meet their fundraising goal, the drama club needs to sell 34 tickets at $7.50 each.

Answer:

The drama club wants to raise at least $500 in ticket sales. They already sold 50 tickets at $5 each. Let the number of tickets they need to sell at $7.50 be represented by 't'.

Therefore, the drama club needs to sell at least 34 tickets at $7.50 each to meet their goal.

Answer:  " w = (all real numbers) " —as explained below.

_________

Step-by-step explanation:

_________

Given the following "inequality":

_________

 " -3(w – 3) ≥ 9 – 3w " ;   Solve for "w" ;

                                         and see if the answer ["value for "w"]; is:

                                           "all real numbers."

_________  

  →  " -3(w – 3) ≥ 9 – 3w " ;  

_________

Method 1):

_________

On the "right-hand side" of the "inequality";

  Factor out a "(-3)" ;

_________

  " -3(w – 3) ≥  ( -3 * ? = 9?) – (-3 * ? = 3w? ) " ;

_________

                        1)   " -3 * (what value?) = 9 "?

                          Let "x" be the 'unknown value' :

                             →  " -3x = 9 " ;

                                Divide each side of the equation by "(-3)"  ;

                                  to isolate "x"  on one of the equation;

                                 & to solve for "x" ;

                                  -3x / -3 = 9 / -3 ;

                              to get:  " x = -3 " ;  

                               _________

                        2)   " -3 * (what value?) = 3w " ?

                        Let "x" be the 'unknown value' :                      

                           →   " -3x = 3w " ? ;

                         → Divide each side or the equation by ("-3").

                             → to isolate "x" on one side of the equation;

                                →  & to solve for "x" ;

                                    -3x / 3 = 3w / -3 ;

                                    to get:  x = -1w ;

_________

So:    " -3(w – 3) ≥  -3* (? = 9?) – (-3 * ? = 3w?) " ;

_________

Rewrite as:  

         " -3(w – 3) ≥  -3* [(-3 – (-1w)] " ;

_________

Now, let us consider the Following Portion of the "right-hand side" of the inequality:;

                            " (-3 – (-1w)]  =  " (-3 + 1w) " ;  

                    → {since:  "subtracting a "negative value is the equivalent of adding that particular value's positive value"} ;

         and bring down the "(-3)" on the "right-hand side" of the inequality; and rewrite the inequality as:

_________

           " -3(w – 3) ≥ -3(-3 + 1w) "  ;

        →  Now, divide EACH SIDE of the inequality by "(-3)" :

 {Note: Each time when one multiplies or divides an inequality by a "negative value"—the inequality sign flips to the other direction.}.

          →  [ -3(w – 3)]  / -3  ≥ [-3(-3 + 1w ] / -3 ;  

                 to get:

             →  " (w – 3) ≤ (-3 + 1w) " ;

_________

Note: " (-3 + 1w) " ; ↔ " [(1w + (-3)]  =  " 1w – 3 " =  "w – 3 " ;

_________

Rewrite the inequality:

_________

             →  " (w – 3) ≤ (w – 3 ) " ;

             ↔ "  w – 3  ≤  w – 3  "  ;

        The same value is equal to each other: not less than or equal to each other:   For instance:

              →  " w – 3  ≤  w – 3 " ;

If we add "3" to each side of the equation:

              →  " w – 3 + 3  ≤  w – 3 + 3 " ;

  We get:    " w  ≤ w " .   "w = w".  "w is not "less than" itself.  So all real numbers apply!

_________

Method 2)

_________

Given the following "inequality":

_________

 " -3(w – 3) ≥ 9 – 3w " ;   Solve for "w" ;

                                         and see if the answer ["value for "w"]; is:

                                           "all real numbers."

_________

On the "left-hand side of the inequality;

we have:

_________

 " -3(w – 3) " ;

_________

Take note of the "distributive property of multiplication" :

   → " a(b + c) = ab + ac " ;

_________

As such:

_________

We can expand:

     " -3(w – 3) = (-3*w) + (-3*-3) " ;

                     =  -3w + (9) ;

_________

Now, we can rewrite the original inequality:

_________

     " -3w + 9 ≥ 9 – 3w " ;

_________

Note: " -3w + 9 = 9 + (-3w) = 9 – 3w " ;  

                                      → {since: adding a "negative value" gets the same value as subtracting that value's "positive equivalent"};

       And we can rewrite our inequality as:

_________

     " 9 – 3w  ≥ 9 – 3w " ;

_________

Note: We have the same value on each side.

 "(9 – 3w)" is not greater than itself; it is "equal to itself".

 Any and all real numbers as values for "w" will result in the same value for any particular expression's Exact Same Expression!

_________

 So:  "w = (all real numbers)" .

_________

Hope this is helpful to you!

 Best wishes!

_________

Answer:

3 months

Step-by-step explanation:

Let after m months they saved same amount of money.

Given,

Saving of Jaclyn = $ 120,

Amount earned by him/her per month = $ 40,

So, the total amount contained by him/her in m months = Saving + earning for m months

= 120 + 40m,

Similarly, saving of Pedro = $ 180,

Amount earned by him/her per month = $ 20,

So, the total amount contained by him/her in m months = 180 + 20m

Thus, we can write,

120 + 40m = 180 + 20m

40m = 180 + 20m - 120

40m - 20m = 60

20m = 60

⇒ m = [tex]\frac{60}{20}[/tex] = 3.

Hence, it will take 3 months before which Jaclyn and Pedro have saved the same amount of money.

Linear equations can be solved by applying arithmetic operations separately for variables and constants. If they both save their entire allowances, 3 months will it take before Jaclyn and Pedro have saved the same amount of money

Let us assumed that the saving of Jaclyn and Pedro will be the same after n months.

Now, from the given data.

Saving of Jaclyn = $ 120

Amount earned by Jaclyn per month = $ 40

Total amount in hand of Jaclyn after work for n months will be the addition of current saving and the amount earned by Jaclyn after n months.

Thus,

[tex]\rm{Amount \;after \;n \;months}= 120 + 40n[/tex],

Similarly, the saving of Pedro = $ 180

Amount earned by Pedro per month = $ 20

Total amount in hand of Pedro after work for n months will be the addition of current saving and the amount earned by Pedro after n months.

Thus,

[tex]\rm{Amount \;after \;n \;months}= 180 + 20n[/tex]

According to the question,

[tex]\begin{aligned}&120 + 40n = 180 + 20n\\&40n = 180 + 20n - 120\\&40n - 20n = 60\\&20n = 60\\&n=\dfrac{60}{20}\\&n=3\end{aligned}[/tex]

Hence, If they both save their entire allowances, 3 months will it take before Jaclyn and Pedro have saved the same amount of money.

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Answer:

75

Step-by-step explanation:

300/4=75.

The second train will catch up with the first train after 5/3 hours.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a train that leaves a train station at 1 p.m. it travels at an average rate of 60 mi/hr. A high-speed train leaves the same station an hour later. it travels at an average rate of 96 mi/hr. The second train follows the same route as the first train on a track parallel to the first.

We have -

Assume that the second train catches the first in x hours. Then, we can write -

60(x + 1) = 96x

60x + 60 = 96x

96x - 60x = 60

36x = 60

x = 60/36

x = 5/3 hours

Therefore, the second train will catch up with the first train after 5/3 hours.

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