evaluate this piecewise function at x= -6 and x=2

Answer:

B

Step-by-step explanation:

first for the easy one : the curve line is dotted, if the line points are NOT part of the solution. and it is solid, if the points are included.

you know what the curve line indicates ? it indicates the points for which there is equality.

so, if there is a ">=" or "<=" relation, then that includes equality, and the curve is solid.

if there is only a true inequality ("<", ">"), then the curve is dotted, as the equality is not included.

so, I how this is now really clear.

in our case here (I suspect it really looks like this)

y + 4x <= x² + 2

we have a "<=" sign, so, the curve is ..., well ? ... well ? ...

well ? ... well ? ... solid !

and we still treat inequalities as much as possible as regular equalities.

so,

y <= x² - 4x + 2 (after subtracting 4x from both sides).

and now you see it, right ?

all y values that are smaller or equal to the quadratic expression.

SMALLER ! so, BELOW the curve (as the smaller y values are represented by the lower part of the y-axis).

Using compound interest, it is found that $390.6 was earned in interest in the next 90 days.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, the parameters are:

P = 28214.35, r = 0.055, n = 365, t = 3/12 = 0.25.

Hence the amount after 90 days is:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(90) = 28214.35\left(1 + \frac{0.055}{365}\right)^{365 \times 0.25}[/tex]

A(90) = $28,604.95

28604.95 - 28214.35 = $390.6 was earned in interest in the next 90 days.

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Answer:

$2.55

Step-by-step explanation:

2d + $14.00 – $7.00 = $12.10; $2.55

By solving a system of equations, we conclude that Kelli's speed on still water is 6.1km/h

Let's say that the speed of Kelli in still water is S. And we know that the speed of the river is 5km/h.

When she swims upstream, her velocity is:

(S - 5km/h)

When she swims downstream, her velocity is:

(S + 5km/h)

With the given information, we can write for a distance D:

(S - 5km/h)*1h = D

(S + 5km/h)*6min = D

First, let's rewrite 6 minutes into hours.

1 hour = 60min

6 min = 6/(60) hours = 0.1 hours

Then the system of equations that we need to solve is:

(S - 5km/h)*1h = D

(S + 5km/h)*0.1h = D

D is the same distance in both cases, then we can write:

(S - 5km/h)*1h = (S + 5km/h)*0.1h

Now we can solve this for S.

S*1h - 5km = S*0.1h + 0.5km

S*1h - S*0.1h = 5km + 0.5km

S*(0.9h) = 5.5km

S = 5.5km/0.9h = 6.1km/h

Kelli's speed on still water is 6.1km/h

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Considering the given probability distribution, distribution D is valid.

A probability distribution is valid if:

In this problem:

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Using the normal distribution, the probabilities are given as follows:

a) 0.6517 = 65.17%

b) 0.0823 = 8.23%.

c) 0.6109 = 61.09%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 8.9, \sigma = 2.8[/tex]

Item a:

The probability is the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 8.9}{2.8}[/tex]

Z = 0.39

Z = 0.39 has a p-value of 0.6517.

0.6517 = 65.17% probability that the time is less than 10 minutes.

Item b:

The probability is the one subtracted by the p-value of Z when X = 5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 8.9}{2.8}[/tex]

Z = -1.39

Z = -1.39 has a p-value of 0.0823.

0.0823 = 8.23% probability that the time is more than 5 minutes.

Item c:

The probability is the p-value of Z when X = 15 subtracted by the p-value of Z when X = 8, hence:

X = 15:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{15 - 8.9}{2.8}[/tex]

Z = 2.18

Z = 2.18 has a p-value of 0.9854.

X = 8:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8 - 8.9}{2.8}[/tex]

Z = -0.32

Z = -0.32 has a p-value of 0.3745.

0.9854 - 0.3745 = 0.6109 = 61.09%.

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Answer:

12 hours

Step-by-step explanation:

1) Find the distance using: Distance = speed × time.

Distance = 40 × 15

= 600 km

2) Use the time formula to find the time taken. The formula is Time = distance / speed.

Time = 600 / 50

= 12 hours

Answer:

1/64

Step-by-step explanation:

F(3) means to use 3 in place of x in the given equation.

f(x) = (1/4)^x

f(3) = (1/4)^3

Either use exponents rules:

= 1^3 / 4^3

= 1 / 64

or just use the meaning of exponents

= 1/4 × 1/4 × 1/4

= 1/64

The difference between m and r from the given expressions is 8

Given the following exponents

x^m/x^5=x^7

x^m = x^5 * x^7

x^m = x^12

Equate the powers

m = 12

For the expression

(x^r)³ = x^12

x^3r = x^12

3r = 12

r = 4

Take the difference

m - r = 12 - 4

m - r = 8

Hence the difference between m and r is 8

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The graph of the given equation is given below.

