please help me..
here is a part of a proof that chen wrote. what is his error?
(refer to the picture)​

Rearrange:

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

                    f*(x)-(-x^2-3*x)=0  

STEP

1

:

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  fx + x2 + 3x  =   x • (f + x + 3)  

Equation at the end of step

2

:

 x • (f + x + 3)  = 0  

STEP

3

:

Theory - Roots of a product

3.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2      Solve  :    x = 0  

 Solution is  x = 0

Equation of a Straight Line

3.3     Solve   f+x+3  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  f+x+3  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of f is -3/1 so this line "cuts" the f axis at f=-3.00000

 f-intercept = -3/1  = -3.00000  

Calculate the X-Intercept :

When f = 0 the value of x is -3/1 Our line therefore "cuts" the x axis at x=-3.00000

 x-intercept = -3/1  = -3.00000  

Calculate the Slope :

Slope is defined as the change in f divided by the change in x. We note that for x=0, the value of f is -3.000 and for x=2.000, the value of f is -5.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -5.000 - (-3.000) = -2.000 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -2.000/2.000 = -1.000  

Geometric figure: Straight Line

 Slope = -2.000/2.000 = -1.000

 x-intercept = -3/1 = -3.00000

 f-intercept = -3/1 = -3.00000

x = 0

Step-by-step explanation:

[tex] \large\underline{\sf{Solution-}}[/tex]

Given function is

[tex]\rm \longmapsto\:f = \bigg(x, \: \dfrac{ {x}^{2} }{ {x}^{2} + 1} \bigg) : x \: \in \: R[/tex]

To find the range of the function f, Let assume that

[tex]\rm \longmapsto\:y = \dfrac{ {x}^{2} }{ {x}^{2} + 1} [/tex]

[tex]\rm \longmapsto\: {yx}^{2} + y = {x}^{2} [/tex]

[tex]\rm \longmapsto\: {yx}^{2} - {x}^{2} = - y[/tex]

[tex]\rm \longmapsto\: - {x}^{2} (1 - y) = - y[/tex]

[tex]\rm \longmapsto\: {x}^{2} (1 - y) = y[/tex]

[tex]\rm \longmapsto\: {x}^{2} = \dfrac{y}{1 - y} [/tex]

[tex]\rm\implies \:x = \sqrt{\dfrac{y}{1 - y} } [/tex]

For x to be defined,

[tex]\rm \longmapsto\:y \geqslant 0 \: \: and \: \: 1 - y > 0[/tex]

[tex]\rm \longmapsto\:y \geqslant 0 \: \: and \: \: - y > - 1[/tex]

[tex]\rm \longmapsto\:y \geqslant 0 \: \: and \: \: y < 1[/tex]

[tex]\bf\implies \:y \: \in \: [0, \: 1)[/tex]

Hence,

[tex]\bf\implies \:Range \: of \: f \: \in \: [0, \: 1)[/tex]

Answer:

6

Step-by-step explanation:

[tex] {(3 \sqrt{13}) }^{2} - {9}^{2} = {x}^{2} \\ 9(13) - 81 = {x}^{2} \\ 117 - 81 = {x}^{2} \\ 36 = {x}^{2} \\ x = 6

Use Pythagorean theorem

[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \sf\longmapsto P^2=(3√13)^2-9^2[/tex]

[tex]\\ \sf\longmapsto P^2=117-81[/tex]

[tex]\\ \sf\longmapsto P^2=36[/tex]

[tex]\\ \sf\longmapsto P=6[/tex]

Answer:

0.125

Step-by-step explanation:

Hope it helps

Answer:

(5/4) / 10

= (5×10)/4

= 50 / 4

= 25/ 2

= 12.5

Step-by-step explanation:

brainliest plz

Answer:

x > 8.125 or 8 & 1/8

Step-by-step explanation:

