Find the value of the polynomial:

Given:

A line passes through the point (1,4) and is parallel to the x-axis.

To find:

The equation of the line.

Solution:

If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.

The point-slope form of a line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.

The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:

[tex]y-4=0(x-1)[/tex]

[tex]y-4=0[/tex]

[tex]y-4+4=0+4[/tex]

[tex]y=4[/tex]

The required equation is [tex]y=4[/tex].

Therefore, the correct option is B.

Given:

The function are:

[tex]f(x)=Kx^2+4x-3[/tex]

[tex]g(x)=2x-7[/tex]

The graph of f(x) intersect the line g(x) at one point.

To find:

The value of K.

Solution:

The graph of f(x) intersect the line g(x) at one point. It means the line g(x) is the tangent line.

We have,

[tex]f(x)=Kx^2+4x-3[/tex]

Differentiate this function with respect to x.

[tex]f'(x)=K(2x)+4(1)-(0)[/tex]

[tex]f'(x)=2Kx+4[/tex]

Let the point of tangency is [tex](x_0,y_0)[/tex]. So, the slope of the tangent line is:

[tex][f'(x)]_{(x_0,y_0)}=2Kx_0+4[/tex]

On comparing [tex]g(x)=2x-7[/tex] with slope-intercept form, we get

[tex]m=2[/tex]

So, the slope of the tangent line is 2.

[tex]2Kx_0+4=2[/tex]

[tex]2Kx_0=2-4[/tex]

[tex]x_0=\dfrac{-2}{2K}[/tex]

[tex]x_0=-\dfrac{1}{K}[/tex]

Putting [tex]x=x_0,g(x)=y_0[/tex] in g(x), we get

[tex]y_0=2x_0-7[/tex]

Putting [tex]x=-\dfrac{1}{K}[/tex] in the above equation, we get

[tex]y_0=2(-\dfrac{1}{K})-7[/tex]

[tex]y_0=-\dfrac{2}{K}-7[/tex]

Putting [tex]x=-\dfrac{1}{K}[/tex] and [tex]f(x)=-\dfrac{2}{K}-7[/tex] in f(x).

[tex]-\dfrac{2}{K}-7=K\left(-\dfrac{1}{K}\right)^2+4(-\dfrac{1}{K})-3[/tex]

[tex]-\dfrac{2}{K}-7=\dfrac{1}{K}-\dfrac{4}{K}-3[/tex]

[tex]-\dfrac{2}{K}-7=\dfrac{-3}{K}-3[/tex]

Multiply both sides by K.

[tex]-2-7K=-3-3K[/tex]

[tex]-2+3=7K-3k[/tex]

[tex]1=4k[/tex]

[tex]\dfrac{1}{4}=K[/tex]

Therefore, the value of K is [tex]\dfrac{1}{4}[/tex].

Answer:

i think (4,2)

Step-by-step explanation:

Hello!

x² - 4x + 6 = 9 <=>

<=> x² - 4x + 6 - 9 = 0 <=>

<=> x² - 4x - 3 = 0 <=>

<=> x = -(-4)±√(-4)²-4×1×(-3)/2×1 <=>

<=> x = 4±√16+12/2 <=>

<=> x = 4±√28/2 <=>

<=> x = 4±2√7/2 =>

=> x = 4+2√7/2 and x = 4-2√7/2 =>

=> x = 2+√7 and x = 2-√7

The equation has two solutions.

Good luck! :)

Answer:  [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]

how i got it?

[tex]x^2 - 4x + 6 = 9[/tex]

*subtract 9 on both sides*

[tex]x^2 - 4x + 6 - 9 = 0[/tex]  ( which turns to) [tex]x^2 - 4x - 3=0[/tex]

a=1 or x, b=-4, c=-3

Step 2: Use quadratic formula with a=1, b=-4, c=-3.

[tex]x= - (-4) + or - \sqrt{-4}x^{2} -4(1)(-3) / 2(1)[/tex]

which turns to: x= 4 + or - √28 divided by 2

the final answer should be [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]

Answer:

We can make 120 three digit distinct numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the number is xyz, we have:

Total number of possible 3-digit numbers:

Answer:

-4/5

Step-by-step explanation:

sin theta = opp/ hyp

sin theta = -3 /5

Using the Pythagorean theorem

opp ^2 + adj ^2 = hyp ^2

(-3) ^2 + adj ^2 = 5^2

9+ adj ^2 = 25

adj ^2 = 25 - 9

adj ^2 = 16

Taking the square root of each side

adj = ±4

Since we are in the 3rd quadrant  sin and cos are both negative so adj must be negative

adj = -4

cos theta = adj / hyp

cos theta = -4/5

Answer:

If there are two line which is parallel in a triangle the triangle has a ratio

Step-by-step explanation:

So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8

Answer:

Step-by-step explanation:

Answer:

a). 3/4 kg de papa

Step-by-step explanation:

Given that,

Patata colocada en balanza = 1 1/4 Kg

Flor de papa total quiere = 2 kg

Encontrar,

Se agregará más peso en la báscula para que sea de 2 kg =?