We have given the equation of the line is f(x)=-1/5x+4f(x)

We have to determine the coordination.

line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.

Therefore we get f(x)=y

y=-1/5x+4....(1)

Plug x=0 in (1) then y=4

Plug x=5 in (1) then

y=-1/5(5)+4

=-1+4

=3

Therefore we get the coordinates (0,4) and (5,3)

Therefore the graph is given below,

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Answer:

  (a)  I, III, and IV

Step-by-step explanation:

We want to identify areas on a graph where the solutions to an inequality might be found.

The boundary line for the inequality y ≤ 2/3x -4 has a positive slope and a negative y-intercept. That means it must pass through quadrants I, III, and IV.

Quadrant II is above the line, but the y ≤ () inequality tells you the shading is below the line, where y-values are less than those on the line. There can be no solutions in quadrant II.

Solutions are found in quadrants I, III, and IV.

___

For reference, the second attachments shows the quadrant numbering.

Answer:

60%

Step-by-step explanation:

There are 6 professors younger than 55 (49, 43, 53, 41, 33, 34).

6/10 = 60%

Hello!

Let's solve !

⇒ (x - 3)² = 5

⇒ x² - 6x + 9 = 5

⇒ x² - 6x + 4 = 0

⇒ x = -(-6) ± √36 - 4(1)(4) / 2

⇒ x = 6 ± √20 / 2 = 6 ± 2√5 / 2

⇒ x = 3 ± √5

∴ The solutions are x = 3 + √5 and x = 3 - √5.

Answer:

p=(x−3)25

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     (x-3)^2-(5*p)=0 

STEP1:

 1.1    Evaluate :  (x-3)2   =  x2-6x+9 

Equation at the end of step1:

x2 - 6x - 5p + 9 = 0

STEP2:

Solving a Single Variable Equation:

 2.1     Solve   x2-6x-5p+9  = 0

Answer:

I believe the answer to be c 75°

Step-by-step explanation:

a 4 sided shape is 360 total degrees

The equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

The line that is parallel to the y-axis and passes through the point (7,0)

As we know the line equation:

Parallel to the y-axis

x = c

Passes through the point (7,0)

x = 7

Thus, the equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)

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Suppose [tex]-4y+2\ge0[/tex]. Then by definition of absolute value,

[tex]|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}[/tex]

On the other hand, suppose [tex]-4y+2<0[/tex]. Then

[tex]|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}[/tex]

Recall the definition,

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

Answer:

124

Step-by-step explanation:

1^3-1=0

2^3-1=7

3^3-1=26

4^3-1=63

5^3-1=124

Hence the next one in the pattern is 124.

The type of function that these sets of points are known to produce is the cubic function.

This is a function that is known to be a polynomial of degree 3. This type of polynomial is one that the coefficients are known to be complex numbers.

This is a cubic function given that the x axis is known to go through these points (-3,0), (-1,0), (2,0).

b. Given the sets of pints that we have, we have the equation

f(x) = a(x+3)(x+1)(x-2)

Such that

f = -2 =

4 = a x 1 x -1 x -4

4 = 4a

a = 1

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The measure of <2 is 92 degrees

The complete question is in the attached image

The angles are given as:

<1 = 4x - 4

<2 = 4x

The sum of angles on a straight line is

<1 + <2 = 180

So, we have:

4x - 4 + 4x = 180

Evaluate the like terms

8x = 184

Divide by 8

x = 23

Substitute x = 23 in <2 = 4x

<2 = 4 * 23

Evaluate

<2 = 92

Hence, the measure of <2 is 92 degrees

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To draw the median of the triangle from vertex A, the mid point of BC must be determined. The median of the vertex A is given at (-1/2, 1). See explanation below.

Recall that B = (3, 7)

and            C = (-4, -5).

Connecting D' and A gives us the median of the vertex A. See attached graph.

Recall that
A → (4, 2); and

B → (3, 7)

Hence, the Midpoint will be

[tex][(\frac{4+3}{2} )[/tex], [tex](\frac{2+7}{2} )][/tex]

→  [tex](\frac{7}{2}, \frac{9}{2} )[/tex]

Recall that

C → (-4, 5)

Hence,

[tex]\overline{C D_{2} }[/tex] =  [tex]\sqrt{[(-4 -\frac{7}{2} })^{2} + (-5-\frac{9}{2} )^{2} ][/tex]

Simplified, the above becomes

= √(586)/2)

= 24.2074/2

= 12.1037

The length of the Median from C to AB ≈ 12

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Answer: Digit Place Value

                7                Tens

                5                Ones

                 .  

