Evaluate functions from their graph .

Answer:

5

Step-by-step explanation:

We would like to find out the value of [tex] x + y + z [/tex] from the given equations , which are ;

[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0[/tex]

[tex]\longrightarrow \\ x^2+y^2+z^2=25[/tex]

Now consider ,

[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\\[/tex]

[tex]\longrightarrow \dfrac{xy + yz + zx }{xyz }=0\\[/tex]

[tex]\longrightarrow xy + yz + zx = 0(xyz)\\ [/tex]

[tex]\longrightarrow xy + yz + zx = 0\\ [/tex]

[tex]\longrightarrow 2(xy + yz + zx)=0(2)\\[/tex]

[tex]\longrightarrow 2(xy + yz + zx)=0[/tex]

Now recall the identity ,

[tex]\longrightarrow (a + b + c)^2=a^2+b^2+c^2+2(ab + bc + ca)[/tex]

Plug in the values ,

[tex]\longrightarrow (x+y+z)^2= 25 + 0\\ [/tex]

[tex]\longrightarrow (x + y + z )^2=25\\[/tex]

[tex]\longrightarrow (x + y + z)=\sqrt{25}\\[/tex]

[tex]\longrightarrow \underline{\underline{\boldsymbol{ x + y + z = 5}}}{} [/tex]

And we are done !

Answer :

⠀

Step-by-step explanation:

Given,

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = 0}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ {x}^{2} + {y}^{2} + {z}^{2} = 25 }}}}[/tex]

⠀

To Find :

[tex]{ \longrightarrow \qquad{ { \sf{ x + y + z }}}}[/tex]

⠀

Solution :

[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = 0}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{yz + zx + xy}{xyz} = 0}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ {yz + zx + xy} = 0}}}}[/tex]

⠀

Multiplying both sides by 2 :

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0.2}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0}}}}[/tex]

⠀

We know,

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + zx) }}}}[/tex]

⠀

As, It is given that,

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ {x}^{2} + {y}^{2} + {z}^{2} = 25 }}}}[/tex]

⠀

and as we get,

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0}}}} \\ \\{ \longrightarrow \qquad{ { \sf{ 2( {xy + yz + zx} )= 0}}}}[/tex]

⠀

Now, We'll substitute it in the formula :

[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = 25 + 0 }}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = {25} }}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ {x + y + z}^{} = \sqrt{25} }}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \bf{ \pmb {x + y + z}^{} = {5} }}}}[/tex]

⠀

Therefore,

Answer:

Slope of top rail f(x) is 7

Slope of top rail g(x) is 7

Top and bottom rails are parallel.

Step-by-step explanation:

The table shows the  distance, in inches, of the top rail f(x) and bottom  rail g(x) from the floor for the middle of each  numbered stęp x.

x        f(x)      g(x)

1          9        43

2          16        50

3          23        57

To find the slope of top rail :

x        f(x)      

1          9        

2          16        

3          23        

[tex](x_1,y_1)=(1,9)\\(x_2,y_2)=(2,16)\\Slope = m = \frac{y_2-y_1}{x_2-x_1}=\frac{16-9}{2-1}=7[/tex]

Slope of top rail f(x) is 7

To Find the slope of bottom rail:

x     g(x)

1      43

2      50

3      57

[tex](x_1,y_1)=(1,43)\\(x_2,y_2)=(2,50)\\Slope = m = \frac{y_2-y_1}{x_2-x_1}=\frac{50-43}{2-1}=7[/tex]

Slope of top rail g(x) is 7

We know that if the slopes of two lines are equal then are said to be parallel lines

Since the slopes of both the rail are equal . So, Top and bottom rails are parallel.

Answer:      12*x-7-(13*(x-12)*x)=0

Step by Step Solution

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Rearrange:

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

                    12*x-7-(13*(x-12)*x)=0

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (12x - 7) -  (13 • (x - 12) • x)  = 0

STEP

2

:

Equation at the end of step 2

 (12x - 7) -  13x • (x - 12)  = 0

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  -13x2 + 168x - 7  =   -1 • (13x2 - 168x + 7)

Trying to factor by splitting the middle term

4.2     Factoring  13x2 - 168x + 7

The first term is,  13x2  its coefficient is  13 .

The middle term is,  -168x  its coefficient is  -168 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   13 • 7 = 91

Step-2 : Find two factors of  91  whose sum equals the coefficient of the middle term, which is   -168 .

