Which must be true in order for the relationship
ZYX WVU to be correct?
N
ZY || WV
ZZZY and ZW=ZV
ZY YX and WV = VU
ZZZW and ZX=ZU

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

Learn more about Vertex at;
https://brainly.com/question/1435581
#SPJ1

Answer: [tex](x+3)^2 + (y-4)^2 = 9[/tex]

Step-by-step explanation:

See attached image, this is straight formula substitution.

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

Learn more about inequality:

https://brainly.com/question/25275758

#SPJ1

(a) The inequality follows from the binomial theorem.

[tex](a - b)^2 = a^2 - 2ab + b^2 \ge 0 \implies a^2 + 2ab + b^2 = (a+b)^2 \ge 4ab \\\\ \implies \dfrac{(a+b)^2}4 \ge ab \\\\ \implies \dfrac{a+b}2 \ge \sqrt{ab} ~~~~~~~~ (1)[/tex]

By the same reasoning,

[tex]\dfrac{c+d}2 \ge \sqrt{cd}[/tex]

Adding these results together, we have

[tex]\dfrac{a+b}2 + \dfrac{c+d}2 = \dfrac{a+b+c+d}2 \ge \sqrt{ab} + \sqrt{cd}[/tex]

and since [tex]\sqrt{ab}[/tex] and [tex]\sqrt{cd}[/tex] are both positive, they also satisfy the AM-GM inequality,

[tex]\dfrac{\sqrt{ab} + \sqrt{cd}}2 \ge \sqrt{\sqrt{ab}\times\sqrt{cd}} = \sqrt[4]{abcd}[/tex]

and the 4-variable result follows,

[tex]\dfrac{a+b+c+d}2 \ge 2\times\dfrac{\sqrt{ab}+\sqrt{cd}}2 \ge 2 \sqrt[4]{abcd} \\\\ \implies \dfrac{a+b+c+d}4 \ge \sqrt[4]{abcd} ~~~~~~~~ (2)[/tex]

(b.i) With [tex]m=\frac{a+b+c}3[/tex], we have

[tex]\dfrac{3m}4 = \dfrac{a+b+c}4 \implies m - \dfrac m4 = \dfrac{a+b+c}4 \\\\ \implies m = \dfrac{a+b+c+m}4[/tex]

(b.ii) From (2) it follows that

[tex]\dfrac{a+b+c+m}4 \ge \sqrt[4]{abcm} = \sqrt[4]{abc\times\dfrac{a+b+c+m}4}[/tex]

Using the result from (b.i), this is equivalent to

[tex]\dfrac{a+b+c}3 \ge \sqrt[4]{abc\times\dfrac{a+b+c}3}[/tex]

Take 4th powers on both sides.

[tex]\left(\dfrac{a+b+c}3\right)^4 \ge abc \times \dfrac{a+b+c}3[/tex]

Divide both sides by [tex]\frac{a+b+c}3[/tex].

[tex]\left(\dfrac{a+b+c}3\right)^3 \ge abc[/tex]

Finally, take the cube root of both sides.

[tex]\dfrac{a+b+c}3 \ge \sqrt[3]{abc}[/tex]

as required.

After solving the algebraic expression a(b-c)-b(a+c)-c(a-b) we get the equivalent answer as  ₋2(ab ₊ ac).

What is equivalent of algebraic expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given the expression is a(b₋c)₋b(a₊c)₋c(a₋b)

The first step is to multiply the terms.

⇒(a×b ₋ a×c) ₋ (b×a ₊ b×c) ₋ (c×a - c×b)

= (ab ₋ ac) ₋ (ba ₊ bc) ₋ (ca ₋ cb)

Now open the brackets.

= ab ₋ ac ₋ ba ₋ bc ₋ ca ₊ cb

Now comes main step of combining the like terms.

Put similar terms together on both sides of the equation.The two phrases are equal if each of the terms in both of them is the equivalent.

= ab ₋ ba ₋ ac ₋ ca ₋ bc ₊bc

Since, bc is a  like term with opposite sign, therefore bc  gets cancelled.

= ab ₋ ba ₋ ac ₋ ca

= ₋2ab ₋ 2ac

Take 2 as a common term from both the terms.

= ₋2(ab ₊ ac)

Hence we get the required equivalent of a(b-c)-b(a+c)-c(a-b) as

₋2(ab ₊ ac)

Learn more about "equivalent expressions" here-

brainly.com/question/24734894

#SPJ2

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

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,

To learn more about the graph visit:

https://brainly.com/question/4025726

#SPJ1

Answer:

kkrg=u/d

-678/09

=12 ans

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

Read more on functions here:

https://brainly.com/question/2833285

#SPJ1

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.

More can be learned about compound interest at https://brainly.com/question/25537936

#SPJ1

Answer:

Step-by-step explanation:

find 2^-6 as a fraction​

2^-6 = 0.015625

0.015625 as a fraction

(0.015625/1) × (1000000/1000000) =

15625/1000000

simplified = 1/64.

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

                  Let's find [tex]\boldsymbol{\sf{2^{-6}}}[/tex] as a fraction

                  Did you know that if we have a number with negative

                  exponents, we flop it over? This is how it's done-:

                  [tex]\boldsymbol{\sf{2^{-6}=\displaystyle\frac{1}{2^6}}}[/tex]. And Now we need to evaluate

                 [tex]\boldsymbol{\sf{\displaystyle\frac{1}{64}}}[/tex].

done!!