                7                Tenths

                3                Hundredths

                3                Thousandths

Step-by-step explanation: this should help its not the answer but it's support

[tex] \sf{\red{ANSWER \: \: :}}[/tex]

x = 18 1/3

[tex] \sf{\purple{EXPLANATION \: \: :}}[/tex]

x - 20 + 2x = 35

- 20 + 3x = 35

3x = 35 + 20

3x = 55

x = 55/3

x = 18 1/3

The inequality that can be used to model Evelyn situation is

x + y = 60

x + y = 605x + 8y ≥ 700

The inequality

x + y = 60

5x + 8y ≥ 700

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Using proportions, it is found that you need an income of $124,722.22 to claim a $22,450 contribution in 2011.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

To claim a $22,450 contribution in 2011, this amount has to be 18% of your income, hence:

0.18x = 22450

x = 22450/0.18

x = $124,722.22.

You need an income of $124,722.22 to claim a $22,450 contribution in 2011.

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The value of the probability P(E and F) is 0.2802

Events are known to be independent if the occurrence of one does not affect the other.

Given the following parameters

P (E) =0.471

P(F) = 0.595

If E and F are independent, then;

P(E and F) = P(E)P(F)

P(E and F)  = 0.471 * 0.595
P(E and F)  = 0.2802

Hence the value of the probability P(E and F) is 0.2802

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Answers:
 1)  The value of AB  is:  " 59 units."
 2) The value of BC  is: "21 units."
_______
 3) The value of AB  +  BC ;

     =   59  units  +   21  units ;

     =   [the value of AC ] ;

     =  {" 80 units ".}.
_______

Step-by-step explanation:                                            

Given the following—and based on the assumption that we are dealing with:  "geometric lines"—and/or: "geometric line segments"—we are asked to:  
  "Find the value of:  " AB and BC" .
    {Given: " AB = (8x + 3) ;  BC  = (2x + 7) ;  AC = 80 ".}.
----------------------------------------------------------------------------------------------=-
Note:  The following "line graphs" are "Not Drawn to Scale."

        |    (8x + 3)     |      (2x + 7)       |

        |<--------------->|<------------------->|

<----·|----------------->|<------------------->|  {Note:  "Not drawn to scale."}.
       A                   B                         C
<-----|----------------->|<------------------->|

       A                                               C

<-----|<--------------------------------------->|  

<-----|----------------------------------------->|          

       A             {"AC = 80 ".}             C

 <---|------------------------------------------>|
       A       {"AC = 80 ".}.                  C

       |  (8x + 3) ;   +       (2x + 7)      =  80 ;  

<-----|----------------->|<--------------------->I
       A                    B                         C

So:  We have to find the value of:
     1) AB ; which is: (8x + 3) ;  And:
     2) BC ;  which is:  (2x + 7) .

To get these values; we need to find the value for "x".

So:   (8x + 3)  +  (2x + 7)   = 80  ;  
      ➝  8x + 3 + 2x + 7 = 80 ;

      ➝ Now, Let us combine the "like terms" on the "left-hand side" of the equation:
    +8x + 2x + 3 + 7  ;

      ➝  to get: + 8x + 2x = + 10x  ; and:
                       +3 + 7 = 10 ;

      To get:  "10x + 10" ;

Now, we can rewrite the equation:
       {" 70 ÷ 10 = 7 ."}.   " 10x + 10 = 80 ;

_____________________
To solve for "x" ; there are many ways:
_____________________
Method 1)  We have:  " 10x + 10 = 80 " ;
 ➝ Now, subtract "10" from each side of the question;
       10x + 10 − 10 = 80 − 10 ;
to get:  10x = 70 ;

 ➝  Now, divide each side of the equation by: "10" ; to isolate "x" on one side of the equation;  & to solve for "x" ;

  10x /10 = 70 /10 ;   to get:  " x = 7 "

Method 2)
 At the moment above in which we have:
" 10x = 70 " ;   we know that "10x ÷ 10 = 1x" ; and then "70 ÷ 10 = 7 ".

       {Note that any value; divided by "10" ;  is equal to:
{"that value" moved Back by:  "One" decimal space.}.  

So:  " 1x = 7 " ; ↔ " x = 7 ".