     -91    +    -1    =    -92

     -13    +    -7    =    -20

     -7    +    -13    =    -20

     -1    +    -91    =    -92

     1    +    91    =    92

     7    +    13    =    20

     13    +    7    =    20

     91    +    1    =    92

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

4

:

 -13x2 + 168x - 7  = 0

STEP

5

:

Parabola, Finding the Vertex:

5.1      Find the Vertex of   y = -13x2+168x-7

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens down and accordingly has a highest point (AKA absolute maximum) .    We know this even before plotting  "y"  because the coefficient of the first term, -13 , is negative (smaller than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   6.4615  

Plugging into the parabola formula   6.4615  for  x  we can calculate the  y -coordinate :

 y = -13.0 * 6.46 * 6.46 + 168.0 * 6.46 - 7.0

or   y = 535.769

Answer:

x = 49

Step-by-step explanation:

Since the line is parallel, the value of 2x - 8 is equal to 90.

=> 2x - 8 = 90

=> 2x = 98

=> x = 49

Answer:

x = 49

Step-by-step explanation:

2x - 8 and the right angle are corresponding angles and are congruent , then

2x - 8 = 90 ( add 8 to both sides )

2x = 98 ( divide both sides by 2 )

x = 49

Answer:

first we need to add all of the swans together, then from there you take the amount of mute swans and divide it by the sum of all the swans! finally, multiply by 100 to convert into a percent and round it to 12.2%

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

First, add the total of all the swans together

5+34+2=41

Next, take the total and divide it by the number of mute swans there are

41÷5=8.2

Finally round 8.2 to the nearest whole percent

8.2=8

The answer is 8%

Answer:

0 and 2π/3

3rd and 4th

Step-by-step explanation:

Answer:

The sample size is       [tex]n  =  246[/tex]

Step-by-step explanation:

From the question we are told that

    The standard deviation is [tex]\sigma  =  4\ lb[/tex]

    The confidence level is  C  = 95%

    The total  width is  [tex]w = 1 \  lb[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

       [tex]\alpha = (100 -95 )\%[/tex]

=>    [tex]\alpha = 0.05[/tex]

From the normal distribution table  the critical value  for  [tex]\frac{\alpha }{2}[/tex] is  

    [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the sample size is mathematically represented as

       [tex]n  =  [\frac{Z_{\frac{\alpha }{2}}  * \sigma }{E}]^2 [/tex]

Here E is the margin of error which is mathematically represented as

     [tex]E =  \frac{w}{2}[/tex]

=>   [tex]E =  \frac{1}{2}[/tex]

=>   [tex]E = 0.5 [/tex]

So

      [tex]n  =  [\frac{1.96 * 4 }{0.5}]^2 [/tex]

    [tex]n  =  246[/tex]

Answer:

12

Step-by-step explanation:

P = is you add Length (L) plus Legnth (L) plus Width (W) plus Width (W)

4+4+2+2

Domain is the x-intercept(first number) for example if I were told to find the domain in (1,3)(4,7)(8,9) the domain would be 1,4, and 8 because they're the x-factors and then plotting a point, the x-factors come first.

Range is the y-factors(second number) and given an example above, the ranges would be 3,7, and 9 because when plotting, they are the second number.

You can tell if it is a function or not if the X-factors repeat. For example, the first one is NOT a function because the 2 repeats for the x-factor. Number 2 IS a function because the x-factor doesn't repeat.

Sorry if this doesn't make sense, that's the best way I can explain!

Answer:

k=0 or 4

Step-by-step explanation:

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

so the vertex is at

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

The vertex lies in the x-axis, so

[tex]3k+4-(\frac{k+4}{2})^2 = 0\\4(3k+4)-(k+4)^2=0\\12k+16-k^2-8k-16=0\\-k^2+4k=0\\-k(k-4)=0\\k-0, 4[/tex]

Answer:

Step-by-step explanation:

Let the larger number = x

Smaller number = y

6x + 7y = 114 ------------(I)

10x - 9y = 66 ------------(II)

Multiply equation (I) by 9 and multiply the equation (II) by 7. After that add the two equations. So that, y will be eliminated and we can find the value of x

         (1)*9        54x + 63y = 1026

         (II)*7        70x - 63y  =  462    {Now add}

                        124x           = 1488   {Divide both sides by 124}

                                        x = 1488/124

x = 12

Plugin x =  12 in any of the equation. Here, We are substituting in  equation (I)

6*12 + 7y = 114

  72 + 7y =114

         7y = 114 - 72

         7y = 42

          y = 42/7

y = 6

The numbers are 12 , 6

Answer:

+7 will be the opposite or reciprocal of -7

Step-by-step explanation:

Hope it Helps!!!!