[tex]\orange\hspace{300pt}\above3[/tex]

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]

As the intervals moves from left to right on the graph, the average rate of change increases

The function is an exponential growth function.

This is known because it has an initial value at (0, 2), and the value increases to the right

The average rate of change of exponential growth functions increases towards the right.

This means that:

The initial statement is "as the intervals moves from left to right on the graph, the average rate of change increases

Because the average rate of change keeps changing, the final statement is:

Since the average rate of change is also changing, the function is changing and approaches infinity

Read more about exponential growth function at

https://brainly.com/question/11487261

#SPJ1

Answer:

x = 15

y = 60

Step-by-step explanation:

Angles (x + 50) and (3x + 20) follows corresponding angle theorem.

-----

⇒ x + 50 = 3x + 20

⇒ x - 3x = 20 - 50

⇒ -2x = -30

⇒ x = 15

The angles (x + 50) and (2y - 5) lies on a straight line which sum ups to 180°

⇒ (x + 50) + (2y - 5) = 180

⇒ 2y + x + 45 = 180

⇒ 2y + 15 + 45 = 180

⇒ 2y + 60 = 180

⇒ 2y = 120

⇒ y = 60

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.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

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)

Learn more about reimbursement at https://brainly.com/question/14250839

#SPJ1

Answer:

B ∩ (¬A ∩ ¬C)

Step-by-step explanation:

You want to exclude the section C shares with A, the one C shares with B and the one it shares with both. Intersecting ¬A (not A) with ¬C (not C) you obtain the entire area except A and C, which then can be intersected with B to obtain the highlighted area.

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

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!

______

The statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)

According to the statement, we have an original function f(x) = 10ˣ and a transformation rule for horizontal translation g(x) = f(x + 4). By applying this rule, we have that g(x) = 10ˣ ⁺ ⁴, which have these features:

Therefore, the statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)

To learn more on transformation rules: https://brainly.com/question/9201867

#SPJ1

Answer:

-31 degrees

Step-by-step explanation:

-4-27=-31

(a) The maximum displacement of the wave is 14 cm.

(b) The time for the wave to bounce opposite directions before coming to rest  is 3.0 s.

(c) The period of the wave is 3.0 s and the amplitude is 14 cm.

(d) The graph’s frequency is 0.33 Hz

(e) The wave attained maximum displacement at time 6 s and 7.5 s.

A) The maximum displacement of the wave is the point of maximum rise of the curve = 14 cm

B) Time of motion of the wave; This is the time for the wave to bounce opposite directions before coming to rest makes a complete cycle

It takes the wave 0.75s to bounce up and the 2.25 s to bounce down, and finally it came to rest at 3.0 s.

C) The period of the wave is the time taken for the wave to make a complete cycle = 3 s

Frequency of the wave

f = 1/T

f = 1/3 = 0.33 Hz

The frequency indicates the number of cycles in a second.

D) Position of the wave at time 6 s and 7.5 s

The wave attained maximum displacement at time 6 s and 7.5 s.

Read more about wave period at; https://brainly.com/question/10320118

#SPJ1

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

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

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)

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ1

Answer:

Please see the attached picture ! :D

-------- HappY LearninG <3 ----------

Answer:

2.99 x 10⁸ meters per second

Step-by-step explanation:

Scientific notation (also called "Standard form") is written in the form of [tex]a \times 10^n[/tex], where  [tex]1\leq a < 10[/tex]  and  [tex]n[/tex] is any positive or negative whole number.

To convert a number into scientific notation, move the decimal point to the left or right until there is one digit before the decimal point.

The number of times you have moved the decimal point is the power of 10 ([tex]n[/tex]).

If the decimal point has moved to the left, the power is positive.

If the decimal point has moved to the right, the power is negative.

To convert the given number to scientific notation

The decimal point for the given number 299000000 is after the last zero:

⇒  299000000.

Move the decimal point 8 places to the left:  

⇒ 2.99000000

Get rid of the redundant zeros:

⇒ 2.99

Multiply by 10 to the power of the number of decimal places moved:  

⇒ 2.99 x 10⁸

Therefore, the speed of light using scientific notation is:

The ordered pair which is a solution of the system of equations is; (4.9, 0).

The equations given in the task content can be solved as a system as follows, since y = y;

4x -19.4 = 0.2x -4.2

4x -0.2x = 19.4 -4.2

3.8x = 15.2

x = 15.2/3.8

x = 4.9

y = 4(4.9) -19.4

y = 0.2

Hence, the best ordered pair solution is; (4.9, 0).

Read more on ordered pair;

https://brainly.com/question/1528681

#SPJ1

The type of follow-up questions that can be asked to obtain the data needed to make a decision about the validity of that statement are:

This refers to the type of questions that are asked to a person in order to get extra information about a topic.

Hence, we can see that from the complete question, there is the need to perform tests to get results which would involve the procurement of data, controlled experiments, etc, and the follow-up questions that can be used are given above.

Read more about follow-up questions here:

https://brainly.com/question/4330760

#SPJ1

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

Learn more on independent events here: https://brainly.com/question/1374659

#SPJ1

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