8( -x - 7) > 16

-8x - 49 > 16

     + 49 + 49

-8x > 65

x > 8.125 or 8 & 1/8

Step-by-step explanation:

450/180= 2.5 kilos

it is a one to one relationship

f(x)=x/180

where x is the amount given to her

Step-by-step explanation:

[tex]2\frac{3}{5} +5\frac{1}{4}[/tex]

= [tex]\frac{13}{5} +\frac{21}{4}[/tex]

= [tex]\frac{52 + 105}{20}[/tex]

= [tex]\frac{157}{20}[/tex] Or [tex]7\frac{17}{20}[/tex]

Please give me a brainliest answer

Answer:

x+2

Step-by-step explanation:

i put mi x as one so

....that how i get my anwser

Answer:

A, C, E

Step-by-step explanation:

Substitute the x- coordinate of the points into the equation and if the result is equal to the y- coordinate of the point then it is a solution.

A (- 2, 5 )

y = 2² + 1 = 4 + 1 = 5 → (- 2, 5 ) is a solution

B (- 1, 0 )

y = (- 1)² + 1 = 1 + 1 = 2 ≠ 0 ← not a solution

C (1, 2 )

y = 1² + 1 = 1 + 1 = 2 → (1, 2 ) is a solution

D (2, 4 )

y = 2² + 1 = 4 + 1 = 5 ≠ 4 ← not a solution

E (3, 10 )

y = 3² + 1 = 9 + 1 = 10 → (3, 10 ) is a solution

Answer:

B

Step-by-step explanation:

When x is equal to 0, you look at the graph and you get y is equal to 3, which is choice B

Answer:

1. a^4.

2. 9c³.

3. 8z^6.

4. 4b²a.

5. 20q(if the 2 isn't an exponent)

if it is,

20q².

6.x²y².

7. j²k²i.

All the best.

Answer:

Step-by-step explanation:

[tex]1.(a^{2})^{2}= a^{2*2}=a^{4}\\\\\\2. (3c)^{3}=3^{3}*c^{3} = 27c^{3}\\\\\\3.(2z^{2})^{3}=2^{3}*(z^{2})^{3}=8z^{2*3}=8z^{6}\\\\\\4.a(2b)^{2}=a*2^{2}b^{2}=4ab^{2}\\\\\\5.5(q^{2})^{2} = 5q^{2*2}=5q^{4}\\\\\\6.(xy)^{2}=x^{2}y^{2}\\\\\\7i(jk)^{2}=ij^{2}k^{2}[/tex]

Answer:

-2

Step-by-step explanation:

It's (x,y)

Here, (3,-2)

-2 is y

:)

Answer:

What is the two perfect squares of 237?

Step-by-step explanation:

The Two perfect squares of 237

I guess It didn't have any square

although its square is 15.39480432

Answer : The demonstration is below :)

Step-by-step explanation :

We use Pythagoras' theorem :

AB² = AC² - BC² = 15² - 9² = 144 = 12²

DB² = AD² - AB² = 13² - 12² = 5²

cos(a) = BD/AD = 5/13

The spider's movement is an illustration of a parabola.

(a) The equation

The spider passes through the origin.

So, we have:

[tex]\mathbf{(x,y) = (0,0)}[/tex]

The spider jumps to a maximum height of 20mm, midway 160mm.

So, the vertex is:

[tex]\mathbf{(h,k) = (80,20)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

So, we have:

[tex]\mathbf{0 = a(0 - 80)^2 + 20}[/tex]

[tex]\mathbf{0 = 6400a + 20}[/tex]

Subtract 20 from both sides

[tex]\mathbf{6400a =- 20}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{320}}[/tex]

Substitute [tex]\mathbf{a =- \frac{1}{320}}[/tex] and [tex]\mathbf{(h,k) = (80,20)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/tex]

(b) The focus, directrix and the axis of symmetry

The focus of a parabola is:

[tex]\mathbf{Focus = (h,k+p)}[/tex]

Where:

[tex]\mathbf{p = \frac{1}{4a}}[/tex]

So, we have:

[tex]\mathbf{p = \frac{1}{4\times -1/320}}[/tex]

[tex]\mathbf{p = -\frac{320}{4}}[/tex]

[tex]\mathbf{p = -80}[/tex]

So, we have:

[tex]\mathbf{Focus = (80 , 20-80)}[/tex]

[tex]\mathbf{Focus = (80 ,-60)}[/tex]

The axis of symmetry is:

[tex]\mathbf{x = h}[/tex]

So, we have:

[tex]\mathbf{x = 80}[/tex]

The directrix is:

[tex]\mathbf{y = k - p}\\[/tex]

So, we have:

[tex]\mathbf{y = 20+80}[/tex]

[tex]\mathbf{y = 100}[/tex]

Read more about parabolas at:

https://brainly.com/question/5430838

Answer:

Answer:18.5

Step-by-step explanation:

10+8=18

18*5=90

90/4

22.5-4=18.5

Have a happy day! <3Miss Hawaii

Answer:

16

Step-by-step explanation:

sum of 8 and 10=18

5 times of sum of 8 and

10= 18×5=80

1/4 of 5 times of sum of 8 and

10= 1/4×80=20

and then subtracted 4 from

20 =20-4=16

Answer:

$60378

Step-by-step explanation:

$58,000 represents 100% of the original cost

100 + 4.1= 104.1% = 104.1/100 = 1.041

Multiplying by 1.041 gives the cost after the increase

price = 53000 x 1.041  = $60378

Answer:

112

Step-by-step explanation:

Answer:

The correct answer is 7.5%, 7.59, 7 49/50

Step-by-step explanation:

Hope This Helps!

Answer:

7 49/50, 7.59, 7.5%

Step-by-step explanation:

7 49/50=7.98 if you solve the fraction

7.5%=0.075 if you move the decimal two places

Hope this helps :)

Answer:

p=6/8

Step-by-step explanation:

there are 8 sections total and 6 sections that are not yellow

you have a 6 in 8 chance of landing on a color that isn't yellow/

6/8

hope this helps!

Answer:

Help with what?

Answer:

16x - 9

Step-by-step explanation:

2x(3x + 5) - 3 (2x² - 2x + 3) ← distribute parenthesis

= 6x² + 10x - 6x² + 6x - 9 ← collect like terms

= 16x - 9

Answer:

16X-9

Step-by-step explanation:

(2x)(3x)+(2x)(5)+(-3)(2x²)+(-3)(-2x)+(-3)(3)

6x²+10x+6x²+6x +-9

combine like terms

6x² +10x +-6x² +6x+-9

(6x² +6x² )+(10x+6x)+(-9)

16x+-9

16x-9

Answer:

Step-by-step explanation:

a) vertex = (3, 18).

b) This tells us that the doorway is 8 units high.

c) Y intercept is at (0, 0).

d) x intercepts are (0, 0) and (6, 0).

e) The base is horizontal.

The rate of change of this function in miles per week is 3 miles per week.

We have a table as shown in the question.

The rate of change in miles per week is -

(19 - 13)/(3 - 1) = (22 - 19)/(4 - 3)

6/2 = 3/1

3 = 3

3

Therefore, the rate of change of this function in miles per week is 3 miles per week.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

Answer:

youre gonna put 4 on x axis and -3 on y

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think its 64 degrees

Angles on a straight line equals 180⁰

180⁰-64⁰

116⁰

x=116⁰

Answer: See attached image for graph

PQ: √50

QR: √18

PR: √68

Step-by-step explanation: We will use the 2D distance formula in order to get each side length. The distance formula is:

Thus, we just apply this formula for each side length.

Answer:

$2x

Step-by-step explanation:

His salary doubled (x2), so you can eliminate B & C because they are + & -. You can eliminate A because that would represent his current salary. So, that leaves $2x.