_____________
Method 3) :

When we have:  " 10x /10 = 70 /10 " ;  we have " 1x " on the "left-hand side" of the equation;  and:  "{ 70 /10 }" = {" 70 ÷ 10 = 7 ."}.

Note that: {" 70 ÷ 10 = 7 "} ; can be determined in many ways;
    For instance: {" 70 ÷ 10 = ? "} ;  

 ➝  The zeros for Both the numerator and denominator "cancel out"—

and we have:  " [tex]\frac{70}{10}[/tex] " ;  
 ➝  Cancel out each of the two (2) "zeros" ; and we have:  " [tex]\frac{7}{1} = 7.[/tex] "

 ➝  This is assuming that we figure out that:  " [tex]\frac{10x}{10}=1x =x[/tex] ."

___________

Now; let's find the correct values for this Brainly Question:
1) AB  =  8x + 3 ;  
Substitute our calculated value for "x" ; and solve:

➝  AB = 8x + 3 ;  ↔  8(7)  + 3   =  56  + 3  = 59 .

➝ BC  = 2x + 7 ;  ↔ 2(7)  +  7   =  14 + 7   =  21 .
Note:
➝  AC  =  80 = AB  + BC   ≟   59 + 21  ≟  80 ?  Yes!

____________
Answers:
 1) The value of AB  is:  " 59 units."
 ___
 2) The value of BC  is:   "21 units."
___

 3) The value of AB + BC  ;

           = 59 units + 21 units  =  {The value of AC }  =  "80 units".}.

_____
Hope this answer—along with explanations—is helpful to you.

  Best wishes in your academic pursuits!

______

Answer:

-31 degrees

Step-by-step explanation:

-4-27=-31

Answer:

  (c)  0

Step-by-step explanation:

The answer to this question requires that you read a graph.

Finding the value of h(2) means finding the value of "y" that corresponds to x=2.

The x-axis of this graph is identified by the "x" at the right side, under the arrow at the end of the x-axis. The y-axis is similarly identified by the "y" to the right of the y-axis at the top of the graph.

Each axis is labeled with numbers.

To find the y-value associated with x=2, first find the vertical line labeled 2 on the x-axis. It is 2 grid squares to the right of the y-axis.

Follow this vertical line until you reach the point where it intersects the line segment(s) representing h(x). At one of these, you encounter a solid dot. At the other point of intersection, you see an open circle (empty dot). The open circle means the point is not included in the function graph.

The value of h(2) is the y-value at the point where the vertical line x=2 meets the defined point on the function graph, the solid dot. The y-value is found by following the horizontal grid line to the y-axis, and reading the y-value there.

The point on this graph where the axes cross, the "origin," has no markings indicating the x- and y-values are zero there. You must infer that from the markings that are shown.

The point on the graph where x=2 lies on the horizontal line y=0. That is ...

  h(2) = 0

The function r =f(t) is f(t) = 1 - 8t/3

The function is given as:

3r + 8t = 3

Make r the subject

3r = 3 - 8t

Divide by 3

r = 1 - 8t/3

This means that:

f(t) = 1 - 8t/3

To calculate f(-3), we have:

f(3) = 1 - 8 * 3/3

Evaluate

f(3) = -7

Also, we have:

1 - 8t/3 = 2

Add 2 to both sides

-8t/3 = 3

Solve for t

t = -9/8

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Complete question

Consider the relationship 3r+8t=3

Write the relationship as a function  r = f(t)

Evalute f(-3)

Solve for f(t) = 2

a) The amount of meal reimbursement (in $) you expect to receive from the NSLP for last month is $146,205.

b) The total amount of milk reimbursement (in $) you expect for last month is $103,950.

c) The total amount of reimbursement (in $) your district will receive for last month is $250,155 ($146,205 + $103,950).

d) The average reimbursement (in $) per meal for both lunch and milk combined last month is $2.53 ($250,155/99,000).

Reimbursement is a process by which an entity is compensated for the expenses it incurs under a stated program.

Examples of expenses under the reimbursement policy include  business expenses, insurance costs, and overpaid taxes.

Annual NSLP lunches = 31.2 million

Lunches                        Free         Reduced Price     Full-Price       Total

National Quantity     16.1 million       3.2 million      11.9 million    31.2 million

District Lunches            27,000             18,000            54,000          99,000

Reimbursement rate      $2.68               $2.28              $0.25           $0.195

Reimbursement         $72,360           $41,040          $13,500         $19,305

Total reimbursement = $146,205 ($72,360 + $41,040 + $13,500 + $19,305)

Amount for milk reimbursement = $103,950 ($0.35 x 1.5 x 2 x 99,000)

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