The opposite of the number, -7, is its reciprocal, which is: 7.

The opposite of a number is its reciprocal or the value on the number line that would occupy the same distance from zero in the opposite direction.

For example, opposite of b is -b.

The reciprocal of -7 is 7. Therefore, the opposite of the number, -7 is: 7.

Learn more about opposite of a number on:

https://brainly.com/question/2206063

#SPJ2

1)

First 2 triangles can be proven similar but are not necessarily congruent since you can't from them using the side-angle-side or angle-side-angle or triple side rule.

2)

ONM = QNP since they are vertically opposite angles.

MON = NPQ given equal on the figure

ON=NP given

The two triangles are proven congruent using the angle-side-angle property.

3)

Last 2 pairs cannot be proven congruent as there is not enough info.

Answer:

$53,523

Step-by-step explanation:

This is an addition. You must add the two prices.

$18,298 + $35,225 = $53,523

Answer:

Step-by-step explanation:

75 = 3 x 25 = 3 x 5²

32 = 2 x 16 = 2 x 4²

68 = 4 x 17 = 2² x 17

So

the largest perfect square number that is a factor of 75 is 25

the largest perfect square number that is a factor of 32 is 16

the largest perfect square number that is a factor of 68 is 4

Answer:

150

Step-by-step explanation:

If 7-5=2 books cost 300 and you want to find the cost of 1 book, you would need to divide that 300 by 2.

300÷2=150

Answer:

Step-by-step explanation:

6d + 5 = c

hope that helps :)

Answer:

It is part of the argument.

Step-by-step explanation:

AB + BC = AC.

So, the line segment EG , F lies on the line segment;

Therefore, by segment addition postulates we have below:

EG = EF + FG

By substitution AB=EF

EG = AB + FG                

~~~~~~~~~~~~~~~~~~~~

Given: AB ≅ BC

BC ≅ EF

Prove: EG = AB + FG

~~~~~~~~~~~~~~~~~~~~~~

~lenvy~

Answer:

It is part of the argument.

Step-by-step explanation:

The answer above is correct.

Answer:

123 + (456 + 789)

Step-by-step explanation:

since this is an addition problem, the parenthesis don't matter, and they can be put wherever you want.

(123 + 456) + 789

123 + 456 + 789

(123 + 456 + 789)

123 + (456 + 789)

technically, any of these would work, but I think the kind of answer the problem is looking for is;

123 + (456 + 789)

Answer:

( 2, 3, 4 )

Step-by-step explanation:

Answer:

The answers are below...

IAI = 1        4       -1              IAxI= -14       4       -1          

       5       6        3                         4       6       3

       -2      7       2                         -17      7       2

IAI = B -120

IAxI = A  -240

X = 2

Answer:

The answer I got was wrong, but I have a solution process, at least.

Step-by-step explanation:

600*48.57+1150*46.10+250*53.46-2000*35.49

=21942+53015+13365-70980

=17342

Now we need to subtract the commission that Cynthia is paying her broker. $88 per $1000 means Cynthia owes her broker 17*88=$1496. Now we subtract that from 17342 to get $15,846.

Answer:its A. $9,889.82

Step-by-step explanation:

Answer:

we need the coordinates really. I can tell you that for any 2 coordinates the distance between them can be found using the Distance formula D=sq. rt (x1-x2)^2 + (y1-y2)^2

Answer:

Since you did not list the ratio, i will tell you what to do. say the ration is 5:6, meaning for every 5 teddy bears there are 6 dolls. I would divide 240 by 6, then multiply by 5.

Answer:

[tex]b^{3}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

A quadrilateral's interior angles have a sum of 360°.

Given that we have 85°, 100°, and 90°(the right angle), and an unknown angle.

We can add these angles plus the unknown angle to equal a total of 360°.

85 + 100 + 90 + x(our unknown missing angle) = 360

simplify

275 + x = 360

Isolate x by subtract 275 from both sides;

-275       -275

x = 85, ∠1 = 85°

We can also double check:-

85 + 100 + 90 + 85 = 360

360 = 360 which is correct.

Step-by-step explanation:

First you add the number of used and unused feets of foil

223 + 77 = 300

After that you divide the feets of rolls by the total number of foils

that is, 300 / 6 = 50

therefore there are 50 feets in each foil

if this helped pls give brainliest

P > -1

Step-by-step explanation: i have the exact same quiz

Answer:

2.7

Step-by-step explanation:

I hope it helsp if its right pls amrk me as brainliest