Procedimiento:

Peso requerido para ser colocado = Peso total - peso colocado

= 2 - [tex]1\frac{1}{4}[/tex]

= 2 - 5/4

= (8 - 5)/4

= 3/4 kg

Answer:

0.125

Step-by-step explanation:

1=40000

x-5000

x=5000÷40000=1/8=0.125

Answer: 3000 stamps

Step-by-step explanation:

Given

Chris and Josh have 1800 stamps

Josh and Jessica have 2200 stamps

Jessica and Chris have 2000 stamps

Suppose Chris, Josh, and Jessica have [tex]x,y, \text{and}\ z[/tex] stamps

[tex]\therefore x+y=1800\quad \ldots(i)\\\Rightarrow y+z=2200\quad \ldots(ii)\\\Rightarrow z+x=2000\quad \ldots(iii)\\\text{Add (i), (ii), and (iii)}\\\Rightarrow 2(x+y+z)=1800+2200+2000\\\Rightarrow x+y+z=3000[/tex]

Thus, all three have 3000 stamps

Answer:

The diameter is 2 meters

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

2 pi = pi *d

Divide each side by pi

2 = d

The diameter is 2 meters

60° because it's an equilateral triangle

Answer:

18 is 64 days

20 is 1 37/128

Step-by-step explanation:

I looked it up if I am being completely honest with you but it should be correct

The volume of a cylinder is V=πr^2*h.

The volume of this cylinder is V=π(7)^2*12, which it V=588π.

Answer: yes

A prime factor is number that can only divided by itself and one

Since, 17 can only be divided by 17 and 1, the student is correct

Step-by-step explanation:

Answer:

27 attendees

Step-by-step explanation:

First, we can find the cost per attendee.

78÷26

3

So $3 per attendee.

Then divide 81 by 3 to find the number of possible attendees.

81÷3=27

I hope this helps!

Answer:

Simultaneously equation

Answer:

It must be a positive number since it represents a number of hours.

Step-by-step explanation:

Given Pieter's equation :

7h – 5(3h – 8) = –72

Opening up the bracket

7h - 15h + 40 = - 72

7h - 15h = - 72 - 40

-8h = - 112

Divide both sides by -8

-8h / -8 = - 112 / - 8

h = 14

Since, h represents the number of hours, and the value of h equals 14 (h cannot be negative), hence, option 2 is correct.

Answer:

B.It must be a positive number since it represents a numbers of hours.

Step-by-step explanation:

Answer:

3x

Step-by-step explanation:

factoring it we get

3x(4x-3)

Answer:

Total chairs = 18×22= 396

so no. of extra chairs need = 468-396 = 72

Now( 72/18) rows = 4 rows

Therefore 4 more rows are needed here

Hope it helps you

Answer: 4

Step-by-step explanation:

The amount of chairs in the hall can be found by multiplying 22 by 18 and getting 396. The amount of chairs needed is 468, so 468-396 gets you the amount of chairs still needed and the number 72. There are 18 chairs in each row, and 72/18 is 4. So 4 more rows are needed.

Answer:

3x^2y

Step-by-step explanation:

Its common factor it this ^ this symbol represent power

After answering the question provided, we can predict that the result will be as  The position and direction of the relevant parabola will determine the appropriate response.

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

It is hard to tell which equation may be the equation of the parabola without further details on the parabola's orientation and location.

The equations in options A and B are parabolas with upward or downward openings and a vertex at the origin. The equation of a parabola with its vertex at the origin and an opening to the right or left is in Option C. The equation of a parabola with an upwards or downwards opening and its vertex at the point is in Option D. (0,0).

The position and direction of the relevant parabola will determine the appropriate response.

To know more about equation visit:

https://brainly.com/question/649785

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Answer:

add 2 equations given

3y+x+2y- x = 10

5y =10

y = 2

find x using the value of y

x = - 2

these values of x and y are can satisfy both equations .so (-2,2) lies on both lines

Answer: where's the pic?

Step-by-step explanation:

Answer:

5m-n-4p

4a^2+6x-3

Step-by-step explanation:

3m-4n +7p

-5m +9n -6p

+7m -6n -5p

----------------------

Combine like terms

3m-4n +7p

-5m +9n -6p

+7m -6n -5p

----------------------

(3-5+7)m  +(-4+9-6)n  +(7-6-5)p

5m-n-4p

a^2  -3x +1

a^2   +9x -6

2a^2 +0x +2

----------------------

Combine like terms

a^2  -3x +1

a^2   +9x -6

2a^2 +0x +2

----------------------

(1+1+2)a^2 +(-3+9+0)x +(1-6+2)

4a^2+6x-3

#1

[tex]\\ \sf\longmapsto 3m-4n+7p+(-5m+9n-6p)+7m-6n-5p[/tex]

[tex]\\ \sf\longmapsto 3m-4n+7p-5m+9n-6p+7m-6n-5p[/tex]

[tex]\\ \sf\longmapsto 3m-5m+7m-4n+9n-6n+7p-6p-5p[/tex]

[tex]\\ \sf\longmapsto 5m-n-4p[/tex]

#2

[tex]\\ \sf\longmapsto a^2-3x+1+a^2+9x-6+2a^2+2[/tex]

[tex]\\ \sf\longmapsto a^2+a^2+2a^2-3x+9x+1-6+2[/tex]

[tex]\\ \sf\longmapsto 4a^2+6x-3[/tex]